# Questions tagged [chi-squared]

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

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### Distribution of a Random Variable

Given that $X_1,\dots,X_n \sim N(\mu, \sigma^2),$ where $\mu$ and $\sigma^2$ are both unknown. Suppose that the sample mean $\bar X$ has a $N(\mu, \sigma^2/n)$ distribution and sample variance $S^2$ ...
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### How to quantify the relationship between known group assignment and cluster assignment

Consider this data frame: ...
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### Multiple single $2 \times 2$ $\chi$-square tests of independence and Bonferroni correction

I have conducted 6 chi-square tests for independence and all of these tests are $2 \times 2$ tables. Do I need to perform Bonferroni corrections for all these 6 chi-square tests? I appreciate your ...
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### Power of Fisher test vs chi squared

Consider an $m \times n$ contingency table and test of independence. Suppose the expected counts are such that chi-squared test is not recommended (close to zero in some cells), as it becomes pretty ...
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### The reason why a test is undersized?

Now I have a statistic $T_n$ for testing $H_0 \leftrightarrow H_1$, and I have proved that: $$n T_n \rightarrow_d \chi_K^2$$ under $H_0$. Then an asymptotic $\chi^2$ test can be used, an asymptotic ...
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### Measuring Inverse Relationship between 2 variables

I am having trouble deciding on the best test to use to measure if there is nonmonotonic or inverse relationship, would would be best test for this? to give an example if I want to see for facebook if ...
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### What does independence mean in terms of the input assumptions of the chi-square test?

I have been checking out this paper that mentions some assumptions that have to be met in order to use the Chi-square test, one of the assumptions reads as follows: The study groups must be ...
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### How should I interpret different p-values when all of them are far from the significance level?

I was hoping to demonstrate the other day that a given data set is normally distributed, and a chi-squared test seemed appropriate. I made my null hypothesis that the data set was normally distributed,...
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### sampling distribution of sample variance (normal distribution)

It is mentioned in Stats Textbook that for a random sample, of size n from a normal distribution , with known variance, the following statistic is having a chi-square distribution with n-1 degrees of ...
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### When is this effect size for chi-squared appropriate?

A paper I am reviewing contains the following measure of effect size for chi-squared $r = \sqrt{\frac{\chi^2_{obs}}{df+2}}$ where $\chi^2_{obs}$ is observed chi-squared and $df$ is its associated ...
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### Comparing multiple distinct proportions between two groups

I have two groups (group 1: $n=100$, and group 2: $n=200$), and multiple proportions for each group (where the number represents the proportion of individuals in the group with each disease). Example: ...
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### Intuitive understanding of chi-squared variance

The chi-square distribution is a sampling distribution of normal variance. A chi-square distribution with m degrees of freedom can be expressed as sum of squares of m , i.i.d standard normal variables....
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### product of asymptotic standard normal distribution

Suppose $Z_n\xrightarrow{d} Z \sim N(0,I_p)$, why $Z_n^TZ_n\xrightarrow{d}\chi^2_p$? I encounter this problem when we get the asymptotic distribution of the maximum likelihood estimator (MLE). Suppose ...
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### Sample size for Pearson's chi-square test of independence

I'm trying to do a $\chi^2$ test of independence between two variables. The problem I have is that I'm struggling with the sample size for the test. I always end up with some cells that have 0 samples....
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### Why are exact tests preferred over chi-squared for small sample sizes?

I am aware that tests such as Fisher's exact test are sometimes preferable to chi-squared if your expected values are low in a contingency table, when looking to test homogeneity of groups (...
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### Appropiate test for comparing integer distance distributions

I am trying to determine if wildfires occur closer to forests or not. For this, I have two matrices with the same shape: A matrix of ones and zeros where each value represents whether a fire is ...
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### Chi Squared Analysis on Google Keywords Clicks

I'm trying to look at Clicks vs Conversions with Chi Squared. I'm trying to look at good keywords vs bad keywords. A good keyword is one that I would get revenue from the keyword 1.2 times the spend ...
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### Confidence intervals/ellipses when variables are correlated

I was looking to create a confidence ellipse for my X and Y variable in order to identify potential outliers. I'm new to this area so my understanding and use of this method may be wrong (please ...
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### Does it have any meaning to compute the $\chi^2$ and the exact Fisher test on big contingency tables

I have several datasets containing integers. I want to perform a bivariate analysis between a specific subset of variables. However, some of them have a lot of modalities. Is computing a $\chi^2$ ...
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### How are values for expected probabilities for chi square null hypothesis calculated? Is there a package in Python/formula?

I am trying to prove seasonality and I came across this post: Is this an appropriate method to test for seasonal effects in suicide count data? The author "computed the expected probabilities for ...
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### Distribution of the pooled variance in paired samples

Suppose a bivariate normal populations with means $\mu_1$ and $\mu_2$ and equal variance $\sigma^2$ but having a correlation of $\rho$. Taking a paired sample, it is possible to compute the pooled ...
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### Impossible to get about 70% of height of Likelihood when I project the edge 1 sigma joint distribution on the 1D Likelihood

This post has been initially asked on maths.exchange but I didn't get any help, so I try to transfer it on this forum hoping someone could help me (I am going to delete the post on maths.exchange to ...
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### Impurity measurement of a group

I tried to use Gini Impurity to measure the impurity of a group of animals but is having trouble adding the distance between different animals to the equation. For example, the gini impurity of group (...
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### Analyzing the statistical independence of a Bernouli sequence

For my research, I need to check whether a sequence of Bernoulli trails (1 as success and 0 as failure) is a Bernoulli process and are statistically independent. As per the following discussion, and ...
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### Why is the chi-square test more popular than the G-test?

Pearson's chi-square test and the G-test are two goodness-of-fit hypothesis tests for categorical data -- i.e., testing whether a sample came from a given distribution on a finite set. The respective ...
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### Why Is A Squared Standard Normal Variable A Chi Square Variable

If for any $i \in \lbrace1,2,...n\rbrace$ where $Z_i \sim N(0,1)$ and all $Z_1, Z_2, ..., Z_n$ are independent of each other, why is it that $Z_i^2 \sim \chi^2_1$ and $\sum_i Z_i^2 \sim \chi^2_n$ ...
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### Cochran-Mantel-Haenszel test versus multiple Chi-square tests

Recently i've learned about Cochran-Mantel-Haenszel (CMH) test and its application for data analysis. I'm wondering why i have to perform a single ...
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### Chi-squared test, Poisson distribution, type I error overestimated - well-suited test for discrete distributions?

UPDATE I edited my original question to make it as clear as possible. My goal is to find a reliable goodness-of-fit test for Poisson-distributed samples. There are a few discussions here related to ...
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### What statistical analysis can I use to assess whether different groups use different themes in chat conversations?

Currently, I’m analyzing publicly available chats of 3 groups of people. Within these chats, I label lines for themes 1-5. Any single line could fall under multiple of the five themes so for instance: ...
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### What statistical test should be used to compare groups when the assumption of independence is violated?

I would like to test if there are statistically significant differences between three groups (defined by an outcome measurement) for some categorical and continous variables, respectively. Normality ...
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### Error in Gamma Ray data: chi square value

I have Gamma-ray data for which I am fitting the stars with a constant (one parameter) first to remove the unwanted or garbage data. I plotted counts vs MJD value. For this data as Poisson, the error ...
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### How to convert continuous variable dataset into binary discrete values using Chi-Square testing for decision making

I have a dataset that contains continuous values for an attribute ranging from 0 - 100. I want to convert these continuous variables into two discreet values (say Label L1 and Label L2), So that the ...
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### Goodness of fit --$\chi^2$ Statistics

I have an elementary question about $\chi^2$ statistic. Let us say that an experiment makes a set of measurements $E_i \pm \delta_i$, with $i=1, \ldots, n$. $\delta_i$ are the uncertainties in ...
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### Chi Square Test on non-numeric data in R

Currently, I'm working on an R project for the university. Based on this table: https://drive.google.com/file/d/13aJr5MHLxJ5Zgv0ZdoQzPU7PutLGTDS4/view?usp=sharing A company would like to introduce an ...
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### chi squared test in python libraries

As I understand it, statsmodels.stats.contingency_tables.Table.test_nominal_association() and scipy.stats.chi2_contingency() ...
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### Is there any anova-like approach for calculating contingency tables across multiple levels within a factor

I want to compare success rates across a large number of different levels within a third factor to detect if there are statistically significant differences for at least one of the groups. I'm not ...
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### How to determine the expected chi^2 value?

My advisor is able to determine that a chi^2 value will be near 30 in this particular circumstance. I calculated a chi^2 for a dataset and fitted line to be 31.89 which validates his claim. How is he ...
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### Is there an intuition behind the formula of chi-square?

Why in this formula $\chi^2 = \sum_i \frac{(x_i - m_i)^2}{m_i}$, we divide by $m_i$ instead of $m_i^2$? Dividing by the squared value has a clear logic for me that we are comparing the difference ...