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

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What is the approach for analyzing split tests (as in AB test) with more than two variations?

Is there a framework for this? First for how to determine required sample sizes, but then how to evaluate outcome (multiple comparisons between variations etc)?
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1answer
29 views

How to interpret p values obtained with $\chi^2$-test?

I have the following observed and expected values and I am trying to determine the goodness of fit with $\chi^2$ test. On calculating the p I obtain the value 0.9999742, but how is it possible that ...
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1answer
43 views

chi squared with proportions

We want to know whether there are any differences in the location of mole hills that occur in two fields. We have been looking at the distance from a fence that mole hills occur. We have separated ...
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32 views

Using F-test for (generalised) linear models

I am working with regression on a data set and I am looking for a way to compare the results. From the data ($x$) and observed values ($y$) where $y\in[0, 1]$, I have three models: 1 (baseline): ...
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18 views

Calculate the non centrality parameter (ncp) for non central chi squared distribution

I have the 0.975-quantile value (0.191) and the degree of freedom (k=1). How can i calculate the non centrality parameter ? in R if possible. Q0.975(k=1, ncp= ??) = 0.191
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37 views

Silly question about proportion test [duplicate]

I am stuck with understanding of simple chi-squared test on proportion. We have $$\sum \frac{(Observed_i - Expected_i)^2}{Expected_i}$$ and say that it follows chi squared distribution (sum of ...
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2answers
30 views

Why is the probability of my chi square statistic equal to 0

Binary logistic regression in R I have derived the chi square statistic and degrees of freedom for my model (200.7839, 8, respectively) however, when I attempt to determine the probability associated ...
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1answer
21 views

ANOVA - why are the mean squares chi-squared distributed?

I recently came across Analysis of Variance (ANOVA), and it seems that the total sum of squares of the residuals (or "within groups / treatments") divided by the degrees of freedom is Chi-squared ...
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16 views

Dealing with sampling zeros

I would like to perform a $\chi^2$-test, but due to low sample size in some cases, I have sampling zeros. One example of such a case: ...
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1answer
56 views

Is chi square test too strict?

Below is the histogram and the model distribution which goodness-of fit that I want to test Judging by the eye, I would say this is a pretty good fit. However, when I run the ...
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10 views

Chi squared test on multiple survey responses?

I have completed a questionnaire using a variety of categories (i.e. some questions are yes/no, some are a different categories etc.). I want to find out whether there is a relationship between age ...
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11 views

SAS Wald Chi square test to test regression parameters large sample size

I have a logistic regression model built on sample1 proc logistic data = sample1; model outcome= x ; run; I want to test whether the coefficient for x estimated from sample 2 equals the ...
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75 views

Can I relax the independence assumption for a Chi-Squared test on observational email data?

I'm trying to determine if there is a difference in response rates between email subject lines with the purpose of generating sound hypotheses for A/B testing email campaigns. The data I'm using is ...
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14 views

Chi squared null-hypothesis test. Long tail

I have the following data. ...
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1answer
37 views

Linear Algebra take on Chi-Squared

If I have a system where my output is the sum of my input and white gaussian noise: $Y=x+w$ and $w$~$N(0,\sigma^2I)$ now, I want to determine the distribution for $||y/\sigma||^2 = y^Ty/\sigma^2$ ...
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19 views

When shall I use multiple comparison adjustment if I perform a series of Chi-square?

I am presenting some descriptive statistics about % of access to a service in different regions (12) of a country in my bar graph over two time period points. As the results are based on 12 2X2 tables ...
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113 views

Pooled Variance for Dependent $t$-test statistic?

I'm looking into finding a way to calculate Cohen's $d$ for correlated samples. Assuming pooled variances, we end up getting $$\text{SE}\left( \Delta \text{ of means}\right) = ...
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23 views

Calculate Confidence (Error) Bands for Chi Square fit with errors using Iminuit

I want to fit some data with errors to a polynomial, say $y(x)=a+bx$. I made a $\chi^2$-fit using Iminuit but now I want to calculate the error bands ( 68,3% Confidence Bands). What is the fastest way ...
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2answers
61 views

What is the appropriate statistical test when calculating the busiest day of the week?

We have 10 years of data and Monday is the busiest (most visits to the hospital) on average. If we wanted to assess whether that is true and report a p-value, what is the appropriate statistic? We ...
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35 views

SD probability problem involving chi-square distribution

Preparing for an exam in statistics, I have been pondering the following problem: Given that in country X 14 % of people hold a university degree, find the probability that for random sample of size ...
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1answer
63 views

Why does chi square test seem to depend on sample size?

This question relates to my ENT anti-answer in another forum, but is based on a statistical perspective. Traditionally, the chi test does not depend on how many samples you take, so it should be as ...
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21 views

P values and calculating residuals in chi-squared contingency tables

Given an n x m contingency table I calculate a chi-squared value and probability for that table telling me if there are cells that differ significantly from the mean. I go to calculate the adjusted ...
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1answer
12 views

converting a chi-square with more than one degree of freedom into a pearsons r

I want to run a power analysis for a study using correlations between two continuous variables. Previous research with the variable I am interested in used a Kruskal-Wallis test to look at differences ...
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6 views

How do I manually calculate post-hoc tests of independence between all cells using output from SPSS complex systems module?

I'm trying to run post-hoc tests of independence between all cells using a data set that I need to run the complex samples module in SPSS. How do I use this output that includes population proportion ...
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1answer
145 views

Two Sample chi squared test

This question is from Van der Vaart's book Asymptotic Statistics, pg. 253. #3: Suppose that $\mathbf{X}_m$ and $\mathbf{Y}_n$ are independent multinomial vectors with parameters $(m,a_1,\ldots,a_k)$ ...
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11 views

Alternative to Pearson's Chi Squared for Speech Synthesis Preference Listening tests

I have a simple Preference Listing test: 24 Participants, 10 preference questions each. each participant answers 10 times (once for each of my 10 stimuli pairs). This means 240 data points overall. ...
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18 views

Comparison between two conditions

I want to compare the effects of a treatment with placebo. The values are the number of subjects that reach a particular level of pain threshold. Since the values in before and after are dependent ...
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1answer
93 views

How is MSE divided by $\sigma^2$ always a chi-square distribution?

If I have the expression below, how can I use y~N($\mu$, $\Sigma$) to show it is a $\chi^2$ distribution with ($_n-1$) degrees of freedom? ($n$-1)($s^2$)/$\sigma^2$ how is this ~$\chi^2$ $_n$-$_1$? ...
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18 views

Defining the size of control group in chi square statistics

I'm trying to compare the prevalence rate of autism in offspring of mothers with and without gestational diabetes. I gathered data from 1000 women, 8 children have autism (prevalence rate 8/1000). ...
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1answer
20 views

Measuring statistical significance for NYC restaurant inspection grades

I recently had a timed interview question on the following data set: https://data.cityofnewyork.us/Health/DOHMH-New-York_City-Restaurant-Inspection-Results/xx67-kt59/about The question was: is there a ...
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9 views

Approach for determining winner in A/B test with more than 2 version?

I've heard people take the top performing variation (say there are 4 variations total), and then do either a t-test or a chi-square test against each of the other versions. My issue with this is ...
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63 views

To perform chi sq test correctly

In R I have 2 groups: data1 and data2 that contains the first game a user has played. There are 16 games named 1,2...,16. ...
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17 views

Showing DF Times S-squared / sigma-squared is a chi-square [duplicate]

I am a beginning grad student (distance student, so nobody to ask in person), learning about distributions. I am trying to prove that $(n-1)s^2$ divided by $\sigma^2$ produces a non-central $\chi^2$ ...
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12 views

How to calculate Wald Chi-squared test for contingency table

I am trying to understand the documentation from SAS concerning the Wald Chi-squared test for contingency tables via the surveyfreq procedure. Specifically, I am ...
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27 views

How to report odd sample sizes for the chi-squared test in a paper?

I am testing a 2x2 set of data with chi-squared (expected values are all above 5, so I'm not using Fisher's exact test). The there are two things being compared here. One has sample size 160, and one ...
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14 views

Chi-squared test of independence for biased data

I'm working with a survey dataset consisting of 28807 observations (8470 males and 20337 females). I'm trying to determine the association between dichotomous variables, for instance, sex (Male, ...
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1answer
21 views

Interpretation of post hoc chi square test results

I have a $2\times 3$ table cross-tabulation. I've done a post-hoc test using SPSS but I don't know how to interpret the results. This is the output:
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20 views

Chi-Square value in Kruskal Wallis test very large

I am comparing measurements of 12 different groups to one another. My distributions are not normal and my Levene's test is significant - even after data transformation. I am therefore doing a ...
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79 views

chi-squared goodness-of-fit: effect size and power

How can effect size and power of the chi-square goodness-of-fit test be calculated such that: Effect size is linear and standardized (given effect size $E_{x^2}$, $0 \le E_{x^2} \le 1$) so that ...
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1answer
23 views

Why is the noncentral chi-squared approximate of the deviance bad?

The statistical model under consideration is given by the independent realizations of two independent binomial distributions: $$ x_1 \sim \mathrm{Bin}(n_1, p_1), \quad x_2 \sim \mathrm{Bin}(n_2,p_2), ...
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26 views

Goodness of fit test for bivariate distribution?

I have a dataset which is x-y distributed, and I fitted a model for it. (see below, left and right) How can I test the goodness of fit for the model I fitted? ...
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21 views

Metric invariance: CFI difference test and Chi square difference test. What happens when contradictory results are found?

I have been examining a sample (n > 600) for metric invariance, using AMOS. Using the Comparative Fit Index (CFI) difference test, which seems to be free of sample size influence, I get evidence of ...
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1answer
23 views

Statistical reporting of chi-square and odds ratio

I'm looking to see if the process and reporting are correct. (This isn't homework help. I am playing around with a secondary data set trying to learn more about the research process and statistical ...
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1answer
62 views

Distribution of a quadratic form, non-central chi-squared distribution

Definition. Suppose $\mathbf{y} \sim \mathcal{N}(\boldsymbol{\mu}, I_{n \times n})$. Then $$w = \mathbf{y}^{T}\mathbf{y} = \|\mathbf{y}\|^2 \sim \chi^{2}_{n}\left(\theta = ...
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2answers
32 views

Ljung Box test chi square distribution

I want to prove the following statement: Under $H_{0}$ the test statistic $Q=n(n+2)$ $\sum \limits_{k=1}^h \frac{\hat{p}_{k}^2}{n-k}$ follows a $\chi ^2(h)$ chi-squared distribution with $h$ degrees ...
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1answer
72 views

chi-squared with too many degrees of freedom

I have a third party random number generator with a period approximately greater than $63*(2^{63} - 1)$ which generates numbers in the range $[0,2^{32}-1]$, ie $2^{32}$ different numbers. I've made ...
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1answer
67 views

Detect outliers (anomalies) in salary data

I have a dataset with over 10,000 employees and I'm interested in performing some tests to identify salary anomalies. For example, paychecks for some employees might look like this: ...
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21 views

Does having a significant result from chi-squared test for independence also means that the odds ratio is significantly different from 1?

Suppose I have 2 by 2 contingency table. I performed Pearson's chi-squared test for independence and the results are significant. Does that mean the odds ratio that I calculated based on the 2 by 2 ...
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2answers
72 views

statistics test to compare ratio of two variables in two population R

I have two datasets from two courses. In one of the courses we applied an experiment and I would like to infer whether that experiment causes the average number of posts per students increases or not. ...
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36 views

statistics test to compare ratio of two variables in two population R [duplicate]

I have two datasets from two courses. In one of the courses we applied an experiment and I would like to infer whether that experiment causes the average number of posts per students increases or not. ...