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

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Statistically verifying distribution of users within an A/B Test

Hoping you can help me determine the best way to statistically verify that an A/B test was set up in an unbiased way. The A/B test was set up to split users on my website 50/50 into a test/control ...
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35 views

Computational error on chi-square test for homogeneity

I have the following categorical data Control Treatment c1 285441 33296 c2 40637 4187 c3 737113 97433 c4 34036 3993 In other words, I have ...
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20 views

Use CHIINV or CHISQ.INV to report Chi Square statistic?

I'm looking to report a chi-squared statistic for a chi-squared goodness of fit test using a 2x2 table. ...
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1answer
14 views

Confidence measure/statistic for inferring a category with random independent sampling

Suppose there's a group of dogs and a set of people A,B,C,D. If I know that, in this hypothetical scenario, the person who owns the dog is the person who walks it ...
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Approximation of quadratic form of normal variances, not necessarily non-negative

I am interested in approximating $$ \sum_{i=1}^{n}{w_i u_i^2} $$ where $u_i \sim N(0,1)$ i.i.d. I have seen a few papers on approximating this sum where $w_i \ge 0$, but not in the general case. Why ...
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24 views

Two groups, 29 Likert scale questions - differences between the groups?

I've two groups of individuals, Group A (13) and Group B (30). Both groups got the same series of 29 questions that can be asked as "unimportant - slightly important - moderately important - very ...
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1answer
48 views

The squared-norm of the projection of a Gaussian vector onto an independent $d$-dimensional subspace is a $\chi^2_{2d}$

How we can prove that: The squared-norm of the projection of a $N$-dimensional complex vector with i.i.d. unit-variance and zero mean Gaussian components onto an independent $d$-dimensional subspace ...
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22 views

A/B Testing (Pearson Ch-Square Test) with Unequal Sample Sizes

We have run A/B tests in the past using a 50/50 split, and have used the power prop function for calculating the sample size using the power.prop.test in R. My question is how do I calculate what my ...
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24 views

How to determine the degrees of freedom & calculate the chi-squared test by hand

I have a set of 42 insects, and over a certain amount of time, 17 of those (40%) died. Those 42 individuals have been held in 2 different conditions, 14 of them were in ...
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15 views

Comparing nonlinear models using the Chi-squared asymptotic approximation

I am attempting to identify the best model fit for a nonlinear mixed effects model using the asymptotic approximation to the Chi-squared test. When calculating the appropriate number of degrees of ...
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24 views

Which stats test to use

I am a UK Clinical Psychology Trainee carrying out a small (5000 words) service improvement project based on where I am on placement. The title of the project is: “Quantifying and comparing uptake of ...
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11 views

use fisher or chi-square to test probability density funciton of two group of data in R [closed]

I have two group of data and try to test if their distribution is similar, the capacity of two groups are not the same,but divided with the same interval division, many counts are 0 or 1, so I should ...
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48 views

Why does my p-value = 0?

I created a vector that is 329 rows long, with each row containing a z-score. I derived my degrees of freedom by counting up the number of rows (329) and subtracting 1. Then, I computed a test ...
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1answer
79 views

Proof: $T \sim \chi^2(N-1)$

I'm a maths student, this is my first statics class and I'm studying Confidence Intervals. When it's time to estimate the CI for the mean of $\{X_i\}_{i=1..N}$ - gaussian random variables i.i.d. with ...
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1answer
16 views

Are my data values too small for chi-squared for trend? If so what trend test can I do instead?

I'm doing a project about dilated kidneys, these can be arranged into mild, moderate and severe. There are 53 patients in total. I want to see if there is a trend in the severity of dilatation between ...
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1answer
27 views

Chi-square Analysis for data derived from continuous variables

Let's say I have growth parameters for a population. People who exceed 95th percentile are marked with 1, and people who are otherwise below it are marked as zero. I will then use crosstabs to compare ...
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26 views

Understanding relation of chi-squared test and p-values

I have a fairly simple questions regarding how to do the $\chi^2$ test, as I never really have used this before. I want to test whether a certain fit (a straight line passing through the origin) is ...
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8 views

what is the most suitable method to compare percentage values if there are no mean (no replicates)

I have a problem with my data analysis part in my final year research thesis. I measured methane generation efficiencies (percentage values) for 3 different biogas reactors for 2 months. But data in ...
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Goodness of fit test for binned multi-sample data

Let's say I have two samples and 5 bins. In each bin, I have a (positive) value and a measurement error on that value for each of the two samples. The value and corresponding measurement error ...
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44 views

What statistical test is appropriate for the following?

What statistical test is appropriate for the following? I have student ranking by year (1=freshman, etc), along with their responses to questions that seek to find how developed they are in a number ...
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1answer
31 views

Alternatives to Chi-Squared for Single Categorical Outcome and Single Categorical Predictor w/counts for factors [R]

I am from an applied background, where X2 and G-tests are the default ways to analyze count data (default as in, until today, I had no idea there were other ways, as I was only taught these methods). ...
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163 views

Goodness of fit. How to evaluate if polynomial of order n+1 gives statistically better fit than polynomial of order n?

I fit polynomials with increasing order to some data. What is the best way to evaluate if the additional parameter of polynomial of order n+1 provides a statistically significant better fit than the ...
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77 views

$\chi^2$ tabulated value

I noticed that the critical $\chi^2$ value increases as the degrees of freedom increase in a $\chi^2$ table. Why is that?
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2answers
52 views

Exact formula Yates' correction in R

If I run a chi square in R with the Yates' correction, I get slightly different results from doing it by hand. What is the exact formula R is using for the Yates' correction? I use the simple code: ...
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1answer
108 views

Alternatives for chi-squared test for independence for tables more than 2 x 2

What are some alternatives to the chi-squared test for categorical variables with tables larger than 2 x 2 and cells with a count less than 5, if I don't want to merge classes?
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Can I use the Chi squared test to see if my data fit to the Wigner-Dyson distribution indicating chaotic behaviour?

I recently read the paper about Quantum Chaos in Feshbach resonance spectra of ultracold Erbium [1]. The authors analyze their data statistically using the random matrix theory framework for ...
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23 views

chi-squared to test if two variables have the same frequency distribution

I want to test if x and y have the same frequency distributions using chi-squared. In my code below, I've concluded that because ...
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1answer
25 views

Why need to combine the bins when do Chi-square test

From Chi-Square Goodness-of-Fit test, It says If some of the counts are less than five, you may need to combine some bins in the tails. So how to understand this?
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25 views

25% are significant, can't be right

A couple of classes (like in school) did a test and each pupil solved a couple of problems. Classes are grouped by a small range of the average over the pupils total. I calculate the expected value ...
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1answer
37 views

Possibility to run multiple chi-square tests on 2x5 table

I'm analyzing data in which I have a dependent variable with two possible outcomes (yes or no) and an independent variable with five emotion conditions, neutral, angry, sad, ashamed, and afraid. The ...
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1answer
34 views

Test of proportions or chi-squared? [duplicate]

These data are from an A/B test of free trials to conversion. Someone can sign up for a 30 day free trial of the product. If they like it they stay on and become paying customers. By default (A), ...
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26 views

Effect size for goodness of fit chi-square

I would like to assess the effect size of a goodness of fit chi-square test. I have a variable that can have 3 states and test against a custom expected value. I used a variation Cramér's V for a ...
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21 views

Which test do I need to apply for repeated measures?

My research question is as follows: How does on-ground presence of bird species A, B, and C change in relation to: 1. species A breeding chronology, and 2. time of day/month My data consists of ...
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23 views

What to do after a significant Exact test?

I have significant Fisher exact tests for a 2x3 and 6x3 contingency table. All I can get from it is that the observation regarding columns and rows are not random. But I don't know which combination ...
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1answer
38 views

How to represent goodness of fit for multiple least squares fits

I have many sequences (~50) of time series data that I have fit to a non-linear model using a least squares fit. If I had a single sequence of time series data, and I fit a model to it using a least ...
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1answer
66 views

Expected values vs. fitted values from log-linear model

Let's consider, for instance, a table like this one, with two independent categorical variables: x <- Titanic[,,2,1] I want to model this contingency table ...
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49 views

Observed / expected vs odds ratio

I am trying to understand the difference between the O/E ratio vs the odds ratio. I think the odds ratio can handle small samples better than the O/E ratio. I am wondering if anybody has more ...
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14 views

goodness of fit vs independence test in finite population case

I have a finite population frame. Around 80% of the frame members have e-mail addresses, and a survey was sent via e-mail to those people. Roughly 20% of those to whom e-mails were sent replied to the ...
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14 views

Using F-Statistic and Critical Value to infer Chi Square and P-value

I'm currently running the Granger Causality Test on MATLAB to determine whether the behavior of a set of swaps affects another set of swaps. However, my MATLAB code only appears to be producing ...
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1answer
89 views

chisq.test and wilcox.test don't concord with my graphs and observations?

I want to know if a factor variable have an incidence on another variable (dura). For example : ...
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30 views

How can I analyze / compare point-of-sales data between stores with different product offerings?

Let's say I have two stores, A and B, and let's say I have two products in the same department: product 1 and product 2. Let store B have product 2 which store A doesn't have, both stores have product ...
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1answer
36 views

Chi Squared Kernel and Faster implementation

There is a good implementation of Chi-Squared Kernel in http://www.vlfeat.org/matlab/vl_alldist2.html But this implementation is very slow when input data is huge. This implementation doesn't accept ...
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sadists package/ Sum of (non-central) chi-squares to a power

I try use "sadists" package in R to compute quantiles and probabilities on sum of non-central chi-squares distribution, but there are some issues in this package. I give an example: wts = ...
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25 views

What are the different ways to discretize continuous features?

I'm working on classification problem. I have a set of continuous & discrete features and I'm trying to list my features in their order of significance. Using chi-squared test as a filter & ...
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2answers
91 views

Difference of two squared normal dependent variables

I need to find the distribution of the random variable $Z$ $Z = \frac{(X - \mu_0)^2}{\sigma_0^2} - \frac{(X - \mu_1)^2}{\sigma_1^2}$, where $X \sim \mathcal{N}(\mu_0, \sigma_0)$. We can find the ...
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1answer
86 views

R: prop.test - Chi-squared approximation may be incorrect

I am trying to compare the proportions of two populations, using prop.test My data is straightforward - first population is 6/26 and second is 15/171. I am trying ...
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29 views

how best test for differences among two samples of abundance (count) data measured at the same sites

I want to test for differences in the abundance (counts) of two types of lizards. Both types were sampled at the same sites (n=284). The distribution of both types is overloaded with zeros and lizards ...
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1answer
54 views

How would combining levels in a contingency table (2x3 $\rightarrow$ 2x2) affect the power of a chi squared test?

A 2x2 table has a critical $\chi^2$ value of $3.84$, whilst a 2x3 table has a critical value of $5.99$ (for a significance level of $0.05$). Is it reasonable to think, that if you are able to turn ...
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Is there an alternate $\chi^2$ calculation useful for data spanning a large scale?

I have experimental small angle scattering data which provide information about the structure of a molecule. I can use a PDB file of a molecular structure (contains all the atom names and ...
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Goodness-of-fit test to use for weighted data

Hello. I'm working on a AP stats project, but since what I'm doing is beyond the scope of what we do in class (i.e. learn how to use a calculator), I think it's safe to say this isn't a homework ...