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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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Analyzing/modelling discrete numerical responses and determining associations based on categorical co-variates

I need and would be grateful for some advice regarding the analysis of some data that has been gathered and coded by a third party. The data is part of a project regarding performance in the health ...
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12 views

Rating Scale Data: MoE vs Ch-Square vs Mann-Whitney Rank Test

I am working with Likelihood to Recommend metric that's measured on a scale of 1-10. The objective is to test for statistically significant improvement/decline (period over period) in the metric. On a ...
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50 views

Expected Value Non-Central F Distribution

If $X$ is $\chi^{2}(5,\lambda)$ and $Y$, independent of $X$, is $\chi^{2}(4)$ then what is $$ E\left[\frac{X}{Y} + \frac{Y}{X}\right] = E\left[\frac{X}{Y}\right] + E\left[\frac{Y}{X}\right] $$ $\...
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2answers
14 views

Will Chi Square Test work for high number of categories?

I have a dataset of 1000+ records. In this dataset, I have two categorical features, Ticket-Label and Survived. Ticket-Label has 54 unique categories and Survived has 2 categories. The chi square test ...
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1answer
39 views

Given the marginals of a contingency table, what is the maximum observable value for the $\chi^2$ Pearson statistic?

I know that given a $R\times C$ contingency table observed on $N$ subjects, the maximum value of $\chi^2$ statistics is $N\cdot [\min(R,C)-1]$. But, this is independent of given margins (namely, row ...
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2answers
18 views

A four way categorical variable with a frequency, what is the best solution? Chi-square or something else?

We are doing research to see if images quality affects engagement. We are doing this for 3 products. We are doing this for 4 image quality levels. And for each of them we are checking the engagement ...
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10 views

How to calculate the mean of a sub sample, given the mean of the super sample and the standard deviation of the population?

I need to run a simulation of cash flows for a project. We are selling a service. The service comes with a range of options. Depending on the specific options chosen, the cost of the service can ...
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19 views

Chi Square - alternative for three-way interaction

I am interested in the effect of predictability and expected value on the choice between two payment options. Basically, I have a 2(predictability of the payment option: predictable vs. unpredictable; ...
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21 views

Corelation between two dichotomous variables

I have a data from a research with responses (yes/no) about three questions (A,B,C) and I would to see if the variables are correlated. First of all i compared the proportion of agreement(yes-yes, no-...
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1answer
45 views

How to determine sample size for chi-quared test?

Similar questions have been asked here on CV, however I have not found a solution to my specific question yet. I am trying to plan a sample size for chi-squared test. However, I struggle to find the ...
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14 views

Class frequency comparison (exponential distribution)

I have two different sources of data and I would like to check if their class distributions are similar and how much. The first dataset ($D_1$) has 2M samples and the second ($D_2$) 6M. When I ...
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1answer
25 views

significant $\chi^2$, breakdown shows nothing interesting

Someone I know told me that he had performed $\chi^2$ test of independence with Yates's correction on a $2\times n$ contingency table, seen that $p\lt10\%$ (good enough for his purposes), and ...
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16 views

How to determine if a dichotomous variable is randomly distributed or is predicted by other instances

I have a product with a measurement of X features. Each feature can either be a PASS or a FAIL. Which statistical test can I use to tell if the failures are randomly distributed across all features? ...
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2answers
77 views

Independence of Beta ratios of Gamma variates

If $X= x_1/(x_1+x_2+x_3)$ and $Y= x_2/(x_1+x_2+x_3)$ where $x_1, x_2, x_3$ are independent $\chi^2$-distributed random variables with d.f. $-n_1,n_2, n_3$ respectively. Are $X$ and $Y$ independent? I ...
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1answer
10 views

Measuring blinding procedure in a 3 conditions repeated measures experimentation

I'm confused about what to do, chi-square or something else. I want to measure the efficiency of my blinding procedure. In my study, each participants received 3 conditions (10Hz, 20Hz, sham). After ...
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1answer
28 views

Which stats can test differences between two experiments?

I have an experiment to look at habitat preferences of beetles and the effect of competition. In the first test, a beetle is on his own in an arena and I measured the % of time he spends in each of ...
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3answers
37 views

Two Distributions, One a Sum: Discerning likelihood given error

Given $X, Y$ independent and non-normal, I'm recording histograms of $X$ and of $Z = X + Y$, sampled when $Y$ is not present and when it is, respectfully. I'm trying to figure out $Var(Y)$ and its ...
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2answers
106 views

Independence of ratios of independent variates

If $X= x_1/(x_1+x_2)$ and $Y= (x_1+x_2)/(x_1+x_2+x_3)$ where $x_1,x_2,x_3$ independent chi-square variates with d.f $n_1,n_2,n_3$ respectively, are $X$ & $Y$ independent? I know the condition ...
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1answer
24 views

Are there statistical tests for testing multiple sample proportion?

For categorical variable testing, we have chi-square test. For example, we want to test if a dice is fair (assuming sample has [6,5,7,7,6,5] and ...
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16 views

Creating a contingency table for Chi-Square test

So I have this data I was wondering how to create a contingency table for it to be able to perform the Chi-square test. Please note that the two groups are not equal and every single cell contains a ...
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0answers
7 views

What should I do with chi-square expected values below in this large table?

I asked a question about emotions felt during a particular period, taking the question from previous literature. However, for a number of frustrating reasons, I ended up with small sample size. I now ...
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2answers
37 views

different chi-square test results [duplicate]

I am doing chi-square tests using Scipy. Just realized the test statistics will change even though you simply rescale all data and the testing outcome could change. For example, using ...
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1answer
24 views

Chi-square test with replicate nested

I have a question about how to analyse count data with replicates nested in each treatment. For example, imagine temperature can influence the sex ratio of mosquito larva emerged from eggs. I have two ...
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16 views

How to evaluate relationships with categorical variables?

I am working on the BigMart dataset. One of the variables has a substantial amount of missing values. I'd like to check whether these are missing completely at random. There are 12 variables, 4 are ...
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0answers
82 views

Difference - Probability-To-Exceed (PTE) and $\chi^2$ distribution

I would like to understand the difference between the $\chi^{2}$ distribution and the Probability-To-Exceed ? I have to compare 2 data sets A and B and in the article I am reading, they talk about ...
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2answers
186 views

Correlation vs Chi Square

Up to now I used correlations to study whether two variables are affected by each other. Now I stumbled over the case that the chi square is doing that too ( http://www.r-tutor.com/elementary-...
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37 views

Comparison of random vectors

I feel a little stupid asking this, but anyway: say I've got a random vector $a$ of size $p$ with covariance matrix ${\Sigma_a}$ of size $p\times p$, and another vector $b$ with its cov $\Sigma_b$. ...
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Statistics to show the differences in population of the sample and city and by sex

Hoping for some help. I am trying to run some statistics for demographics from the results of a survey. I have male/female percentages as a result of the survey (45.1/54.9) compared to male/female ...
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0answers
12 views

Statistical Test: 2 Nominal Independent Variables; 1 Nominal and 1 Numerical Dependent Variable

I have a data like this, I want to do statistical test to determine whether "App Opens" and "Click on Cards" differ by "Group" (Control/Treatment). What should I do? Can I separate this dependent ...
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1answer
17 views

Chi-squared test for homogeneity to compare subsets of a population?

Everything I have read states that one of the conditions for inference of chi-squared is that random sampling is carried out (e.g. https://stattrek.com/chi-square-test/homogeneity.aspx). Can I still ...
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Does X^2 divided to DF converge to F distribution when X^2 is Rao Scott chi squared statistic?

I'm studying Rao-Scott chi-squared test, kind of survey sampling analysis method. It uses when we want to test independence between two variables under complex sampling data instead of Pearson chi-...
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Can you do chi-square test of independence on quantized continuous random variables?

Say I have a sample with m observations, each observation has two features X and Y which are continuous random variables. I'm interested in knowing if you can bin X and Y each into N quantiles, ...
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2answers
73 views

Likelihood of rejecting a fair coin (repeated significance testing)

Suppose I have a fair coin and I flip it numerous times, testing after every time using Pearson's $\chi^2$ test of fit to fairness. What is the likelihood that I will, at some point, reject that the ...
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0answers
49 views

What is the most appropriate statisitical test to run?

I'm having trouble figuring out what test to run for the following information. My data looks like this when I arrange it in a table format: So I want to determine if there is any difference in the ...
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2answers
74 views

Is Fisher's/Chi2 “better” than running a regression?

Say I have a variable treatment A/B (0,1) and effect yes/no (0,1). An easy way to calculate a P value from such a dataset would be to use Fisher's Exact test or a Chi2 test. However, we also have ...
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30 views

The interpretation of Chi-Square Independence Test

I'm working with UFO Sightings data set and my goal is to verify if the Shape of UFO ("circle", "cone"...) depends on the Duration of Sight (in seconds). To do that, I decided to perform a Chi-Square ...
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How “sensitive” is chi-square to detect dependence?

I hope I understand chi-square correctly. Taking the categorical data in chi-square wikipedia page as an example, https://en.wikipedia.org/wiki/Chi-squared_test I was wondering how "sensitive" chi-...
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1answer
33 views

Problem of Critical Region and Significance Level (Statistics)

An investment adviser states that the risk (standard deviation) when investing in a certain instrument is greater than $3.$ To corroborate the validity of this statement, he plans to realize: $H_0: \...
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3answers
82 views

Meaning of chi-squared in R Kruskal-Wallis test

I have a simple question to ask, I think it was not covered in other questions. I am running a Kruskal-Wallis test in R, using the function kruskal.test. The output gives me the p-value and a chi-...
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0answers
33 views

Estimating posterior probability from a random grid

I am simulating the evolution of galaxies, and want to find the distributions of input parameters that best reproduce an observation of a particular galaxy. I have a measurement $y \pm \sigma$ of a ...
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0answers
8 views

Pairwise vs aggregate A/B/n hypothesis testing

I'm currently running a hypothesis test on multiple variants (say $n$ variants) of a webpage, trying to optimize conversion, and am unsure if I should run pairwise hypothesis tests of each variant ...
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1answer
70 views

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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0answers
22 views

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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2answers
59 views

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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0answers
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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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0answers
30 views

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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1answer
84 views

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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0answers
11 views

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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0answers
15 views

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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0answers
18 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%, ...