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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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What is the purpose of doing a logistic regression when the predictor is dichotomous?

I would like to expand on this question. Knowing that it is possible to do a logistic regression when the IV is dichotomous, and that I've seen it done in studies: what is the purpose of doing so, and ...
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Testing the goodness-of-fit for the binomial distribution

As specified in the title, I'm trying to understand how to test the goodness-of-fit for the binomial distribution; to this aim, I followed what suggested in this link. Particularly, I'm investigating ...
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Distribution of difference of two random variables with chi-squared distribution

Supose that we have two random variables $X \sim \chi_k^2$ and $Y \sim \chi_k^2$, with the same degrees of freedom. A chi-squared distribution cannot have zero degrees of freedom, so what would be ...
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A Normal random variable divided by a Chi-squared random variable

I am looking to find the pdf of the ratio $Z = \frac{X}{Y}$, where $X \sim$ Gaussian and $Y \sim$ Chi-squared are indepedent random variables. A reference is good enough if you do not want to write ...
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Degrees of freedom of likelihood ratio test with equal dimension on the null and the parameter space?

Let $x_1,\dots,x_n$ be iid samples from a $N(\mu,\sigma^2)$ and consider the hypotesis $$H_0:\theta\in\Theta_0,\,\,\,\,\,\,vs\,\,\,\,\,\,H_1:\theta\in\Theta _{0}^c$$ where $\Theta _{0} = \{\mu>0,\...
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+100

Failing to implement Bayesian Chi2 goodness of fit test

I am trying to implement one of the methods described in Valen Johnson's A Bayesian Chi-Squared Test for Goodness of Fit. It presents a couple of variants depending on whether the random variable of ...
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Is there a relationship between the L2-norm and the Pearson chi-square test?

Suppose I have two datasets, $\mathbf{a}$ and $\mathbf{b}$, with some data weighting term (or error term), $\mathbf{e}$. I can compute the L2-norm for these two sets by the following: $$(\mathbf{a}-\...
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Compare overall proportions between 2 samples

I want to compare multiple proportions between two samples. There are 60 brands of toys (T1, T2, T3...T60). I would like to know if overall, the proportion of respondents who own each brand of toy is ...
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16 views

Estimate the sample size needed for a chi-square test comparing four percentages

I am trying to compare the percentage of males among four countries using Chi-square test. From a previous similar study, I know that the percentage of males in these four countries are 0, 10%, 30%, ...
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24 views

How Can I Test for Multicollinearity in my Categorical Predictor Variables when Doing Ordered Logistic Regression?

I have a dataset where my dependent variable measures 'How much Trump’s locker room video should have mattered in the election'. The categories are coded between 1-5, where 1 represents 'should not ...
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2answers
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How can I calculate the mean of the cube of random variable that follows chi-square distribuion?

If $X + 1 \sim \chi^2_{1}$, what is the mean of the cube of $X$? I'm confused between raw moment and central moment. My idea is, since the mean of $X$ is 0, I should calculate the raw moment. ...
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1answer
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Confidence interval for the square of binomial probability

I have a binomial distribution where the estimate for p is 0.03 out of 1000 sample trials. Using the normal approximation and Chi-square distribution for the square of normal distribution, how can I ...
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1answer
135 views

Proving Asymptotic distribution of $\sqrt n( \widehat\sigma^2 -\sigma^2)$

I am looking at trying to derive an expression for the asymptotic distribution. We have $X_1,\ldots, X_n$ i.i.d $N(\mu, σ^2)$. So we have defined $\hat \sigma^2 = \frac 1n \sum_{i=1}^n(X_i-\mu)^2$. (...
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3answers
51 views

Square of Binomial is Chi-Square?

my statistics professor said in passing that if you square the binomial test statistic, you can derive the chi-square statistic. I tried working out the proof, but I can't seem to reduce the chi-...
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25 views

Statistical inference of a variable based on categorical respone levels.

Suppose that we have a variable $X$ with three levels $1$ ,$2$ and $3$ accordingly.Also we have a catergorical respone variable with two levels $Y=\left\{Healed,Not Healed\right\}$ which tells as if ...
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Why error sum of squares has n-2 df (possibly not duplicate, please read on)? (Regression Question Series - Part 4)

In simple linear regression, the error sum of squares is given by $$ \text{SSE} = \sum_{i=1}^n(y_i - \hat{y_i})^2 \\ \hat{\sigma}^2 = s^2 = \dfrac{\text{SSE}}{n-2} $$ where $n-2$ is the degrees of ...
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Characteristic function for a Chi-squared distribution

I would like to directly derive the probability density function (PDF) for a Chi-squared distribution with $k$ degrees of freedom using characteristic functions. If $X_{1}, X_{2}, \dots, X_{k}$ are ...
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1answer
22 views

What goodness-of-fit tests avoids the ambiguity in chi-square statistic?

The chi-square statistic is a fairly standard goodness-of-fit test defined as: $$\chi^2 = \sum_k^N \left ( \frac{d_k-m_k}{\Delta d_k}\right )^2$$ where $\mathbf{d}$ is a vector of data with error $\...
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3answers
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Fairness of 6 sided die NOT using Chi Square Test

So I was reading a lot of online articles using the chi-square test to determine the fairness of a die. Correct me if I am wrong, but isn't the drawbacks of using a goodness of fit test is that you ...
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1answer
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What is the anova variation of a paired t-test in my case?

I have the following case: I inventoried birch trees in 10 areas, once in 2000 and once last year (same areas inventoried in both years). If I want to see if there is a difference in the average ...
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1answer
23 views

Comparing categorical data

I'm comparing two groups in a large dataset. For some of the variables, the following 5 choices are available: 1, 2, 3, 4, 5 or more This seems like categorical data- but would it be considered ...
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Comparing inter-rater agreement between two groups of raters: can I use chi-square test or only ICC?

I have 5 raters divided in two groups, "experts" (2) and "not expert" (3). They rate each one of 30 items with a score "none, mild, medium, high" expressed by 0, 1, 2, 3. I'm interested in verifying ...
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How run run followup (post-hoc) tests for multiple Chi-square tests

I have been looking around on the net looking for the best way to do a post-hoc analysis for multi factor significant chi-square test, with no success. I have a data-set of patients with different ...
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3answers
62 views

Paired categorical data--which test to use

I am trying to determine which statistical test to use for the following: I used a rubric to determine students' level of achievement on two different tasks (see table below). I want to know if their ...
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1answer
36 views

False Chi-Square Significance?

I am a newcomer to Chi-Square analysis. I have the following dataset: Healthy Disease Females 537653 4467 Males 362013 3365 ...
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2answers
114 views

Optimizing $\chi^2$ using MCMC

I have measurements of an object. Let's say I have its length $L$, mass $M$, and age $t$: $$\mathbf y = (10~\text{m},\ 0.01~\text{g},\ 5~\text{s}).$$ I also have the uncertainties on my measurements ...
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1answer
21 views

How to compare two Crosstabs for significance?

I have two crosstabs and need to determine whether their differences are significant. Both tables have the same independent variable but different populations. E.g., The only test I know to do is to ...
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1answer
65 views

Chi-square or binomial logistic regression?

I am unsure about which statistical test suits my needs, in particular I wonder whether chi-square should be used or not. The responses I get from my experiments are not continuous, but discrete, ...
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14 views

Fitting data on a time demanding stochastic Model

I have a multi-parameter (8 at least) model which is very time consuming. It's not an analytical function but instead is a model which integrates many differential equation and some times the result ...
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Which analysis should I use? impact of course lengths on student outcomes

I am examining the impact of course lengths on student outcomes. I have two independent variables (16 week, 8 week) and four dependent variables (pass, retention, success, and mastery rates). I am ...
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Chi-square origin of the name

What are the origins of the names and letters in these distributions: What is the origin of the name in chi-square distribution $\chi_k^2$? And the origin of $t$ in student's $t$-test? And naming $...
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Chi Square Post Hoc - One dependent variable

I'm new to R (and statistics in general) so apologies in advance for what's probably a very remedial question, but I'd appreciate any help! I'm trying to assess if there's a statistical advantage to ...
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Significant difference of small count data in 2xn contingency tables

My data consists of multiple contingency tables (2xN, often N > 30) with frequencies of two nominal variables: they are frequencies of shared collocations of various word-pairs taken from the corpus. ...
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23 views

chi-square goodness of fit from the logistic regression

I am trying to get the chi-square goodness of fit from my logistic regression where the results are as below. ...
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25 views

Normality assumption for Chi Square goodness of fit

Does Chi Square goodness of fit require normality assumption? Is it a parameteric or non-parametric test? What it its relation with t-test (parametric test) and u-test (non-parametric test)?
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How to compare two categorical distributions with small counts

I would like to compare pairs of distributions (e.g. the two rows ‘expect’ and ‘simul’ in the table below) to answer the question: is the ‘simul’ distribution significantly different from the ‘expect’ ...
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1answer
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Compare two discrete distributions using Chi-Sq

(I am not quite sure whether the following post is better suited for CrossValidated or for StackOverflow because I have both a theoretical question about the use of the Chi-Squared test and a more ...
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Appropriate statistical test for frequencies of motifs

I have a graph composed of 26 nodes, labelled A to Z. Some nodes are connected by edges, but not all nodes are connected to all other nodes. I enumerate all possible sub-graphs comprised of four ...
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1answer
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Approximation of the critical value for $\alpha$ of $\Gamma(n-1,1)$

Say I have the critical region for a test statistic $T$ and some constant $c$, as follows, $$ n(T - 1)^2 \ge c $$ where $nT \sim \Gamma(n-1, 1)$ and the probability of rejection is $\alpha = P(n(T - ...
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Proving an inequality with independent chi-square RV's

I've been asked to prove the following inequality, where $X_1$ and $X_2$ are chi-square random variables on $\nu_1$ & $\nu_2$ degrees of freedom, respectively. $$E\left[\frac{X_1}{(X_1 + X_2)^2}\...
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2answers
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How to interpret the results of a chi square and p-values of a distribution uniformity test

I am reading about a method called consistent hash designed to distribute load among servers. The best case scenario would be a discrete uniform distribution where each server would get the same ...
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2answers
53 views

Calculate confidence that a population is evenly distributed between several values

I apologize if this is too basic, or is poorly worded. It's been a long time since I sat in a stats class, and I'm having trouble figuring out how to search for what I need. I have a system that ...
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0answers
43 views

Chi-Square tables in APA format using R or SPSS

Does anyone know how to automatically generate APA formatted crosstabulated Chi-Square tables in R or SPSS? I haven't been able to find a satisfying solution so far. The closest one is APATables R ...
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1answer
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How do I best use a fit statistic like chi-squared fit for a model that predicts two independent sets of measurements?

I have a model $M(\vec{x})$ for a vector of model parameters $\vec{x}$ that predicts two sets of measurements that I have taken - $v(h)$ and $L(h)$. The two independent data sets each have their own ...
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Expectation of inverse non central chi-squared

If $X\sim \mathcal{N}_p(\theta,\sigma^2)$ then $X^{'}X/\sigma^2\sim$ non-central $\chi^2_p$ with non-centrality parameter $\theta^{'}\theta/\sigma^2$. How to find out the expectation of $\sigma^2/X^{...
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1answer
29 views

Interpret Chi-square test

I'm trying to test for dependence between gender and passing a study unit. The contingency table is as below ...
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4answers
59 views

Frequencies/percentages different from zero - which test?

I conducted an experiment and had participants indicate binary judgments by either pressing "1" or "0" when seeing different types of stimuli. Now I want to test whether the proportions of number ...
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3answers
56 views

Hypothesis test for intervention with class imbalance before intervention. Alternative to McNemar

I want to assess an intervention to cure a disease. An example is described by the following matrix: ...
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Questions about analyzing proportions over time with Chi-square and building logistic regression/GLM models.

First-year med student who has been out of the stat game for some time. I'm looking at data for different residency sub-specialties (counts) and particularly interested in quantifying and comparing ...
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0answers
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Chi squared test: which is the correct null hypothesis?

I'm reviewing some literature in my field, specifically looking at whether physical activity (PA) has any beneficial effects on cognitive performance. The results across the studies are quite mixed. ...