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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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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Show change of expression of sample variance and explain the distribution

Show that $$ \sum\left(Y_{i}-\mu\right)^{2} / \sigma^{2}=(n-1) S^{2} / \sigma^{2}+\left[(\bar{Y}-\mu)^{2} n / \sigma^{2}\right] $$ can be changed into a form $$ \frac{1}{\sigma^{2}} \widehat{S}_{1}=\...
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Appropriate dataframe, statistical test and multinomial regression in R

I am trying to see if my independent variables "dependency" "democracy" and "capacity" have an effect on my outcome variable "total_policy". Here, "...
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General procedures to check conditions for hypothesis testing?

I am going to have a linear by linear test(lbl_test in R, and the related doc can be found here) but the math underlying it is still a mystery to me after trying my best to comprehend this ...
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Hypothesis testing that a sentiment appeared more often

Im new to statistics and have a question that I cant answer. It's also difficult for me to tell if an online guide has the right solution for my question. So any help from you would be great. What I ...
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Chi squared test questions

As part of a small study, I've have put together a table with results from a population of individuals stratified by age. For each line, I would like to perform a comparison between a variable and the ...
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Effect sizes for $\chi^2$ tests when $df > 1$

Rosenberg (2010) discusses the Phi coefficient measure of effect size for $\chi^2$: $r = \sqrt{\frac{\chi^2}{n}}$, "where the $\chi^2$ value comes from a two-group contrasts (thus a single degree ...
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Use Chebyshev's inequality to find a lower bound of a Chi-Square Distribution

I'm trying to solve the following exercise but I'm not sure if what I'm doing is right. "Let $X$ be an r.v. distributed as $\chi_{40}^{2}$. Use Tchebichev’s inequality in order to find a lower ...
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What test should I use when I have words as the independent variable and YES or NO as the dependent variable? [closed]

I have a count of how many times each word showed for a person that said YES and the count of the same words for people that said NO. I want to know if some of those words are actually statistical ...
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Outliers and Data Analysis

I have data for gamma-ray bursts. They follow more or less an exponential model. I tried to first fit it with a constant to get rid of invalid plots and which do not show any model. From the remaining ...
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Is this way of calculating the chi-squared value correct?

I have read that the chi-squared value is calculated as follows: $$\chi^2 = \sum \frac{(\text{observed value} - \text{expected value})^2}{\text{(expected value)}}$$ However, this answer mentions it as:...
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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 ...
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Two sample test of independent proportions with weighted data?

In analysis of survey data, response data may often be weighted to reflect the sampling procedure or relative importance of the respondents. For instance, a consumer survey may sample 50 respondents ...
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Comparing counts between two groups with replicates [closed]

I hope you can help me. I need to compare count data (number of grazed plants among plants previously marked inside a plot) recorded in 4 different sites (considered replicates), each of them ...

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