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# sklearn.GridSearchCV predict method not providing the best estimate and accuracy score

I was playing around with the credit default dataset in UCI ("https://archive.ics.uci.edu/ml/machine-learning-databases/00350/default%20of%20credit%20card%20clients.xls")

These are the steps i have undertaken so far:

1. Created a Pipeline for Perceptron
2. Parameter values were provided for learning rate and epochs.
4. GridSearch provided me with best score for a particular learning rate and epoch
5. used predict method on the gridsearch and recalculated accuracy score

Parameters provided for gridsearch

{'perceptron__max_iter': [1,5,8,10], 'perceptron__eta0': [0.5,.4, .2, .1]}

Question: The best parameters provided by GridSearch are not really the best parameters. I am not getting same scores using predict method on the gridsearch. Why is this the case? WHat am i doing wrong?

So acc to gridsearch best param are : {'perceptron__eta0': 0.5, 'perceptron__max_iter': 8}

Accuracy score : 0.7795238095238095

However if i use these best parameters and call predict on gridsearch gives a totally different value, accuracy score dips to 0.5882222222222222

import pandas as panda

from sklearn.model_selection import learning_curve, train_test_split,GridSearchCV
from sklearn.preprocessing import StandardScaler
from sklearn.pipeline import make_pipeline, Pipeline
from sklearn.metrics import accuracy_score, mean_absolute_error, classification_report
from sklearn.linear_model import Perceptron, LogisticRegression
from sklearn.svm import SVC
from sklearn.tree import DecisionTreeClassifier
from sklearn.ensemble import RandomForestClassifier
from sklearn.neighbors import KNeighborsClassifier

from matplotlib import pyplot as plot
import seaborn as sns

from numpy import bincount, linspace, mean, std

remote_location = "https://archive.ics.uci.edu/ml/machine-learning-databases/00350/default%20of%20credit%20card%20clients.xls"

data.rename(str.lower, inplace = True, axis = 'columns')

_y_target = data['default payment next month'].values

columns = data.columns.tolist()
columns.remove('default payment next month')

_x_attributes = data[columns].values

## meaning of stratify = _y_target. returns test and training data having the same proportions of class label '_y_target'
_x_train,_x_test,_y_train, _y_test = train_test_split(_x_attributes, _y_target, test_size =0.30, stratify = _y_target, random_state = 1)

## lets check the distribution. we can see 4times the lower value as was the case before as well. train/test set distributed well
print("label counts in y train %s" %bincount(_y_train))
print("label counts in y test %s" %bincount(_y_test))
parameter_grid = {'perceptron__max_iter': [1,5,8,10], 'perceptron__eta0': [0.5,.4, .2, .1]}

pipeline = make_pipeline( StandardScaler(),Perceptron(random_state = 1))
gridsearch = GridSearchCV(estimator = pipeline, param_grid = parameter_grid, cv = 10, n_jobs = 1, scoring = 'accuracy')

search = gridsearch.fit(_x_train, _y_train)
print(search.best_params_)
print(search.best_score_)

_y_prediction = gridsearch.predict(_x_test)

print("Accuracy score %s" %accuracy_score(_y_test,_y_prediction))
print("Classification report  \n %s" %(classification_report(_y_test, _y_prediction)))

My output is as below:

{'perceptron__eta0': 0.5, 'perceptron__max_iter': 8}
0.7795238095238095
Accuracy score 0.5882222222222222
Classification report
precision    recall  f1-score   support

0       0.78      0.66      0.71      7009
1       0.22      0.35      0.27      1991

avg / total       0.66      0.59      0.62      9000

accuracy score on the train set is ~0.78.
accuracy score on the test set is ~0.59.
Rephrasing you questions: why do my model performance on the test set is worse than on my train set?

This phenomena is very common - and I can think of two potential explanations:
1) Overfitting: your trained model had learned the 'noise' in the train set and not the actual pattern.
Then when you use your model to predict on the test set, it predicts the noise he had encountered(which is not relevant for the train set - thus lower accuracy).
2) Train set and data set are not generated from the same process/describe different parts of it. In this case - the pattern learnt by the trained model is not relevant to the test set and accuracy will drop.
This may happen in situations where the train/test split is done without considering the actual underlying process. For example - an image classification problem where you model whether this picture is an animal or not and the train data has only human and dogs sample and the train set has only fish and airplanes pictures. This is less likely to be the explanation, since your using grid search, which adds randomness to this splitting.

• thank you for your response. however i am using the same gridsearch instance and calling predict operation on it. according to scikit docs (scikit-learn.org/stable/modules/generated/…), predict method on gridsearch instance will use the same best params . in that case, wouldnt i be getting the same results. infact i get better results when i manually run it using learning rate of 0.1 and 10 epochs. – user1906450 Oct 28 '18 at 14:42
• Yes, it uses the same best params. But from what I understand, you use the predict on a different data set - X_test. – yoav_aaa Oct 28 '18 at 14:49
• oh ok my bad , i didnt mention the train_test_split part of the code. updated the original question. the class distribution among test set and train set is pretty much the same 1:4. so if i understand your point well, in this particular instance using perceptron model on the data sets leads to overfitting. p.s. i dont see this behavior when i replace perceptron model in the pipeline with other models such as SVM, decisiontrees, etc – user1906450 Oct 28 '18 at 14:52
• The more complex the model is the more probable it will overfit. – yoav_aaa Oct 28 '18 at 14:59
• hmm.. it actually performs better for logistic regression. i have also plotted the learnnig curve and i can see clear overfit cases for decisiontrees,randomforests. give me a moment , i will share the jupyter notebook. if it makes my code clear. will that be too much to ask? – user1906450 Oct 28 '18 at 15:05


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# Math Help - microstates

1. ## microstates

when you flip a coin 50 times, the total number of microstates is 250. How can you show this by using the binomial theoreom. Thank you!

2. ## Re: microstates

Originally Posted by apatite
when you flip a coin 50 times, the total number of microstates is 250. How can you show this by using the binomial theoreom.
${2^{50}} = {\left( {1 + 1} \right)^{50}} = \sum\limits_{k = 0}^{50} {\left( {\begin{array}{*{20}{c}} {50} \\ k \end{array}} \right)}$

format: plain


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Effect of different graph operations at algebraic connectivity of graph laplacian?

The algebraic connectivity of a graph G is the second-smallest eigenvalue of the Laplacian matrix of G. This eigenvalue is greater than 0 if and only if G is a connected graph. The magnitude of this value reflects how well connected the overall graph is.

for an example, "adding self-loops" does not change laplacian eigenvalues (specially algebraic connectivity) of graph. Because, laplacian(G)= D-A is invariant with respect to adding self-loops.

My question is:

Does anyone has studied effect of different operations (such as edge contraction) on spectrum of laplacian? do you know good references?

Remark: the exact definition of the algebraic connectivity depends on the type of Laplacian used. For this question I prefer to use Fan Chung definition in SPECTRAL GRAPH THEORY. In this book Fan Chung has uesed a rescaled version of the Laplacian, eliminating the dependence on the number of vertices.

-
It would help if you provide some motivation and background. Please see How to ask a good question? and the site's FAQ. –  Kaveh Mar 11 '11 at 21:54
I'm also interested in the edge contraction case. I've spend some time previously trying to find references about the relation between eigenvalues and minor operations, with no success. –  Hsien-Chih Chang 張顯之 Mar 16 '11 at 1:33
To me, the motivation seems fairly clear. –  Suresh Venkat Sep 24 '11 at 20:12
I second Suresh, knowing how various operations influence the Laplacian is interesting in itself and this problems shows up in various contexts. –  Marcin Kotowski Sep 24 '11 at 20:50

Intuitively operations that preserve connectivity will not decrease the eigenvalues. For example, adding edges to the graph does not decrease the connectivity.

In general, if H is a subgraph of a graph G, by interlacing we know that the i-th largest Laplacian eigenvalue of H is no larger than the i-th largest Laplacian eigenvalue of G. A proof can be found in Proposition 3.2.1 of the book "Spectra of graphs" by Brouwer and Haemers. Note that the definition of Laplacian used in the book is not normalized; it has node degrees on the diagonal and -1 (or 0 if there is no edge) in the off-diagonal entries.

-
Thanks Chang. Your answer is really useful for me. But if we use the definition of Laplacian that is not normalized, then many of comparisons seems to be meaningless. For example we have Algebraic Connectivity(K10)=10 and Algebraic Connectivity(K20)=20. however, both graphs are fully connected simple graphs. But if we use the normalized Laplacian, then NormalizedAlgebraicConnectivity(K10) = NormalizedAlgebraicConnectivity(K20)=1 and therefore comparison of normalized version seems to be more rational and natural. –  b.a Mar 16 '11 at 2:03
@behnam: I agree with you. But after the normalization, some of the nondecreasing properties may differ. (Say one can ensure a strict decreasing on the largest Laplacian when deleting edges for the unnormalized ones, but not for the normalized ones.) –  Hsien-Chih Chang 張顯之 Mar 16 '11 at 17:16
@Hsien-Chih Chang "Intuitively operations that preserve connectivity will not decrease the eigenvalues. For example, adding edges to the graph does not decrease the connectivity." Are you sure? Do you have a proof? Is the following a counter example? Start with a path graph and add edges to form the Lollipop graph. The cover time gets worse; it goes from $\Theta(n^2)$ to $\Theta(n^3)$. What is happening to the eigenvalues in this example? –  Tyson Williams Sep 25 '11 at 13:36


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### Home > MC1 > Chapter 5 > Lesson 5.2.2 > Problem5-54

5-54.

How many even numbers are there on the cube? How many possibilities are there for what can be rolled?

There are 3 even numbers (2, 4, 6) and 6 possibilities, so the probability of rolling an even number is

$\frac{3}{6}\text{ or }\frac{1}{2}$

Follow the same steps as outlined in part (a).

1, 2, 3, and 6 are all factors of six.


text:
maths

Construction / Practical Geometry (High)

Welcome to the simple thought process to construction problems in practical geometry.

In the lesson on basics, the four fundamental elements of practical geometry is explained. And, the construction of various shapes using the fundamental elements is explained.

That is extended to the following.

•  Construction of triangles using secondary information (sum of sides, difference of sides, and perimeter of sides).

•  Scaling of lines, triangles, and other shapes.

•  Consturction of elements of circle (tangents and chords)

The reasoning on how each of the procedures work is provided, which makes it easy for students to retain knowledge and work out the procedure.

maths > construction-high > construction-triangles-secondary-parameters

Construction of Triangles With Secondary Information

Triangles are defined by $3$$3$ independent parameters. Usually, the three independent parameters are chosen from $6$$6$ primary parameters -- the three sides and the three angles.

The sum of two sides, or perimeter of the triangle, etc. are secondary parameters.

If one or more of given parameters is of secondary type, then how to construct the specified triangle? A short overview of approaching such problems is provided in this lesson.

An overview of constructing triangles with angle-side-sum of two sides is provided. Sum of two sides is a secondary parameter.
An overview of constructing triangles with angle-side-difference between two sides is provided. Difference between two sides is a secondary parameter.
An overview of constructing triangles with angle-side-negative difference between two sides is provided. Negative difference between two sides is a secondary parameter.
An overview of constructing triangles with angle-angle-perimeter is provided. Perimeter is a secondary parameter.

maths > construction-high > construction-scaling-line-triangle-polygons-circle

Construction: Scaling a line, triangle, polygon, circle

dividing a line in a given ratio (The method employed is based on properties of similar triangles.)
scaling or dividing a line in a given ratio (The method employed uses properties of traversal of pair of parallels.)
scaling a triangle in a given ratio
scaling a polygon in a given ratio
scaling a circle

maths > construction-high > construction-tangent-chord-circle

Construction of Tangents and Chord for a Circle


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# Difference between revisions of "2017 AMC 8 Problems/Problem 16"

## Problem 16

In the figure below, choose point $D$ on $\overline{BC}$ so that $\triangle ACD$ and $\triangle ABD$ have equal perimeters. What is the area of $\triangle ABD$? $[asy]draw((0,0)--(4,0)--(0,3)--(0,0)); label("A", (0,0), SW); label("B", (4,0), ESE); label("C", (0, 3), N); label("3", (0, 1.5), W); label("4", (2, 0), S); label("5", (2, 1.5), NE);[/asy]$

$\textbf{(A) }\frac{3}{4}\qquad\textbf{(B) }\frac{3}{2}\qquad\textbf{(C) }2\qquad\textbf{(D) }\frac{12}{5}\qquad\textbf{(E) }\frac{5}{2}$

## Solution

We know that the perimeters of the two small triangles are $3+CD+AD$ and $4+BD+AD$. Setting both equal and using $BD+CD = 5$, we have $BD = 2$ and $CD = 3$. Now, we simply have to find the area of $\triangle ABD$. Since $\frac{BD}{CD} = \frac{2}{3}$, we must have $\frac{[ABD]}{ACD]} = 2/3$. Combining this with the fact that $[ABC] = [ABD] + [ACD] = \frac{3*4}{2} = 6$, we get $[ABD] = \frac{2}{5}[ABC] = \frac{2}{5} * 6 = \boxed{\textbf{(D) } \frac{12}{5}}$


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#### Volume 22, issue 4 (2018)

 Recent Issues
 The Journal About the Journal Editorial Board Subscriptions Editorial Interests Editorial Procedure Submission Guidelines Submission Page Ethics Statement ISSN (electronic): 1364-0380 ISSN (print): 1465-3060 Author Index To Appear Other MSP Journals
Quantitative bi-Lipschitz embeddings of bounded-curvature manifolds and orbifolds

### Sylvester Eriksson-Bique

Geometry & Topology 22 (2018) 1961–2026
##### Abstract

We construct bi-Lipschitz embeddings into Euclidean space for bounded-diameter subsets of manifolds and orbifolds of bounded curvature. The distortion and dimension of such embeddings is bounded by diameter, curvature and dimension alone. We also construct global bi-Lipschitz embeddings for spaces of the form ${ℝ}^{n}∕\Gamma$, where $\Gamma$ is a discrete group acting properly discontinuously and by isometries on ${ℝ}^{n}$. This generalizes results of Naor and Khot. Our approach is based on analyzing the structure of a bounded-curvature manifold at various scales by specializing methods from collapsing theory to a certain class of model spaces. In the process, we develop tools to prove collapsing theory results using algebraic techniques.

##### Keywords
bilipschitz, sectional curvature, Alexandrov, collapsing theory
##### Mathematical Subject Classification 2010
Primary: 30L05, 51F99, 53C21
Secondary: 20H15, 53B20


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## University COVID-19 update

### Questions about buildings and services? Visit the list of Modified Services.

Please note: The University of Waterloo is closed for all events until further notice.

# Welcome to Combinatorics and Optimization

Spring 2020 Undergraduate Research Assistantship Program (URA). ***ON-LINE APPICATIONS OPEN November 1, 2019.***

Tutte's Distinguished Lecture Series

The very successful Tutte's 100th Distinguished Lecture Series has now completed. That success has led to a Tutte Distinguished Lecture once per term. The next lecture will happen in the Spring term.

*Recordings of occurred talks are all available on C&O's YouTube Channel

Grad Studies: Fall 2020 applications now open

1. July 17, 2020SAGT 2020 Best Paper Award

Jochen Koenemann, Kanstantsin Pashkovich and Natig Tofigzade were announced the recipients of the SAGT 2020 Best Paper Award for their paper "Approximating Stable Matchings with Ties of Bounded Size".

2. July 1, 2020C&O welcomes four new faculty members

The C&O department is very pleased to welcome four new faculty members, Assistant Professors Logan Crew, Stephen Melczer, Oliver Pechenik and Sophie Spirkl.

3. June 30, 2020Jun Yan awarded an Alumni Gold Medal

At the Spring convocation, Jun Yan was awarded an Alumni Gold Medal in recognition of his academic excellence during his undergraduate studies in Combinatorics & Optimization and Pure Mathematics. Jun Yan was also a recipient of the 2020 William Tutte Centenary Scholarship.

1. Aug. 6, 2020Algebraic Combinatorics Seminar - Jordan Long

Title: Subdivergence-free gluings of trees

 Speaker: Jordan Long Affiliation: University of Waterloo Zoom: Contact Karen Yeats

Abstract:

Motivated by questions in quantum field theory, we introduce a purely combinatorial problem of counting subdivergence-free gluings of trees. We present closed-form expressions counting subdivergence-free gluings for four different families of trees, as well as an algorithm to count subdivergence-free gluings of arbitrary pairs of trees. This is joint work with Clair Dai and Karen Yeats.

2. Aug. 6, 2020Algebraic Combinatorics Seminar - Mushegh Shahinyan

Title: Counting the $c_2$ invariant on the circulant family of graphs

 Speaker: Mushegh Shahinyan Affiliation: University of Waterloo Zoom: Contact Karen Yeats

Abstract:

The algebro-geometric invariant on Feynman Diagrams called the $c_2$ invariant is a useful tool for detecting properties of Feynman periods. We present this identity on graphs that originate from the scalar $\phi_4$-theory with a purely combinatorial perspective and go over some strategies for computing it. We will further narrow our focus onto the circulant family of graphs and present some explicit results.

3. Aug. 6, 2020Algebraic Combinatorics Seminar - Olha Silina

Title: Abelian covering graphs and their properties

 Speaker: Olha Silina Affiliation: University of Waterloo Zoom: Contact Karen Yeats

Abstract:

A covering graph is a structure obtained from a graph by ‘replacing’ every vertex with a coclique of size $r$. The main focus of this talk is connections between (spectral) characteristic of a cover and properties such as being walk- or distance- regular.

All upcoming events


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## Strong convergence of an implicit iteration process for a finite family of nonexpansive mappings.(English)Zbl 1090.47055

In [Numer. Funct. Anal. Optim. 22, 767–773 (2001; Zbl 0999.47043)], H.-K. Xu and R. G. Ori introduced an implicit iteration process for a finite family of nonexpansive mapping and proved the weak convergence of this process to a common fixed point of a finite family of nonexpansive maps in a Hilbert space. They posed the question: What assumptions would have to be made on the finite family of nonexpansive mappings and/or their parameters $$\{ \alpha _{n}\}$$ to guarantee the strong convergence of the sequence $$\{ x_{n}\}$$ generated by their implicit iteration process? The authors prove the strong convergence of the sequence $$\{ x_{n}\}$$ in a much more general uniformly convex Banach space under the condition that one member of the finite family of nonexpansive mappings is semi-compact or any one of the contractive assumptions of Proposition 3.4 of their paper holds.

### MSC:

 47J25 Iterative procedures involving nonlinear operators 47H09 Contraction-type mappings, nonexpansive mappings, $$A$$-proper mappings, etc. 47H10 Fixed-point theorems 47J05 Equations involving nonlinear operators (general)

Zbl 0999.47043
Full Text:

### References:

 [1] C.E. Chidume, Iterative algorithms for nonexpansive mappings and some of their generalizations, Nonlinear Anal. and Appl., R.P. Agarwal, et al. (Eds.), Kluwer Academic Publishers, 2003, pp. 383-429. · Zbl 1057.47003 [2] Kirk, W.A., On nonlinear mappings of strongly semicontractive type, J. math. anal. appl., 27, 409-412, (1969) · Zbl 0183.15103 [3] Petryshyn, W.V., Fixed point theorems for various classes of 1-set-contractive and 1-ball-contractive mappings in Banach spaces, Trans. amer. math. soc., 182, 323-352, (1973) · Zbl 0277.47033 [4] Shahzad, N., Approximating fixed points of non-self nonexpansive mappings in Banach spaces, Nonlinear anal., 61, 1031-1039, (2005) · Zbl 1089.47058 [5] Tan, K.K.; Xu, H.K., Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process, J. math. anal. appl., 178, 301-308, (1993) · Zbl 0895.47048 [6] Xu, H.K., Inequalities in Banach spaces with applications, Nonlinear anal., 16, 1127-1138, (1991) · Zbl 0757.46033 [7] Xu, H.K.; Ori, R., An implicit iterative process for nonexpansive mappings, Numer. funct. anal. optim., 22, 767-773, (2001) · Zbl 0999.47043 [8] Zhou, Y.; Chang, S.S., Convergence of implicit iteration process for a finite family of asymptotically nonexpansive mappings in Banach spaces, Numer. funct. anal. appl., 23, 911-921, (2002) · Zbl 1041.47048
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.


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## anonymous one year ago Physics Define Newton's first law, second law, as well as third law with full solution within single answer. First person to have the most accurate wording will be awarded medals from all participants.

1. anonymous

Newton' first law=inertia

2. anonymous

*full solutions

3. anonymous

inertia=an object will keep moving unless unless acted upon by an unbalanced force

4. anonymous

correct

5. imqwerty

1st law - a body tends to remain at its original position. :) nd this is called inertia .example - when u shake a tree the fruits fall down cause they try to resist any change in their original position nd thus they fall :)

6. anonymous

second law: when force is applied to an object, acceleration is made

7. anonymous

8. imqwerty

lol :D

9. anonymous

@heretohelpalways not quite. Pay attention to the proportion

10. anonymous

between the force applied and resulting acceleration.

11. anonymous

with mass being the constant

12. anonymous

As well as the resulting acceleration with changing mass with constant being the force applied.

13. anonymous

Try to draw a relationship and describe each of them

14. anonymous

mass*acceleration=force

15. anonymous

yes

16. anonymous

BUt

17. anonymous

Try to explain the relationship between the amount of force applied and resulting acceleration.

18. anonymous

AND relationship between mass and acceleration given a force assumed to be constant

19. anonymous

example: 300*0.07= 21 newtons

20. anonymous

Yes.

21. imqwerty

:)

22. anonymous

Final answer being the applied force and resulting acceleration have a PROPORTIONAL RELATIONSHIP whereas mass and acceleration has INVERSE PROPORTIONAL RELATIONSHIP when force is kept constant.

23. anonymous

In essence.

24. imqwerty

25. anonymous

elaborate

26. anonymous

balanced forces=net force of zero=that's not the case

27. anonymous

hmmmmm, I'll think of something

28. anonymous

Oh astrophysics came

29. anonymous

recoil of a gun when it fires

30. anonymous

That's a spot on

31. anonymous

can you elaborate the concept?

32. anonymous

Why aren't you shooting yourself with that? Why does recoil not kill you? Account for the drastic difference of surface areas being responsible for dispersion of forces into two opposite directions perfectly alined with one another.

33. imqwerty

example of 3rd law - when u walk u put force on ground nd the ground puts a normal force on u wid the help of which u can walk :)

34. anonymous

sorry, got to go now. I am being serious. I'll answer this question again later or tomorrow. I'll give a medal to imqwerty.

35. anonymous

Great! I hope you enjoyed my contest series @heretohelpalways

36. anonymous

I aim to make this stimulating for everyone .

37. anonymous

Mr. Astrophysics what have you got to say?

38. imqwerty

:) #%#\$%

39. Astrophysics

I'll keep it simple I suppose. Newton's first law is a body acted on by no net forces with constant velocity (that means 0 acceleration) you can see this with a linear position time graph. You can also see this on a ice hockey table, the slicker the surface further the puck slides (given an initial velocity of course). So what you want to see from here is that when a body is at rest or moving with a constant velocity, we say it's at equilibrium, mathematically. $\sum \vec F = 0$ don't forget the components! Newton's second law of motion is simply is net force = mass x acceleration, $\sum \vec F = m \vec a$ writing it out we can say if a net external force acts on a body, the body accelerates. The direction of acceleration is the same as the direction of the net force where the m x a = the net force. I think you can think of your examples for this, pretty straight forward. Newton's third law often called action - reaction, it is stated as if a body A exerts force on body B (action) , then the body B exerts a force on body A (reaction), the two forces have the same magnitude but are opposite in direction. $\vec F_{A~on~B} = - \vec F _{B ~ on~A}$ it's like a rocket blasting off, or kicking a ball, anything really. Hope that helps!

40. anonymous

@imqwerty medal to astrophysics

41. Astrophysics

Haha, thanks :)

42. anonymous

Are you a professional physicist?

43. Astrophysics

Nope! But I do aspire one to be!

44. Astrophysics

We do have one professional physicist here @Michele_Laino :-)

45. anonymous

Wow

46. anonymous

Are you taking physics in your unit I assume?

47. Astrophysics

Yup! I still have a long way to go haha.

48. anonymous

Certainly any degree of comparison would be absurd to 1st year medical student. XD

49. anonymous

Physics is just super amazing

50. Astrophysics

Haha, well medical students run away from physics :P

51. Astrophysics

Thanks for the medal, it was fun!

52. anonymous

Likewise! See you around.

53. imqwerty

:D

54. anonymous

`

55. anonymous

Interesting, Newton formulated his Second Law as a way to define acceleration, saying that a net force acting on a mass produces an acceleration in the same direction as the net force, i.e.$\vec{a} = \frac{ \vec{F} }{ m }$Only later was it adopted in its now familiar form$\vec{F} = m \vec{a}$

56. Astrophysics

Actually Newton proposed his second law as such, considering momentum $\vec F = \frac{ d \vec p }{ dt }$


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# Ordering Fractions and Decimals Worksheet

Ordering Fractions and Decimals Worksheet
• Page 1
1.
Which set of numbers is ordered from greatest to least?
 a. $\frac{5}{8}$, 0.8, $8\frac{1}{8}$ , 0.085 b. 0.8, $8\frac{1}{8}$, $\frac{5}{8}$, 0.085 c. 0.085, $\frac{5}{8}$, 0.8, $8\frac{1}{8}$ d. $8\frac{1}{8}$, 0.8, $\frac{5}{8}$, 0.085

2.
Which set of numbers is ordered from greatest to least?
 a. 0.3, $\frac{7}{3}$, $3\frac{1}{7}$, 0.037 b. $\frac{7}{3}$, $3\frac{1}{7}$, 0.3, 0.037 c. 0.037, 0.3, $\frac{7}{3}$, $3\frac{1}{7}$ d. $3\frac{1}{7}$, $\frac{7}{3}$, 0.3, 0.037

3.
Which set of numbers is ordered from greatest to least?
 a. $\frac{4}{9}$, 0.9, $4\frac{1}{9}$, 0.049 b. 0.9, $4\frac{1}{9}$, $\frac{4}{9}$, 0.049 c. $4\frac{1}{9}$, 0.9, $\frac{4}{9}$, 0.049 d. 0.049, $\frac{4}{9}$, 0.9, $4\frac{1}{9}$

4.
Which set of numbers is ordered from greatest to least?
 a. $\frac{1}{7}$, 0.7, $7\frac{1}{7}$, 0.07 b. $7\frac{1}{7}$, 0.7, $\frac{1}{7}$, 0.07 c. 0.07, $\frac{1}{7}$, 0.7, $7\frac{1}{7}$ d. 0.7, $7\frac{1}{7}$, $\frac{1}{7}$, 0.07

5.
Which set of numbers is ordered from greatest to least?
 a. $9\frac{1}{9}$, 0.9, $\frac{1}{9}$, 0.09 b. 0.09, $\frac{1}{9}$, 0.9, $9\frac{1}{9}$ c. $\frac{1}{9}$, 0.9, $9\frac{1}{9}$, 0.09 d. 0.9, $9\frac{1}{9}$, $\frac{1}{9}$, 0.09

6.
Which set of numbers is ordered from greatest to least?
 a. 0.07, 0.7, $\frac{5}{7}$, $7\frac{1}{5}$ b. $\frac{5}{7}$, $7\frac{1}{5}$, 0.7, 0.07 c. $7\frac{1}{5}$, $\frac{5}{7}$, 0.7, 0.07 d. 0.7, $\frac{5}{7}$, $7\frac{1}{5}$, 0.07

7.
Which set of numbers is ordered from greatest to least?
 a. $\frac{4}{5}$, $4\frac{1}{5}$, 0.4, 0.04 b. 0.04, 0.4, $\frac{4}{5}$, $4\frac{1}{5}$ c. 0.4, $\frac{4}{5}$, $4\frac{1}{5}$, 0.04 d. $4\frac{1}{5}$, $\frac{4}{5}$, 0.4, 0.04

8.
Which set of numbers is ordered from greatest to least?
 a. $2\frac{1}{2}$, $\frac{1}{2}$, 0.2, 0.02 b. 0.2, $\frac{1}{2}$, $2\frac{1}{2}$, 0.02 c. $\frac{1}{2}$, $2\frac{1}{2}$, 0.2, 0.02 d. 0.02, 0.2, $\frac{1}{2}$, $2\frac{1}{2}$

9.
Which set of numbers is ordered from greatest to least?
 a. 0.03, 0.3, $\frac{1}{3}$, $3\frac{1}{3}$ b. 0.3, $\frac{1}{3}$, $3\frac{1}{3}$, 0.03 c. $3\frac{1}{3}$, $\frac{1}{3}$, 0.3, 0.03 d. $\frac{1}{3}$, $3\frac{1}{3}$, 0.3, 0.03

 a. 4.5, 0.4, $\frac{45}{40}$, $\frac{4}{15}$ b. 4.5, $\frac{45}{40}$, 0.4, $\frac{4}{15}$ c. $\frac{45}{40}$, 4.5, 0.4, $\frac{4}{15}$ d. $\frac{4}{15}$, 0.4, $\frac{45}{40}$, 4.5


text:
# zbMATH — the first resource for mathematics

Stochastic Taylor expansions for the expectation of functionals of diffusion processes. (English) Zbl 1065.60068
The author considers systems of stochastic ordinary differential equations (SODEs) both in Itô and Stratonovich formulation, driven by a multi-dimensional Wiener process. In order to develop and analyse weak approximation methods, one needs stochastic Taylor expansions of $${\mathbf E}f(X_t)$$, the expectation of a functional $$f$$ of the solution $$X_t$$ to the SODEs in both formulations. In this well-written article a representation of $${\mathbf E}f(X_t)$$ in terms of truncated Taylor expansions and remainder terms is proved. Further, estimates of the remainder terms are given. The representations and the proofs are based on multi-coloured stochastic rooted tree theory. This generalizes the rooted tree theory well-known in the deterministic analysis of Runge-Kutta methods. In particular, the Taylor expansions derived here coincide with those derived in the deterministic setting if the diffusion term vanishes.

##### MSC:
 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis) 65C30 Numerical solutions to stochastic differential and integral equations 60J60 Diffusion processes 41A58 Series expansions (e.g., Taylor, Lidstone series, but not Fourier series)
Full Text:
##### References:
 [1] Arnold L., Stochastic Differential Equations (1974) · Zbl 0278.60039 [2] Burrage K., SIAM J. Numer. Anal. 38 (5) pp 1626– (2000) · Zbl 0983.65006 [3] Burrage K., Appl. Numer. Math. 22 (1) pp 81– (1996) · Zbl 0868.65101 [4] Butcher J. C., The Numerical Analysis of Ordinary Differential Equations: Runge–Kutta and General Linear Methods (1987) · Zbl 0616.65072 [5] Dynkin E.B., Markov Processes (1965) [6] Ikeda N., Kodansha Ltd.: Tokyo, in: Stochastic Differential Equations and Diffusion Processes (1989) [7] Karatzas I., Brownian Motion and Stochastic Calculus (1999) · Zbl 0734.60060 [8] Kloeden P.E., Applications of Mathematics 23, in: Numerical Solution of Stochastic Differential Equations (1999) [9] Øksendal B., Applications of Mathematics 21, in: Stochastic Differential Equations (1998) [10] Platen E., Probab. Math. Statist. 3 pp 37– (1982) [11] Stroock D.W., Multidimensional Diffusion Processes (1979)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.


text:
# 2.4 Complex numbers

 Page 1 / 8
In this section you will:
• Add and subtract complex numbers.
• Multiply and divide complex numbers.
• Simplify powers of $i$ .

Discovered by Benoit Mandelbrot around 1980, the Mandelbrot Set is one of the most recognizable fractal images. The image is built on the theory of self-similarity and the operation of iteration. Zooming in on a fractal image brings many surprises, particularly in the high level of repetition of detail that appears as magnification increases. The equation that generates this image turns out to be rather simple.

In order to better understand it, we need to become familiar with a new set of numbers. Keep in mind that the study of mathematics continuously builds upon itself. Negative integers, for example, fill a void left by the set of positive integers. The set of rational numbers, in turn, fills a void left by the set of integers. The set of real numbers fills a void left by the set of rational numbers. Not surprisingly, the set of real numbers has voids as well. In this section, we will explore a set of numbers that fills voids in the set of real numbers and find out how to work within it.

## Expressing square roots of negative numbers as multiples of $\text{\hspace{0.17em}}i$

We know how to find the square root of any positive real number. In a similar way, we can find the square root of any negative number. The difference is that the root is not real. If the value in the radicand is negative, the root is said to be an imaginary number . The imaginary number $\text{\hspace{0.17em}}i\text{\hspace{0.17em}}$ is defined as the square root of $\text{\hspace{0.17em}}-1.$

$\sqrt{-1}=i$

${i}^{2}={\left(\sqrt{-1}\right)}^{2}=-1$

We can write the square root of any negative number as a multiple of $\text{\hspace{0.17em}}i.\text{\hspace{0.17em}}$ Consider the square root of $\text{\hspace{0.17em}}-49.$

$\begin{array}{ccc}\hfill \sqrt{-49}& =& \hfill \sqrt{49\cdot \left(-1\right)}\\ & =& \sqrt{49}\sqrt{-1}\hfill \\ & =& 7i\hfill \end{array}$

We use $\text{\hspace{0.17em}}7i\text{\hspace{0.17em}}$ and not $\text{\hspace{0.17em}}-7i\text{\hspace{0.17em}}$ because the principal root of $\text{\hspace{0.17em}}49\text{\hspace{0.17em}}$ is the positive root.

A complex number is the sum of a real number and an imaginary number. A complex number is expressed in standard form when written $\text{\hspace{0.17em}}a+bi\text{\hspace{0.17em}}$ where $\text{\hspace{0.17em}}a\text{\hspace{0.17em}}$ is the real part and $\text{\hspace{0.17em}}b\text{\hspace{0.17em}}$ is the imaginary part. For example, $\text{\hspace{0.17em}}5+2i\text{\hspace{0.17em}}$ is a complex number. So, too, is $\text{\hspace{0.17em}}3+4i\sqrt{3}.$

Imaginary numbers differ from real numbers in that a squared imaginary number produces a negative real number. Recall that when a positive real number is squared, the result is a positive real number and when a negative real number is squared, the result is also a positive real number. Complex numbers consist of real and imaginary numbers.

## Imaginary and complex numbers

A complex number    is a number of the form $\text{\hspace{0.17em}}a+bi\text{\hspace{0.17em}}$ where

• $a\text{\hspace{0.17em}}$ is the real part of the complex number.
• $b\text{\hspace{0.17em}}$ is the imaginary part of the complex number.

If $\text{\hspace{0.17em}}b=0,$ then $\text{\hspace{0.17em}}a+bi\text{\hspace{0.17em}}$ is a real number. If $\text{\hspace{0.17em}}a=0\text{\hspace{0.17em}}$ and $\text{\hspace{0.17em}}b\text{\hspace{0.17em}}$ is not equal to 0, the complex number is called a pure imaginary number. An imaginary number    is an even root of a negative number.

Given an imaginary number, express it in the standard form of a complex number.

1. Write $\text{\hspace{0.17em}}\sqrt{-a}\text{\hspace{0.17em}}$ as $\text{\hspace{0.17em}}\sqrt{a}\sqrt{-1}.$
2. Express $\text{\hspace{0.17em}}\sqrt{-1}\text{\hspace{0.17em}}$ as $\text{\hspace{0.17em}}i.\text{\hspace{0.17em}}$
3. Write $\text{\hspace{0.17em}}\sqrt{a}\cdot i\text{\hspace{0.17em}}$ in simplest form.

## Expressing an imaginary number in standard form

Express $\text{\hspace{0.17em}}\sqrt{-9}\text{\hspace{0.17em}}$ in standard form.

$\begin{array}{ccc}\hfill \sqrt{-9}& =& \sqrt{9}\sqrt{-1}\hfill \\ & =& 3i\hfill \end{array}$

In standard form, this is $\text{\hspace{0.17em}}0+3i.$

Express $\text{\hspace{0.17em}}\sqrt{-24}\text{\hspace{0.17em}}$ in standard form.

$\sqrt{-24}=0+2i\sqrt{6}$

## Plotting a complex number on the complex plane

We cannot plot complex numbers on a number line as we might real numbers. However, we can still represent them graphically. To represent a complex number, we need to address the two components of the number. We use the complex plane    , which is a coordinate system in which the horizontal axis represents the real component and the vertical axis represents the imaginary component. Complex numbers are the points on the plane, expressed as ordered pairs $\text{\hspace{0.17em}}\left(a,b\right),$ where $\text{\hspace{0.17em}}a\text{\hspace{0.17em}}$ represents the coordinate for the horizontal axis and $\text{\hspace{0.17em}}b\text{\hspace{0.17em}}$ represents the coordinate for the vertical axis.

the gradient function of a curve is 2x+4 and the curve passes through point (1,4) find the equation of the curve
1+cos²A/cos²A=2cosec²A-1
test for convergence the series 1+x/2+2!/9x3
a man walks up 200 meters along a straight road whose inclination is 30 degree.How high above the starting level is he?
100 meters
Kuldeep
Find that number sum and product of all the divisors of 360
Ajith
exponential series
Naveen
what is subgroup
Prove that: (2cos&+1)(2cos&-1)(2cos2&-1)=2cos4&+1
e power cos hyperbolic (x+iy)
10y
Michael
tan hyperbolic inverse (x+iy)=alpha +i bita
prove that cos(π/6-a)*cos(π/3+b)-sin(π/6-a)*sin(π/3+b)=sin(a-b)
why {2kπ} union {kπ}={kπ}?
why is {2kπ} union {kπ}={kπ}? when k belong to integer
Huy
if 9 sin theta + 40 cos theta = 41,prove that:41 cos theta = 41
what is complex numbers
Dua
Yes
ahmed
Thank you
Dua
give me treganamentry question
Solve 2cos x + 3sin x = 0.5


text:
Chapter 55

The use of cricotracheal resection in the treatment of cancer is rare owing to the rarity of cancers of the subglottis and their lack of confinement to the larynx. Of the three subsites of the larynx, the subglottis is the origin of squamous cell carcinoma, (by far the most common cause of laryngeal cancer), in only 1–2% of patients.1 Cricotracheal resection for the treatment of subglottic stenosis is much more common, and the surgical techniques used for treating subglottic stenosis can be applied to surgical resection of the rare neoplasm that remains confined to the subglottis.

The glottis is defined by the American Joint Committee on Cancer as the superior and inferior surfaces of the true vocal cords occupying a horizontal plane 1 cm in thickness extending inferiorly from the lateral margin of the ventricle. The subglottis is defined as that region which extends from the lower border of the glottis to the lower margin of the cricoid cartilage.2 On the basis of histologic sectioning of whole larynges, Kirschner was able to demonstrate that the conus elasticus represents the definitive anatomic boundary between the glottis and the subglottis.3 Tumors above the plane of the conus elasticus tend to behave as glottic tumors and remain within the confines of the larynx, whereas those below the conus spread more easily beyond the borders of the larynx and metastasize more commonly to the prelaryngeal, paratracheal, and mediastinal lymph nodes. The epithelial lining also can be used to differentiate the glottis (lined by keratinizing squamous cells) from the subglottis (lined by ciliated respiratory epithelium).

While squamous cell carcinoma arises in the subglottis in only 1–2% of all laryngeal cancers, the subglottis is involved by contiguous spread of tumors of glottic origin in 11–33% of patients. These more common tumors are not amenable to cricotracheal resection.4,5 Early primary subglottic carcinomas are asymptomatic. Patients generally present with stage T3 or T4 tumors (Table 55-1), and airway obstruction is relatively common. These tumors usually exhibit circumferential growth, early cartilage invasion, and tumor growth beyond the borders of the larynx. Since glottic tumors with subglottic extension are not amenable to cricotracheal resection, and primary tumors of the subglottis of grade T2 or above are not contained within the subglottis, cricotracheal resection for squamous cell carcinoma is only possible for the rare T1 tumor. Otherwise, subglottic squamous cell carcinoma is treated with either radiation therapy or wide-field surgery, such as laryngectomy or laryngopharyngectomy. Tracheal tumors rarely extend superiorly to involve the subglottis.

Table 55-1. AJCC Staging of Subglottic Carcinoma

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text:
# 1 Introduction

This tutorial introduces basic statistical techniques for inferential statistics for hypothesis testing with “R”. The entire code for the tutorial can be downloaded here. The first part of this tutorial focuses on basic non-parametric tests such as Fisher’s Exact test while the second part introduces parametric tests such as the t-test.

Non-Parametric Tests do not require the data (or the errors of the dependent variable, to be more precise) to be distributed normally. Tests that do not rewuire normal data are referred to as non-parametric tests (test that require the data to be distributed normally are analogously called parametric tests). We focus on non-parametric tests first as this family of test in frequently used in linguistics. In the later part of this section, we will focus on regression modelling where assumptions of about the data become more important.

# 2 Preparation

As all caluculations and visualizations in this tutorial rely on “R”, it is necessary to install “R”, “RStudio”, and “Tinn-R”. If these programms (or, in the case of “R”, environments) are not installed yet, please search for them in your favorite search engine and add the term “download”. Open any of the first few links and follow the installation instructions (they are easy to follow, do not require any specifications, and are pretty much self-explanatory).

In addition, certain “libraries” need to be installed so that the scripts shown below are executed without errors. Before turning to the code below, please install the libraries needed for running the code below. If you have already installed the libraries mentioned below, then you can skip ahead ignore this section. To install the necessary libraries, simply run the following code - it may take some time (between 1 and 5 minutes to install all of the libraries so you do not need to worry if it takes some time).

# clean current workspace
rm(list=ls(all=T))
# set options
options(stringsAsFactors = F)
# install libraries
install.packages(c("stringr", "VGAM", "fGarch"))

Once you have installed “R”, “R-Studio”, “Tinn-R”, and have also initiated the session by executing the code shown above, you are good to go.

# 3 Fisher’s Exact Test

Fisher’s Exact test is very useful because it does not rely on distributional assumptions relying on normality. Instead, Fisher’s Exact Test calculates the probabilities of all possible outcomes and uses these to determine significance. To understand how a Fisher’s Exact test, we will use a very simple example.

Imagine you are interested in adjective modification and you want to find out if “very” and “truly” differ in their collocational preferences. So you extract all instances of “cool”, all instances of “very”, and all instances of “truly” from a corpus. Now that you have gathered this data, you want to test if “truly” and “very” differ with respect to their preference to co-occur with “cool”. Accodingly, you tabulate the results and get the follwoing table.

library(knitr)                 # activate library for tabulating
# generate data
coolmatrix <- matrix(c("truly", "very", 5, 17, 40, 41), ncol = 3, byrow = F)
kable(coolmatrix, caption = "Co-occurrence of cool with adverbs.")
truly 5 40
very 17 41

To perform a Fisher’s Exact test, we first need to create a table with these results in “R”.

# create table
coolmx <- matrix(c(5, 17, 40, 41),
# number of rows of the table
nrow = 2,
# def. dimension names
dimnames = list(Adverbs = c("truly", "very"),
# inspect resulting table
coolmx
##        Adjectives
##   truly    5              40
##   very    17              41

Once we have the created a matrix with these numbers, we can perform the Fisher’s Exact test to see if “very” and “truly” differ in their preference to co-occur with “cool.”

# perform test
fisher.test(coolmx)
##
##  Fisher's Exact Test for Count Data
##
## data:  coolmx
## p-value = 0.03024
## alternative hypothesis: true odds ratio is not equal to 1
## 95 percent confidence interval:
##  0.08015294 0.96759831
## sample estimates:
## odds ratio
##  0.3048159

The results of the Fisher’s Exact test show that the p-value is lower than .05 and that we are therefor justified in assuming that “very” and “truly” differ in their collocational prefernces to co-occur with “cool.”

# 4 Ranking and Sign-Based Non-Parametric Tests

If the depended variable is neither nominal nor categorical, but ordinal (that is if the dependent variable represents an order factor such as ranks), using a chi-square test is not warranted. In such cases it is advisable to apply tests that are designed to handle ordinal data. In the following, we will therefore briefly touch on bivariate tests that can handle ordinal dependent variables.

# 5 Mann-Whitney U-Test / Wilcoxon Rank Sum-Test

It is a rather frequent case that numeric depend variables are transformed or converted into ordinal variables because the distribution of residuals does not allow the application of a linear regression. Because we are dealing with ordinal data, the application of a chi-square test is unwarranted and we need to use another test. In such cases, the Mann-Whitney U-test (also called Wilcoxon rank sum-test) can be used.

The Mann-Whitney U-test can also be used if the groups under investigation represent identical participants that are tested under two conditions.

Imaging we wanted to determine if two language families differed with resepct to the size of their phoneme inventories. You have already ranked the inventory sizes and would now like to now if language family correlates with inventory size. To answer this question, you cerate the table shown below.

# create table
Rank <- c(1,3,5,6,8,9,10,11,17,19, 2,4,7,12,13,14,15,16,18,20)
Groups <- c(rep("Lang.Fam.1", 10), rep("Lang.Fam.2", 10))
Languagefamilytb <- data.frame(Groups, Rank)
# inspect table
Languagefamilytb
##        Groups Rank
## 1  Lang.Fam.1    1
## 2  Lang.Fam.1    3
## 3  Lang.Fam.1    5
## 4  Lang.Fam.1    6
## 5  Lang.Fam.1    8
## 6  Lang.Fam.1    9
## 7  Lang.Fam.1   10
## 8  Lang.Fam.1   11
## 9  Lang.Fam.1   17
## 10 Lang.Fam.1   19
## 11 Lang.Fam.2    2
## 12 Lang.Fam.2    4
## 13 Lang.Fam.2    7
## 14 Lang.Fam.2   12
## 15 Lang.Fam.2   13
## 16 Lang.Fam.2   14
## 17 Lang.Fam.2   15
## 18 Lang.Fam.2   16
## 19 Lang.Fam.2   18
## 20 Lang.Fam.2   20

We will also briefly inspect the data visually using a box plot.

# inspect data
par(mfrow=c(1,2))
boxplot(Languagefamilytb$Rank ~ Languagefamilytb$Groups, col = c("orange", "darkgrey"), main = "")
par(mfrow=c(1,1))

To use Mann-Whitney U test, the dependent variable (Rank) must be ordinal and independent variable (Group) must be a binary factor. We briefly check this by inspecting teh structure of the data.

# perform test
str(Languagefamilytb)
## 'data.frame':    20 obs. of  2 variables:
##  $Groups: Factor w/ 2 levels "Lang.Fam.1","Lang.Fam.2": 1 1 1 1 1 1 1 1 1 1 ... ##$ Rank  : num  1 3 5 6 8 9 10 11 17 19 ...

As the variables are what we need them to be, we can now perform the Mann-Whitney U test on the table.

# perform test
wilcox.test(Languagefamilytb$Rank ~ Languagefamilytb$Groups)
##
##  Wilcoxon rank sum test
##
## data:  Languagefamilytb$Rank by Languagefamilytb$Groups
## W = 34, p-value = 0.2475
## alternative hypothesis: true location shift is not equal to 0

The results of the Wilcoxon rank sum test tell use that the two language families to not differ significantly with respect to their phoeneme inventory size as the p-value is greater than .05.

The Wilcoxon rank sum test can also be used with continuity correction. A continuety correction is neccessary when both variables represent numeric values that are non-normal. In the following example, we want to test if the reaction time for identifying a word as real is correlated with its token frequency.

For this example, we generate data is deliberately non-normal.

# load librarieslibrary(VGAM)
library(fGarch)
# generate non-normal skewed numeric data
r=.1
Frequency=rsnorm(100,0,2,4)
NormalReaction=rsnorm(100,0,2,4)
ReactionTimes=Frequency*r+NormalReaction*sqrt(1-r^2)
# inspect data
par(mfrow=c(1,2))
boxplot(Frequency, col = "orange", main = "Frequency")
boxplot(ReactionTimes, col = "darkgrey", main = "Reaction Times")

par(mfrow=c(1,1))

Both variables are skewed but we can use the Wilcoxon rank sum test with continuity correction which takes the skewness into account.

# perform test
wilcox.test(ReactionTimes, Frequency)
##
##  Wilcoxon rank sum test with continuity correction
##
## data:  ReactionTimes and Frequency
## W = 4740, p-value = 0.526
## alternative hypothesis: true location shift is not equal to 0

When performing the Wilcoxon rank sum test with data that represent the same individulas that were tested under two condition, i.e. if the samples are dependent, then the argument “paired” has to be “TRUE”.

In this example, the same individuals had to read tongue twisters when they were sober and when they were intoxicated. A Wilcoxon signed rank test with continuity correction is used to test if the number of errors that occur when reading tongue twisters correlates with being sober/intoxicated. Again, we create ficticious data.

# create data
Sober <- sample(0:9, 15, replace = T)
Intoxicated <-  sample(3:12, 15, replace = T)
# tabulate data
intoxtb <- data.frame(Sober, Intoxicated)
# inspect data
str(intoxtb)
## 'data.frame':    15 obs. of  2 variables:
##  $Sober : int 8 9 6 8 5 7 0 4 7 6 ... ##$ Intoxicated: int  7 7 11 11 6 7 9 12 3 5 ...

Now, we briefly plot the data.

# inspect data
boxplot(intoxtb$Sober, intoxtb$Intoxicated, col = c("orange", "darkgrey"), main = "", ylab = "Number of errors", xlab = "State", data = intoxtb)

The boxes indicate a significant difference. Finally, we perform the Wilcoxon signed rank test with continuity correction,

# perform test
wilcox.test(intoxtb$Sober, intoxtb$Intoxicated, paired=T)
##
##  Wilcoxon signed rank test with continuity correction
##
## data:  intoxtb$Sober and intoxtb$Intoxicated
## V = 16.5, p-value = 0.02548
## alternative hypothesis: true location shift is not equal to 0

The p-value is lower than .05 which means that the number of errors when reading tongue twisters is affected by one’s state (sober/intoxicated) - at least in this ficticious example.

# 6 Kruskal-Wallis Rank Sum Test

The Kruskal-Wallis rank sum test is a type of “Analysis of Variance” or ANOVA. For this reason, the Kruskal Wallis Test is also referd to as a “one-way Anova by ranks” which can handle numeric and ordinal data.

In the example below, uhm represents the number of filled pauses in a short 5 minute interview while speaker represents whether the speaker was a native speaker or a learner of English. As before, the data is generated and thus artificial.

# create data
Uhms <- c(15, 13, 10, 8, 37, 23, 31, 52, 11, 17)
Speaker <- c(rep("Learner", 5), rep("NativeSpeaker", 5))
# create table
uhmtb <- data.frame(Speaker, Uhms)
# inspect table
str(uhmtb)
## 'data.frame':    10 obs. of  2 variables:
##  $Speaker: Factor w/ 2 levels "Learner","NativeSpeaker": 1 1 1 1 1 2 2 2 2 2 ##$ Uhms   : num  15 13 10 8 37 23 31 52 11 17

Now, we briefly plot the data.

# inspect data
boxplot(uhmtb$Uhms ~ uhmtb$Speaker, col = c("orange", "darkgrey"), main = "", ylab = "Number of errors", xlab = "State")

Now, we test for statistical significance.

kruskal.test(uhmtb$Speaker~uhmtb$Uhms)
##
##  Kruskal-Wallis rank sum test
##
## data:  uhmtb$Speaker by uhmtb$Uhms
## Kruskal-Wallis chi-squared = 9, df = 9, p-value = 0.4373

The Kruskal-Wallis test does not report a significant difference for the number of “uhms” produced by native speakers and learners of English in the ficticious data.

# 7 The Friedman Rank Sum Test

The Friedman rank sum test is also called a randomized block design and it is used when the correlation between a numeric dependent variable, a grouping factor and a blocking factor is tested. The Friedman rank sum test assumes that each combination of the grouping factor (Gender) and the blocking factor (Age) occur only once. Thus, imagine that the values of “Uhms” represent the means of the respective groups.

# create data
Uhms <- c(7.2, 9.1, 14.6, 13.8)
Gender <- c("Female", "Male", "Female", "Male")
Age <- c("Young", "Young", "Old", "Old")
# create table
uhmtb2 <- data.frame(Gender, Age, Uhms)
# inspect table
uhmtb2
##   Gender   Age Uhms
## 1 Female Young  7.2
## 2   Male Young  9.1
## 3 Female   Old 14.6
## 4   Male   Old 13.8
# perform Friedman test
friedman.test(Uhms ~ Age | Gender, data = uhmtb2)
##
##  Friedman rank sum test
##
## data:  Uhms and Age and Gender
## Friedman chi-squared = 2, df = 1, p-value = 0.1573

In our example, age does not affect the use of filled pauses even if we control for gender as the p-value is higher than .05.

Exercises


text:
# Glht Pairwise Comparison

LSMEANS A/ pdiff=ALL; Pairwise comparisons of factor A LSMEANS A/ pdiff lines; Pairwise comparisons of factor A, the lines option produces a compact letter display (cld). test (it uses a pooled standard deviation estimate from all groups). paircompviz: An R Package for Visualization of Multiple Pairwise Comparison Test Results Michal Burda University of Ostrava Abstract The aim of this paper is to describe an R package for visualization of the results of multiple pairwise comparison tests. pairwise-del — For every pairwise comparison, it ignores the sites with gaps. Gabriel's pairwise comparisons test also uses the Studentized maximum modulus and is generally more powerful than Hochberg's GT2 when the cell sizes are unequal. summary(glht(m, mcp(IDE="Tukey")), test=adjusted(type="holm")) # Tukey=>compare all pairs # manual post hoc Mann-Whitney U pairwise comparisons # note: wilcox. Contrasts can be used to make specific comparisons of treatments within a linear model. Mann-Whitney (MW) pairwise tests were made with the wilcox. Games-Howell. Pairwise comparison test that is sometimes liberal. First, it's important to realize that the model you have fitted is inappropriate. This handout uses data from Myers, Fundamentals of Experimental Design, 2nd Ed, p. Relative importance • Standardization for quantitative variables • Relative importance for sets of e↵ects, including categorical variables 2/95 Categorical Explanatory Variables Dumy Variables Multi-Category EV's Interaction. But it requires a fairly detailed understanding of sum of squares and typically assumes a balanced design. # ' @title A Wraper of glht to Get All Pairwise Mean Comparisons # ' @description This function performs all pairwise compararisons among # ' means returning pontual and intervalar estimates followed by # ' letters to easy discriminate values. When we have a statistically significant effect in ANOVA and an independent variable of more than two levels, we typically want to make follow-up comparisons. Because no specific methods exist for MixMod object returned by mixed_model(), we need to specify the vcov. Significant differences between treatments with respect to the control, and between C and D treatments, were tested through post-hoc pairwise comparisons using the function glht in the multcomp 51. An alternative to the Tukey HSD approach is the Scheffe method. We also fitted a linear model that included only the interaction between temperature and genotype:. Season2"Season. are pairwise comparisons that will tell us where those differences lie. * functions such as pairwise. After detecting differences in the factor levels, we are often interested in which factor levels are different from which. Simultaneous Inference in General Parametric Models - Simultaneous tests and confidence intervals for general linear hypotheses in parametric models, including linear, generalized linear, linear mixed effects, and survival models. c) Finally, I carried out pairwise comparisons between the models (R function glht). Mann-Whitney (MW) pairwise tests were made with the wilcox. Pairwise Multiple Comparison Procedures with Unequal N‘s and/orVariances: A Monte Carlo Study Journal of Educational Statistics ,Vol. All analyses were performed in program R ver-. As the name suggests. Then, the AIC-based model selection was applied to explore the best-fitting models, followed by the Tukey's all-pairwise multiple comparison test to examine the differences between species using 'glht'. model,lsm(pairwise~condition)) resulting in. Package 'multcomp' ### adjusted p-values for all-pairwise comparisons in a one-way layout In case of confint. Notice how the Interaction SS is the same in the Type I and Type III analyses. Estou realizando um exercício de parcela subdividida utilizando a função lme{nlme}. This approach works for other types of model objects, including glm and lme. Their weights in grams after six weeks are given along with feed types. 05 (Holm 1977, 1979) with the glht function in package multcomp in R. the chapter that discusses the analysis of longitudinal data where the response. To control the FDR caused by multiple post hoc comparisons, the Benjamini–Hochberg method was used (Benjamini and Hochberg, 1995). It was recommended to instead use pairwise contrast coding. Tukey’s post-hoc tests were used for pairwise site comparisons using the glht function in the multcomp R package (11). The multcomp package allows for multiple comparisons of k groups in general linear models. So I'll assume you know it already (or will learn it before you attempt this stuff). Post-hoc unplanned pairwise comparisons. As a consequence, the biodiversity associated with open woodland is declining. csv("http://statacumen. TukeyHSD- Create a set of confidence intervals on the differences between the means of the levels of a factor with the specified family-wise probability of coverage. There's too much statistics to teach in 90 minutes. Does anyone know if this is a better approach to unequal samples sizes of this magnitude, or if there is another (even better) multiple comparison method for this? If so, any tips on how to approach it in R?. Bray-Curtis dissimilarities, based on OTU relative abundance data, were visualized with principal coordinate analysis. 05 for a one-tailed test (treatment on left > treatment on right) are shaded in gray. Bray-Curtis dissimilarities, based on OTU relative abundance data, were visualized with principal coordinate analysis. Dale Barr recently had a nice blog post about coding categorical predictors, which reminded me to share my thoughts about multiple pairwise comparisons for categorical predictors in growth curve analysis. The main diﬃculty is that the comparisons one is usually interested in, for example all-pairwise diﬀerences, can’t be directly speciﬁed based on model parameters of an AN(C)OVA regression model. # ' @title A Wraper of glht to Get All Pairwise Mean Comparisons # ' @description This function performs all pairwise compararisons among # ' means returning pontual and intervalar estimates followed by # ' letters to easy discriminate values. This project aims to strengthen the statistical skills for Medical students in Vietnam. test a name of the test to use. These are called Tukey contrasts. Pairwise comparisons were made via Tukey's test (glht function in multcomp, correcting P values for multiple comparisons by the single-step method). The plot method does not accept xlab, ylab or main arguments and creates its own values for each plot. Video created by Калифорнийский университет в Сан-Диего for the course "Разработка, осуществление и анализ экспериментов". You can use glht for comparisons with a glm model object. Traditional methods for multiple comparisons adjustments focus on correcting for modest numbers of comparisons, often in an analysis of variance. Take into account all the comparisons involving cola preferences and age. …that's an example of how to apply multiple comparisons to a generalised linear mixed model using the function glmer from package lme4 & glht() from package multcomp. Case study 1: One-way ANOVA. We could perform all pairwise $$t$$-tests with the function pairwise. The table of the model coefficients then look as follows:. Unlike the Tukey HSD, the Scheffe method is not restricted to only the pairwise comparison difference, rather it applies to the set of estimates of all possible contrasts among the factor level means. Not only does sphericity create problems for the F in repeated-measures ANOVA, but also it causes some amusing complications for post hoc tests. Pairwise comparison among model coefficients (including adjustments for multiple comparisons using the Tukey method) was done using cld function in emmeans (Lenth, 2016), which adjusts for multiple comparisons via the glht function in the multcomp library (Hothorn et al. However, the term of a post-hoc test is often used for meaning Case 2 and Case 3. • For m small, is "expensive insurance. Unlike the Tukey HSD, the Scheffe method is not restricted to only the pairwise comparison difference, rather it applies to the set of estimates of all possible contrasts among the factor level means. 1 Simple between-subjects designs. An all-pairwise comparison of Tukey s test was implemented using the glht function (package multcomp [13]) to detect differences among the three environmental conditions [14,15]. There are numerous methods for making pairwise comparisons and this tutorial will demonstrate. Also, lmer() is mentioned but not glmer(). Many classical multiple comparison procedures can be embedded into this framework, including Dunnett's many-to-one comparisons and Tukey's all-pairwise comparisons. W4? Multiple Comparisons Using R. When we have a statistically significant effect in ANOVA and an independent variable of more than two levels, we typically want to make follow-up comparisons. We denote group i values by yi: > y1 = c(18. The usual method for comparing more than two means is a 1-way analysis of variance (ANOVA), the adjective "1-way" telling us that there is only one grouping variable. C) comparison. Using the Kruskal-Wallis Test, we can decide whether the population distributions are identical without assuming them to follow the normal distribution. Psych 610 Handout – R3 Colleen Moore & Mike Amato. glht objects that is required to create a compact letter display of all pair-wise comparisons. Case 4 is usually called a planned comparison test, but again it is often referred as a post-hoc test as well. paircompviz: An R Package for Visualization of Multiple Pairwise Comparison Test Results Michal Burda University of Ostrava Abstract The aim of this paper is to describe an R package for visualization of the results of multiple pairwise comparison tests. It also presents a detailed description of available software implementations in R. % Copyright (c) 2012-2016 Russell V. • If m is large, gives shorter confidence intervals than Bonferroni. Unpaired, one-tailed t-test — Use to compare two between-participants conditions where the alternative hypothesis suggests that the treatment condition causes an increase in the dependent variable: t. Pairwise comparisons indicate that LocInv is signiﬁcantly different from Base (p<1e-04) and There is signiﬁcantly different from Base (p<1e-04), but LocInv and Top are not signiﬁcantly different from each other (p=0. paircompviz: An R Package for Visualization of Multiple Pairwise Comparison Test Results Michal Burda University of Ostrava Abstract The aim of this paper is to describe an R package for visualization of the results of multiple pairwise comparison tests. After detecting differences in the factor levels, we are often interested in which factor levels are different from which. glht allows post-hoc hypothesis testing, similar to THSD, but is more suitable for general linearised (mixed) models. Does anyone know if this is a better approach to unequal samples sizes of this magnitude, or if there is another (even better) multiple comparison method for this? If so, any tips on how to approach it in R?. u1-u2 single pairwise comparison) glht, multcomp. Psych 610 Handout - R3 Colleen Moore & Mike Amato. Previous message: [R-lang] lmer multiple comparisons for interaction between continuous and categorical predictor Next message: [R-lang] False convergence in mixed logit model. The plot method does not accept xlab, ylab or main arguments and creates its own values for each plot. If you are interested all pairwise comparisons of factors you would do something like. Pairwise comparisons Kruskal-Wallis test Two way analysis of variance Example The data set chickwts is available in R, and on the course webpage. this second edition and a section on generalised linear mixed models completes. Interestingly, the normality assumption is not an issue so hopefully we will not worsen this result by using a transformation to try to address the non-constant variance issue. % Copyright (c) 2012-2016 Russell V. BIOL933 2 Lab 9 (Topic 12) Note that in this case the greater precision is afforded to the seed treatments (subplots) and the lesser to the varieties (main plots). Stats: Scheffe' and Tukey Tests When the decision from the One-Way Analysis of Variance is to reject the null hypothesis, it means that at least one of the means isn't the same as the other means. New chapters on graphical displays, >generalised additive models and simultaneous inference have been added to. • If m is large, gives shorter confidence intervals than Bonferroni. There are other ways in which the contrasts to be tested can be expressed in glht. Post hoc test in linear mixed models: how to do? (glht(YOUR MODEL, linfct=mcp(YOUR FIXED FACTOR="Tukey"))) I am interested in doing a post-hoc multiple pairwise comparison within the 4. However, this reduces the power of each of the pairwise comparisons, and only very large differences are detected (a consequence that exacerbates with an increasing number of groups). Studying interactions among co‐evolved invaders might help us in understanding, predicting, and perhaps mitigating the impact of the invading species on the native biota. An Example of ANOVA using R by EV Nordheim, MK Clayton & BS Yandell, November 11, 2003 In class we handed out ”An Example of ANOVA”. General correlation matrix structure was adopted in these analyses. Annual migratory movements can range from a few tens to thousands of kilometers, creating unique energetic requirements for each specific species and journey. The conclusion above, is supported by the Shapiro-Wilk test on the ANOVA residuals (W = 0. solorensis is influenced by the presence of red fluorescent body coloration in the fish's mirror image, rather than through a change in brightness. Pairwise correlation coefficients between LSMeans for different diseases measured in each population were significant in most of the cases. To test all three linear combinations against each other, we would use:. The solution my stats consulted suggested (which I was able to later find support for in an article in Ecological Modelling) was to first analyze all the data using a logistic regression and then do a regular glm conditional on the response being greater than 0. Multiple-Comparison Procedures for One-Way ANOVA 4 of 12 Advantages and disadvantages Since this approach does fewer comparisons than do methods designed for doing all pairwise comparisons (e. Dale Barr (@datacmdr) recently had a nice blog post about coding categorical predictors, which reminded me to share my thoughts about multiple pairwise comparisons for categorical predictors in growth curve analysis. Pairwise sequence alignment allows us to look back billions of years ago Origin of life Origin of eukaryotes insects Fungi/animal Plant/animal Earliest fossils Eukaryote/ archaea When you do a pairwise alignment of homologous human and plant proteins, you are studying sequences that last shared a. Forest grazing that created open condition. Lenth The University of Iowa [email protected] For example, in the Tukey pairwise comparison, the standard output just shows the CI for the difference. There's too much statistics to teach in 90 minutes. In case of significant factor effects, Tukey's HSD tests were implemented for post hoc pairwise comparisons using multcomp::glht (Hothorn, Bretz & Westfall 2008). test()or pairwise. @Lindsey — I was recently faced with this problem. csv") library(xtable) xtab. General Information on the multcomp Package Description. The grouping variables are also known as factors. There are other ways in which the contrasts to be tested can be expressed in glht. multiple statistical comparisons between all pizzas and on all attributes •Her solution will be the basis for a tool to be used throughout her company •Ideally, her solution will be: •Flexible enough to allow her to adjust the statistical testing without having to rewrite large portions of her code •Fast enough to handle a large number of. Tukey’s post-hoc tests were used for pairwise site comparisons using the glht function in the multcomp R package (11). If you are interested all pairwise comparisons of factors you would do something like. There are print, plot and cld methods for class "simple. Among the 24 comparisons made (three pairwise comparisons in each of eight populations), 21 were significant at a P < 0. Using the Kruskal-Wallis Test, we can decide whether the population distributions are identical without assuming them to follow the normal distribution. maindiﬃculty comparisonsone usuallyinterested exampleall-pairwise diﬀerences, can't directlyspeciﬁed based AN(C)OVAregression model. glht for mixed-effects models (lme4) with interactions. The study has 6 groups. This approach works for other types of model objects, including glm and lme. Simultaneous Inference in General Parametric Models - Simultaneous tests and confidence intervals for general linear hypotheses in parametric models, including linear, generalized linear, linear mixed effects, and survival models. [R] How to use the function "glht" of multcomp package to test interaction? [R] glht() and contrast() comparison [R] general linear hypothesis glht() to work with lme() [R] Duncan post-hoc tests in R? [R] Fwd: Re: LSD multiple comparison test [R] pairwise comparisons with multcomp package. The Scheffe method is also a single-step, multi-comparison procedure. emmeans(fit, pairwise ~ cCue:cGroup) If you were interested in comparisons among, e. Although pairwise-ranking, such as Steel procedure, and joint-ranking, such as Kruskal-Wallis test are commonly used, a robust approach against viola-tions of normal distribution and variance homogeneity should be used for the relative treatment eﬀect between control (0) and treatment i: p0i = Pr(X0 < Xi) + 1 2 Pr(X0 = Xi) = R F0dFi [14]. The effect of Wolbachia on viral titres in each host–Wolbachia association was further tested using multiple pairwise comparisons to compare the Wolbachia‐infected flies to the appropriate Wolbachia‐free control (glht function, package multcomp, Hothorn et al. glht", "summary. summary(glht(m, mcp(IDE="Tukey")), test=adjusted(type="holm")) # Tukey=>compare all pairs # manual post hoc Mann-Whitney U pairwise comparisons # note: wilcox. Tukey’s post-hoc tests were used for pairwise site comparisons using the glht function in the multcomp R package (11). C) comparison. The glht() function from the multcomp package also allows for such tests and actually makes it easy to conduct all pairwise comparisons between factor levels (with or without adjusted p-values due to multiple testing). 6 Alternative compact letter display for all pairwise comparisons in the immer example 90 4. Re: multiple comparisons for GAMs I have looked into using glht (‘multcomp’ package) to do multiple comparisons for a model fit with GAM {mgcv} but after reading the description of the ‘multcomp’ package, I believe this method only applies to parametric models and linear hypotheses. The effect of Wolbachia on viral titres in each host–Wolbachia association was further tested using multiple pairwise comparisons to compare the Wolbachia‐infected flies to the appropriate Wolbachia‐free control (glht function, package multcomp, Hothorn et al. Afterfinalizingthe fixedeffects,weobtainedmodellevelP. test, pairwise. There are other ways in which the contrasts to be tested can be expressed in glht. Elder 14 Independence of the Covariate and Treatment Effect ! In our Viagra example, it is plausible that some. [R] How to use the function "glht" of multcomp package to test interaction? [R] glht() and contrast() comparison [R] general linear hypothesis glht() to work with lme() [R] Duncan post-hoc tests in R? [R] Fwd: Re: LSD multiple comparison test [R] pairwise comparisons with multcomp package. The first enabled us to partition the sum of squares correctly. We want to conduct pairwise comparison with the effect of the pre-test factored out, however. If you compare these results to the prior 15-comparisons output, you’ll notice that the p-values drop because you aren’t penalized for those 12 other comparisons. Post-Hoc Tests in One-Way Between Group Designs University of Wisconsin - Madison. Now we must conduct pairwise comparisons with Bonferroni corrections. Using the Kruskal-Wallis Test, we can decide whether the population distributions are identical without assuming them to follow the normal distribution. Model residuals were checked for heterogeneity of variances and normality by visual assessment of diagnostic plots. The plot method does not accept xlab, ylab or main arguments and creates its own values for each plot. Planned comparisons and pairwise post-hoc tests. us and MCP is a command for multiple comparisons. Dunnett's T3. hoc pairwise comparisons of significance was carried out for one-way ANOVA using the glht function of the R Multcom package. Following this theoretical framework, the book explores applications involving the Dunnett test, Tukey's all pairwise comparisons, and general multiple contrast tests for standard regression models, mixed-effects models, and parametric survival models. I'm analysing my binomial dataset with R using a generalized linear mixed model (glmer, lme4-package). Multiple Comparisons – p. The figure shows the multiple comparison of the means. # ———————————————————————————— # Tukey HSD 法による多重比較（Rcmdrでのまちがった計算. Tukey multiple comparisons for parametric models were used to address post hoc comparisons using the multtest R package and the glht function (Hand and Taylor, 1987; Dickhaus, 2012). Unlike the Tukey HSD, the Scheffe method is not restricted to only the pairwise comparison difference, rather it applies to the set of estimates of all possible contrasts among the factor level means. [email protected] Afterfinalizingthe fixedeffects,weobtainedmodellevelP. differences among models to a Chi-square distribution [12]. 1 Simple between-subjects designs. Extract information from glht, summary. pairwise comparisons for population differences with 0. Often we are interested in comparing the mean of level $$i$$ with the mean of level $$j$$. Simultaneous Inference in General Parametric Models - Simultaneous tests and confidence intervals for general linear hypotheses in parametric models, including linear, generalized linear, linear mixed effects, and survival models. Notice how the Interaction SS is the same in the Type I and Type III analyses. Bioinformatics, btz536. The multcomp package allows for multiple comparisons of k groups in general linear models. 0013 - # schizo 0. 05 for a one-tailed test (treatment on left > treatment on right) are shaded in gray. As there is also a comparison between gender, this involves 22 different comparisons. We uncover the. No more than (p-1, where p is the number of. Sorry and thanks in advance I suspect it-----Mario Garrido Escudero PhD student. The default is to have no adjustment and simply perform a Tukey LSD post hoc test (this is not recommended). Foreword: The Elementary Statistics for Medical Students (ESMS) project. Planned comparisons are specific comparisons that are usually planned during the design stage of the experiment. You requested this test in Rcmdr when you checked "Pairwise comparison of the means" >. This means there are a total of six pairwise comparisons we want to look at with a post hoc test:. It was recommended to instead use pairwise contrast coding. Suppose we tested this belief by taking three. glht", "summary. Even within the same species, migration costs can vary largely because of flexible, opportunistic life history strategies. But it requires a fairly detailed understanding of sum of squares and typically assumes a balanced design. If you examine your data for the linear combination that gives the smallest p-value, Scheﬀe would be the appropriate. An object of classes "simple. Dunnett's T3. There are a total of $$g \cdot (g - 1) / 2$$ pairs that we can inspect. ##### Example: Itching ##### itch - read. You requested this test in Rcmdr when you checked "Pairwise comparison of the means" >. We denote group i values by yi: > y1 = c(18. and conducted posthoc pairwise comparisons between genera using the glht Posthoc pairwise comparisons of. As there are six colas and 21 comparisons within each this results in 126 comparisons. simulations. Extract information from glht, summary. HEIGHT as [Response Variable] and check the box beside appropriate pairwise comparison methods (Bonfer-roni, Holm or Tukey), then click [OK]. MultipleComparison Procedures Multiple comparisons means,i. and conducted posthoc pairwise comparisons between genera using the glht Posthoc pairwise comparisons of. No more than (p-1, where p is the number of. Unpaired, one-tailed t-test — Use to compare two between-participants conditions where the alternative hypothesis suggests that the treatment condition causes an increase in the dependent variable: t. However, the term of a post-hoc test is often used for meaning Case 2 and Case 3. The mean of each group being compared is obscured. Often we are interested in comparing the mean of level $$i$$ with the mean of level $$j$$. Also, lmer() is mentioned but not glmer(). General Information on the multcomp Package Description. Coefficients indicate relative increase or decrease of the expected log of fire frequency for categorical change in relation to. , cCue within each cGroup you'd do. Then, tw o GLM models for the Poisson-distributed response. The figure shows the multiple comparison of the means. One Way Analysis of Variance (ANOVA) Example: Researchers wish to see if there is difference in average BMI among three. 05 for a one-tailed test (treatment on left > treatment on right) are shaded in gray. As we have found evidence for difference among the means, we inspect the result of pairwise comparisions, i. hoc pairwise comparisons of significance was carried out for one-way ANOVA using the glht function of the R Multcom package. followed by post-hoc pairwise comparisons if omnibus test permits Mixed Effects Models Types of models that can handle both within-subjects and between-subjects factors. expression and group # # control bipolar # bipolar 0. @Lindsey — I was recently faced with this problem. For Dunnett's procedure, the differences γj − γ1 are tested for all j = 2,. 3267 # # P value adjustment method: fdr 44/50 Other Methods Use Critical Values I Tukey's Honestly Signiﬁcant Diﬀerence I Dunnet's Test for Comparison to Controls I Ryan's Q (sliding range) I. A collection of data samples are independent if they come from unrelated populations and the samples do not affect each other. paircompviz: An R Package for Visualization of Multiple Pairwise Comparison Test Results Michal Burda University of Ostrava Abstract The aim of this paper is to describe an R package for visualization of the results of multiple pairwise comparison tests. Contrasts can be used to make specific comparisons of treatments within a linear model. pairwise comparisons for population differences with 0. rate~sex ylabel<-"growthrate" xlabel<-"sex" Clone. edu/~zhaozhg/Stat8113/data/insulgas. … and now the Bonferroni method in action: ## Bonferroni method. Dale Barr recently had a nice blog post about coding categorical predictors, which reminded me to share my thoughts about multiple pairwise comparisons for categorical predictors in growth curve analysis. test(), pairwise. We use the unifying representations of multiple contrast tests, which include all common multiple comparison procedures, such as the many-to-one comparisons of Dunnett, the all-pairwise comparisons of Tukey and many other procedures. # Pairwise comparisons using t tests with pooled SD # # data: PLP1. Results We detected 63 B. 0013 - # schizo 0. Lenth % % % \documentclass[11pt]{article} \usepackage[margin=1in]{geometry} \usepackage{mathpazo} \usepackage{hyperref. 2, 1976, pp. in which the p-values are multiplied by the number of comparisons. this second edition and a section on generalised linear mixed models completes. • Does not matter how many comparisons are made, so suitable for data snooping. ##### Example: Itching ##### itch - read. Is this typical, and can anyone provide information on this? This seems rather like something to do post hoc?. Also, lmer() is mentioned but not glmer(). Here, the definition of treatment differences (such as Tukey's all-pair comparisons or Dunnett's comparison with a control) might be problem specific. Unlike the Tukey HSD, the Scheffe method is not restricted to only the pairwise comparison difference, rather it applies to the set of estimates of all possible contrasts among the factor level means. Post hoc pairwise comparisons between predicted body mass (log) for different habitat types within roost type (RT). ##### ### Set overall options (hidden) ##### options(show. One Way Analysis of Variance (ANOVA) Example: Researchers wish to see if there is difference in average BMI among three. Even within the same species, migration costs can vary largely because of flexible, opportunistic life history strategies. • For m small, is "expensive insurance. Pairwise structure comparison - compares one query structure against those specified by the user All against all structure comparison - returns a structural similarity dendrogram for a set of structures specified by the user Citation: Holm L (2019) Benchmarking fold detection by DaliLite v. Heiberger Date: Mon 02 Apr 2007 - 02:40:01 GMT > I would like to obtain for each factor of my anova model the > "response variable vs factor" plot with means and 95% Tukey HSD. Foreword: The Elementary Statistics for Medical Students (ESMS) project. glht or confint. emmeans(fit, pairwise ~ cCue|cGroup). TukeyHSD- Create a set of confidence intervals on the differences between the means of the levels of a factor with the specified family-wise probability of coverage. We will demonstrate the how to conduct pairwise comparisons in R and the different options for adjusting the p-values of these comparisons given the number of tests conducted. • For m small, is "expensive insurance. There are three groups with seven observations per group. " Since Minitab does not give the Scheffe method, we will not use it in this class. Now we must conduct pairwise comparisons with Bonferroni corrections. emmeans(fit, pairwise ~ cCue|cGroup). com/teach/ADA2/ADA2_notes_Ch05_itch. Alternatively, we could just apply different. Pairwise correlation coefficients between LSMeans for different diseases measured in each population were significant in most of the cases. In this wiki, I use a post-hoc test to mean all of these four tests. All analyses were conducted in R v. Lenth The University of Iowa [email protected] Tukey pairwise comparison tests between anthromes groups (applied to the negative binomial model Table 3) highlight that six and seven pairwise comparisons are significantly different at 5% and 10% level respectively. 3267 # # P value adjustment method: fdr 44/50 Other Methods Use Critical Values I Tukey’s Honestly Signiﬁcant Diﬀerence I Dunnet’s Test for Comparison to Controls I Ryan’s Q (sliding range) I. …that's an example of how to apply multiple comparisons to a generalised linear mixed model using the function glmer from package lme4 & glht() from package multcomp. This test is appropriate when the variances are unequal. General Information on the multcomp Package Description. Dunnett's pairwise multiple comparison t test compares a set of treatments against a single control mean. I am trying to carry out automated pairwise comparisons (non-parametric). ANOVA is fairly robust to violations of the normality assumption, and thus it typically requires a rather severe violation before remedial measures are warranted. For all other models, results rely on the normal. This is because the A*B interaction was included as the last term in the model, so the SS assigned to it was whatever was left after the main effects of A and B were accounted for. • Presenting and testing pairwise comparisons 2. To test all three linear combinations against each other, we would use:. I'm trying to understanding the way this command made pairwise comparisons, but, where does this z-value comes from? I'm suspected this not come from Tukey's test, but i don't know it's Wald or something i've never use I know it is not an habitual doubt. Not only does sphericity create problems for the F in repeated-measures ANOVA, but also it causes some amusing complications for post hoc tests. However, this reduces the power of each of the pairwise comparisons, and only very large differences are detected (a consequence that exacerbates with an increasing number of groups). Case study 1: One-way ANOVA. , regression coeﬃcients AN(C)OVAmodels, specialcase generalframework sketched previoussec- tion. Because the comparison intervals for the other two groups do not intersect with the intervals for the group 1 mean, they are highlighted in red. New chapters on graphical displays, >generalised additive models and simultaneous inference have been added to. In case the contrast. test(mydata_scales~mydata_conditions, alternative="less", paired =. Tukey Method for All Pairwise Comparisons. Now it is deprecated and when I. a) First I reduced the number of variables by Principal Components Analysis (R function prcomp). As we have found evidence for difference among the means, we inspect the result of pairwise comparisions, i. Alternatively, we could just apply different. Post-Hoc Tests in One-Way Between Group Designs University of Wisconsin - Madison. There are two main advantages of this approach over one factor analyses:. TukeyHSD- Create a set of confidence intervals on the differences between the means of the levels of a factor with the specified family-wise probability of coverage. For this, use the. A different set of techniques have been developed for "large-scale multiple testing", in which thousands or even greater numbers of tests are performed. Pairwise comparison among model coefficients (including adjustments for multiple comparisons using the Tukey method) was done using cld function in emmeans (Lenth, 2016), which adjusts for multiple comparisons via the glht function in the multcomp library (Hothorn et al. Pairwise Comparisons. Post hoc test in linear mixed models: how to do? (glht(YOUR MODEL, linfct=mcp(YOUR FIXED FACTOR="Tukey"))) I am interested in doing a post-hoc multiple pairwise comparison within the 4. " Since Minitab does not give the Scheffe method, we will not use it in this class. There are a total of $$g \cdot (g - 1) / 2$$ pairs that we can inspect. Gabriel's test may become liberal when the cell sizes vary greatly. (Department of International Health) June 30, 2012 1 Testing the difference of locations among 3 or more groups The Analysis of Variance (ANOVA) has already been done by the homework from 26 May to 9 June, for the parallel group comparison design. To test all three linear combinations against each other, we would use:. On Mon, Jan 17, 2011 at 5:46 PM, Marina Sherkina-Lieber < marina. csv("http://statacumen. The only difference between the confidence limits for simultaneous comparisons and those for a single comparison is the multiple of the estimated standard deviation. Elder 14 Independence of the Covariate and Treatment Effect ! In our Viagra example, it is plausible that some. the chapter that discusses the analysis of longitudinal data where the response. rate~sex ylabel<-"growthrate" xlabel<-"sex" Clone. • Presenting and testing pairwise comparisons 2. in which the p-values are multiplied by the number of comparisons. Post-Hoc Tests in One-Way Between Group Designs University of Wisconsin - Madison. Psych 610 Handout – R3 Colleen Moore & Mike Amato. After the result of ANOVA, the results of multiple comparisons will appear in the Output Window. ##### ### Set overall options (hidden) ##### options(show. A pan-neotropical analysis of hunting preferences. The first enabled us to partition the sum of squares correctly. Evidence-based Health Care I (10) ANOVA and multiple comparison Minato Nakazawa, Ph. use it like that glht If you wanted to calculate the pairwise comparisons between rank using Tukey's HSD,. Season2"Season. Unlike the Tukey HSD, the Scheffe method is not restricted to only the pairwise comparison difference, rather it applies to the set of estimates of all possible contrasts among the factor level means. For all other models, results rely on the normal.


text:
Solve the following system of inequalities graphically: 3x + 2y ≤ 150, x + 4y ≤ 80, x ≤ 15, y ≥ 0, x ≥ 0

Asked by Abhisek | 1 year ago |  113

##### Solution :-

Given, 3x + 2y ≤ 150

Putting value of x = 0 and y = 0 in equation one by one, we get value of

y = 75 and x = 50

The required points are (0, 75) and (50, 0)

Checking for the origin (0, 0)

0 ≤ 150, this is true

Hence the solution area for the line would be on the left side of the lines graph which would be including the origin too.

We have x + 4y ≤ 80,

Putting value of x = 0 and y = 0 in equation one by one, we get value of

y = 20 and x = 80

The required points are (0, 20) and (80, 0)

Checking for the origin (0, 0)

0 ≤ 80, this is also true so the origin lies in the solution area.

The required solution area would be toward the left of the lines graph.

Given x ≤ 15,

For all the values of y, x would be same

Checking for the origin (0, 0)

0 ≤ 15, this is true so the origin would be included in the solution area. The required solution area would be towards the left of the lines graph.

Consider y ≥ 0, x ≥ 0

Since x and y are greater than 0, the solution would lie in the 1st quadrant.

The shaded area in the graph satisfies all the given inequalities and hence is the solution area for given inequalities.

Answered by Pragya Singh | 1 year ago

### Related Questions

#### Solve each of the following in equations and represent the solution set on the number line

Solve each of the following in equations and represent the solution set on the number line $$\dfrac{5x}{4}-\dfrac{4x-1}{3}>1,$$ where x ϵ R.

#### Solve each of the following in equations and represent the solution set on the number line.

Solve each of the following in equations and represent the solution set on the number line.$$\dfrac{5x-8}{3}\geq \dfrac{4x-7}{2}$$, where x ϵ R.

#### Solve each of the following in equations and represent the solution set on the number line. 3 – 2x ≥ 4x – 9,

Solve each of the following in equations and represent the solution set on the number line. 3 – 2x ≥ 4x – 9, where x ϵ R.

#### Solve each of the following in equations and represent the solution set on the number line. 3x – 4 > x + 6

Solve each of the following in equations and represent the solution set on the number line. 3x – 4 > x + 6, where x ϵ R.