A test (typically of distribution, independence, or goodness of fit) or a family of distributions related to such a test.

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Why is the Fisher exact test not always used in the cases where a chi squared is appropriate?

According to Wikipedia: Although in practice [Fisher's exact test] is employed when sample sizes are small, it is valid for all sample sizes. If Fisher's exact test can provide the exact ...
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6 views

Significance of the distribution of DNA sequences given a certain nucleotide bias

I have a large sequence of DNA in which every position can have 4 different states, or nucleotides (A,T, G or C). The distribution of the nucleotides in the sequence is non-random and, most ...
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19 views

Which Non-parametric test to use with two Ordinal sets of data

I am trying to find which factors in Ques 6 are strongly related to company being rated high as compared to others in Ques 4 and similarly factors related to company being rated low.
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19 views

Probability of Event from a Chi-Square Table

I have the following table: From here I want to answer the following question: P(CHILD CAN RECOG BEG SOUNDS OF WORDS – YES | CHILD RECOGNIZES LETTERS - Most of them). From my understanding of ...
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48 views

What happens to a $\chi^2_n / n$ random variable as $n \to \infty$?

I have read that $\chi_n^2 / n \to 1$ as $n \to \infty$. Is this true? If so how could I go about proving it?
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16 views

Signs on logistic regression betas flip relative to observed - expected counts from chi-squared test

I conduct a chi-squared analysis on some bins and conclude that an association between the bins and an event exists. I then calculate logistic regression coefficients to validate my hypothesis. Also, ...
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15 views

test for variance by using chi square test in R

how can i know if these data -> 93, 91, 93, 150, 80, 104, 128, 83, 88, 95, 94, 97 58, 139, 91 provide evidence that the pop variance is greater than 0.05 (a=0.05) by chi square test in R? please ...
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22 views

What is wrong with this chi squared test of independence?

I'm trying to learn how to run the chi squared test of independence. I've created two fictional variables, Variable 1 and Variable 2, and I want to know if they are correlated. I'm working with the ...
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12 views

How to integrate observational errors in goodness of fit tests?

I have an astrophysical non-linear curve, specifically a power spectrum. I need to fit this curve with a model and obtain the goodness-of-fit (GOF). This gives me expected and observed values. The ...
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1answer
54 views

Choosing between chi-squared / logistic regression vs difference of mean tests for studying bankruptices

You'd expect more companies to go bankrupt if they have low cash balances. Of course, bankruptcies can also happen even when you have lot of cash on hand (to terminate labor contracts, etc.). The ...
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2answers
47 views

Absolute (i.e., not just relative) probabilities in chi-squared test for proportions

Why do the absolute probabilities affect the p-value of a chi-square test so much? For example: ...
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1answer
118 views

Manually calculated chi-squared statistic differs from that given by chisq.test in R

I'm using R to do a chi-squared test on two sets of data to check if they follow a distribution. In the first case the chi-squared statistic given by chisq.test ...
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102 views

Which test is better suited to compare averaged versus single data sets

I have a light curve, that is photon count rate versus time, of an astronomical object. These data are periodic, since the source signal is periodic. I can fold the data with the period and obtain an ...
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3answers
61 views

What to do when I have expected count <5 warning for a chi squared test?

I applied a survey consisting of 12 questions to 120 people and each questions include 4 nominal categories; I want to make comparison of people's answers according to their socio-demographic ...
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1answer
24 views

Correlation for grouped data

I have a dataset composed by 200.000 projects. Each project is defined according to its size and the presence of active users (1 if the project has active users, 0 otherwise). I've ordered the ...
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2answers
44 views

Test the randomness (uniformly distributed) on a 64 bit float random generator

We have a random number generator which is supposed to generate 64 bit floats, uniformly. We want to test whether it is a good uniformly random. I am not asking the general way to test it, as it was ...
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5 views

Chi goodness and Fishers: some theoretical issues post-experiment

I have run a simple experiment under four conditions: the Control, Technique A, Technique B, and Technique C (which is a+b) The dependent variable is compliance (e.g. Yes/No) These are my results ...
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1answer
34 views

Can I use the chi-squared test of independence with skewed data?

I have two variables, both categorical, one with skewed responses. How do you deal with skewed data in the chi-squared test? Are there any other relevant tests? I want to perform the test in SPSS.
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1answer
31 views

Chi-square test to see if set of dependent correlations are equal

I've got four dependent correlations (i.e., from the same sample) that involve predictor variables $(A,B,C,D)$ and an outcome variable $(E)$. $N=172$. $$\begin{array}{c|cccc}{\rm ...
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92 views

How to use the chi-squared test to determine if data follow the Poisson distribution

The figure below (Figure 1 from p. 646 of this paper) compares observed values against expected values under the Poisson distribution. It then runs a chi-squared test to see if the observed values ...
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28 views

Algorithm for scoring co-varying traits

I am sure this has been done, but I can't find quite the right approach. EDIT: Trying to explain better. The rows of colored boxes below are columns of molecular sequence data -- positions in a ...
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1answer
50 views

Are binomial and McNemar's tests right for my data?

I have performed an experiment, where I have real and synthesised movie data. My participants were shown either a real movie, or a synthesised movie (of talking heads), in a random order, and had to ...
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36 views

Is the Pearson goodness-of-fit test parametric or non-parametric?

In this question there was an interesting discussion concerning the Pearson goodness-of-fit test going on which was far from conclusive: Is there any statistical test that is parametric and ...
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87 views

Chi-square test: difference between goodness-of-fit test and test of independence

Concerning the Pearson chi-square test there seems to be a subtle difference between the goodness-of-fit test and the test of independence. What is confusing is that both tests seem to be calculated ...
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20 views

Chi-square and repeated measure

I have a survey of 20 questions; answers are given on the 5-point Likert scale. Goal: to understand whether the answer on the first question affects answers on other questions. Normally speaking I ...
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22 views

Hypothesis testing for cost-per-click metrics

I have two ads, and I want to figure out which is better. If they both have identical cost, my null hypothesis is that the probability of success in the first is equal to the second, and I can use ...
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19 views

Chi-square in ANOVA

I am comparing models that I created with the lmer function from the lme4 package using ANOVA. Paricipants and verbs are my random factors, and RT are the Reaction Times that I measured. From the ...
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51 views

Fisher's exact test or chi-square test

I have a 2x4 table with nominal data (the columns are simply YES/NO, the rows are four categories) ...
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48 views

Distribution of the convolution of squared normal and chi-squared variables?

the following problem came up recently while analyzing data. If the random variable X follows a normal distribution and Y follows a $\chi^2_n$ distribution (with n dof), how is $Z = X^2 + Y^2$ ...
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48 views

How to derive this as a $\chi^{2}$ distribution?

From Berger&Casella, Chapter 8, Problem 8.5, page 402 for 2nd edition. The problem is: A random sample, $X_{i}$ is drawn from a Pareto population with pdf $$ f(x|\theta,v)=\frac{\theta ...
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1answer
23 views

Validity of an iteration for Goodness of fit to a specific application

I am not a statistics expert and would like to check the validity of a test I hav used on a survey results. Survey Results I asked people (n=264) to characterize a panoramic road they chose in 24 ...
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25 views

Significance test for multiclass classifier

In a multiclass classification problem, I want to measure the significance of my classifier against the null hypothesis (in this case, chance level). In this paper, in section 3.4, for a binary ...
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1answer
47 views

Whether to chi squared or not to

I have an extremely large data set, but I'll simplify it down as, although I think I should use a chi squared test, I've run into difficulties applying it: Let's say I have a list of 20 different ...
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How to deal with 0 values on the diagonals for a chi-squared test [closed]

I am performing a chi-squared test in which differently oriented lines cross-cut each other. Because you cannot have two similarly-oriented lines cross-cutting each other, the diagonals on both my ...
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36 views

Name of this simple descriptive method for showing crosstable combination typicalities?

This might be a basic question, but I have no clue what this descriptive method could be named. Simplified, I have a cross-table with Occupations (e.g., doctor, lawyer, engineer) as rows, and Hobbies ...
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1answer
45 views

Compared results of 2 goodness-of-fit chi-square test

I am conducting Goodness-of-fit test on 2 cities using chi square. ...
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30 views

Compare Frequencies

I have a continuous predictor variable that I have divided into bins (at 0%, 0 to 25%, ...). For each of these bins, I have shown you the histogram below of Number of Companies that are in that range ...
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60 views

Test for difference between 2 empirical discrete distributions

I have test data where I have several large samples from discrete distributions which I am using as empirical distributions. I am wanting to test whether the distributions are actually different and ...
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1answer
83 views

$\chi^2$ test of significance vs. goodness of fit

I have 644 companies out of which 154 went bankrupt. I investigate below if the bankruptcy is related to the sector type: ...
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103 views

Distribution of the ratio of dependent chi-square random variables

Assume that $ X = X_1 + X_2,...+ X_n $, where $\; X_i \sim N(0,\sigma^2)$ and independent. My question is, what distribution $$ Z = \frac{X^2}{X_1^2 + X_2^2 + ... + X_n^2} \;\;\; (1)$$ follows. I ...
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35 views

LLR with Positive and Negative Values vs. Dunning method with Entropy-based Calculation

Ted Dunning has a blog post about calculating G2 (aka LLR) using Entropy calculations as components. I found this really intriguing. Ted's original post: ...
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19 views

Very different group sizes - categorical variable

I would like to test for a difference between 3 groups for a binomial variable. There are around 400 in one group, 900 in the other group and 100,000 in the third group. I am wondering if this huge ...
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1answer
32 views

Evaluate improvement in questionnaire questions

I asked two different groups of subjects to answer a questionnaire of 2 yes/no questions. The "correct" way of answering the questionnaire was to answer yes to both questions. I want to prove or ...
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39 views

Chi-square / Fisher test variable independence for an individual

I have a data set of $\approx$100 individuals showing pulse rate before exercise, pulse rate after exercise, sex, smoker status, weight etc. for each individual. I've been asked to select an ...
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10 views

3-way measure of association, nominal variables

Cramer's V does a great job of capturing the degree of association between two nominal variables. What measure is best suited for capturing a similar association between three nominal variables?
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69 views

Analysing a multiple choice question

I asked my questionnaire's respondents whether they are aware of a particular subject and provided them with a list of four statements to choose from. I need to analyse whether their awareness differs ...
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31 views

Chi Square Goodness of Fit vs. Igloo

I am very new to Chi square goodness of fit tests but have done a fair bit of research. Basically, I have the following 12 data points: 7392, 7656, 7241, 6164, 4984, 4664, 15262, 17053, ...
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33 views

Frequency Distribution Test Vs. Chi Square Goodness of FIt

I need to prove that the higher frequency of an occurrence within a particular range is statistically significant. Let me explain this with an example: X-axis has ages and Y-axis has the ...