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

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A chi-squared test for a matrix of data

Given a observable vector $v=[v_1,v_2,\ldots,v_n]$ and a model $m=[m_1, m_2,\ldots, m_n]$ when $\sum_i v_i=\sum_i m_i$, I can use chi-squared to determine the likelihood that $m$ is a good model for ...
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13 views

How can I test for changes in the distribution of categorical data over time?

Each week at my organization, we receive X number of type A messages, Y number of type B messages, Z number of type C messages...etc. I want to be able to test if the distribution of these message ...
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1answer
11 views

Using contingency tables for testing multiple dependencies

I know that I can determine the correlation / association / dependency between two variables (X= smoker, and Y=cancer) using chi-squared with a 2x2 contingency table: ...
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1answer
15 views

Determining whether a successive instances are conditional or independent

I hope I can appropriately describe the problem. I have an example data set with 610 individuals with made up analogy (it's not really about cars). I want to determine the number of people have x ...
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1answer
20 views

Any reason to report a Chi Square Test of Independence on a 2×2 table when I'm already reporting a 95% CI on the odds ratio?

I'm analyzing a 2×2 contingency table, and am going to a report a 95% CI on the Odds Ratio. Is there any point in prefacing this with a Chi Square Test of Independence? I understand that if the Odds ...
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14 views

min ChiSquare to fit dipole axis

I am trying to fit a dipole. As I am not sure about some aspects (and not sure whether I understand it at all) I would like to ask this question here. Basically I have a distribution of $n$ sample ...
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24 views

Best statistical analysis method for frequency data

I'm designing a between subjects experiment with 1 dependent variable with 2 levels (manipulation & Control) and 4 dependent variables which are all categorical (Yes/No). I would like to see the ...
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1answer
34 views

Test if two gamma distributed populations are different

I have data from two populations of different sizes. Both have Gamma distributions with different shapes and scales (as estimated in r): fitdistr(x/10000, "gamma") #186 members shape 0.586219900 ...
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30 views
+50

Finding quality of fit for two discrete variables with low statistics

I have data from an experiment which I am trying to explain using a model. I do not have an analytic formula for the prediction of the model but instead I got its prediction through a simulation. The ...
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14 views

Comparing the expected and observed values of each item in a dataset separately

I have a set of points and for each point I have both observed and expected values. How can I compare the difference between the observed and expected values are significant for each data point. Note ...
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36 views

Approximate normality of distribution of counts in contigency table

I seem to be struggling with lack of basic understanding of some important concepts. This is a question to the answer of @Glen_b in this post: Warning in R - Chi-squared approximation may be ...
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2answers
110 views

Goodness of fit chi-square test for a number of PCA components

I have been trying to carry out Principal Component Analysis (PCA) in R using the function psych::principal. However the returned $p$-value has been very low in ...
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10 views

Why is the df for the χ² test of independence (r − 1)(c − 1)? [duplicate]

I understanding that if Z1, Z2, …, Zk, are independent standard normal variables, then Z12 + Z22 + … + Zk2 has a χ² distribution with k degrees of freedom. However, say we have a 2 rows and 3 ...
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4 views

If I have a 2x2 table of proportions of treatment effects, what is the best test to use for treatment effect?

I currently have a 2x2 table of proportions for treatment effects that looks like: \begin{table}[h] \begin{tabular}{lll} & Treatment A & Without Treatment A \\ Treatment B ...
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4 views

Chi-square test for independence of categorical variables [duplicate]

I'd like to know about independence of categorical variables. I read an article from https://explorable.com/significance-test-2 H0: “Having breakfast in the morning has no effect on the grades of ...
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1answer
16 views

Testing if subpopulation group is different from population group

Say I have data about the distribution of age groups in a country: 0-10 y : 20% of pop (or 3,000,000 people out of 15,000,000 total) 10-20 y : 30% of pop etc. ...
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6 views

Minimum chi square test in a linear case with x-errors

I've got to use the minimum chi square test in a linear case to find the best straight line. In a general case the chi square sum is : $$ S= \sum\limits_{i=1}^n \big( ...
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42 views

Can p-value = <0.05 with CI that includes 0 using chi2 in Stata?

I am doing a pretty straightforward analysis in Stata comparing proportions of respondents in 2 groups (in this case, rural vs. urban) who agree with different questions on a survey. For one of the ...
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26 views

Confidence interval for variances

I have a lot of variances $\sigma^2(x)$ as these: Now I have two task: remove the vertical outliers and compute the confidence intervals (for all cases, this is only one case). I think that their ...
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1answer
48 views

Are different p-values for chi-squared and z test expected for testing difference in proportions?

I'm trying to test the difference in proportions using the z test method and chi-squared method, but am getting very different answers. Is that normal? My data: ...
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7 views

Distribution of magnitude of weighted circularly-symmetric Gaussian random vector

Let $\mathbf{Z} = \{w_nZ_{-n},...,w_nZ_{n}\}$ where $Z_{n\backslash 0}$ is a circularly-symmetric complex Gaussian variable with 0 mean and variance 1, and $Z_{0}$ is a real valued Gaussian variable ...
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1answer
17 views

How to compute the $\chi^2$-table values?

How one can compute the values of $\chi^2$-tables? I saw two tables where was given for example that if degree of freedom is $1$ and $p=0.001$ then table value is in one table $10.827$ but in the ...
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1answer
233 views

Why does Pearson's chi-squared test detect differences that the GLM model fails to detect?

How can I interpret the following result? I have 4 groups with around 300 observations each: ...
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1answer
33 views

Chi-squared distribution and dependence

We know that for a group of independent random variables $\{X_i\}_{i=1}^n$ s.t each $X_i$ is distributed as a chi-squared distribution with degree of freedom one ($\chi_1^2$), the sum of these random ...
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1answer
22 views

Can I perform a chi-squared analysis with a categorical variable and the means of a continuous variable?

I have one variable that is categorical (with 5 levels), and another variable that consists of either mean or sum scores (0 to 28) due to the way you have to calculate the scores of this measure. Can ...
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2answers
70 views

Help performing hypothesis tests automatically on a large data set in R

I have a data frame in R with 100 variables (columns) and 100 observations (rows). Each row is a patient; the columns are different variables such as gender, height, body-mass index, etc. I know that ...
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1answer
65 views

Test GLM model using null and model deviances

I've built a glm model in R and have tested it using a testing and training group so am confident it works well. The results from R are: ...
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1answer
26 views

Is Chi-square the right test to use when comparing multiple proportions

In my analysis, I have 4 groups: FLU-P (symptoms with virus) FLU-N (symptoms without virus) HCY-P (healthy with virus) HCY-N (healthy without virus) I am looking at the level of antibody ...
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18 views

Is Chi Square the best way to go

I am trying to compare two sets of variables and not certain what analysis is best. I have a variety of demographics for the subjects (independent) to compare to a set of yes/no responses ...
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22 views

Analyzing Proximity Pattern Data in Gorillas

I have a whole bunch of data about proximity patterns between 2 gorillas (distance in meters, taken during set time intervals). I'm interested in comparing the differences in proximity between the 2 ...
2
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1answer
26 views

Distribution of Ratio of 2 Chi-squared

If the limiting distribution of $X_n \sim \chi^2(k)$ and $Y_n \sim \chi^2(j)$ would their ratio $X_n/Y_n$ also converge to a chi-squared limiting distribution, or would it follow the normal because of ...
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32 views

Which statistical test to use to establish different behaviour between groups?

I have got a dataset with a dichotomous groupid variable and many other independent categorical variables. My aim is to find out if subjects in first group behave differently than subjects in second ...
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1answer
26 views

chi-square test of independence

I am trying to do a chi-square test of independence on two samples of counts. You can download the data from here (just click the "download" button): http://www.wikiupload.com/XFEGRHE8B0ECSJU ...
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4 views

Chi-Squared 2 ordinal variable how to sum up categories in R? [migrated]

I'm completely new to statistics and just wrestle with testing some data I recently collected. The picture below shows you the kind of material I'm having. For the first test I just want to run a Chi ...
2
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1answer
30 views

Simulated chi-square distribution doesn't match theoretical

Can someone explain why the distribution of Chi-square values I'm getting (using Pearson goodness-of-fit test) doesn't match the expected Chi-sqaure distribution? The test seems in this case to be ...
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1answer
31 views

Testing Whether a Binomial Distribution Fits Data

I have a sample from a discrete distribution as such: Type: 0 1 2 3 4 5 Occurrences: 88 12 52 43 21 5 My task is to test whether ...
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18 views

Can the chi-squared be used to test monthly means for two time series?

Can chi-squared test be applied to compare two continuous random variables but where instead of counts we split samples into groups and into cells of the table we put means for groups? In our case we ...
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25 views

Fisher's exact test for 3x5 contingency table in R with post-hoc? Consistently with using Fisher or Chi-squared?

I'm struggling with some (relatively simple) stats questions for some work I'm doing in R, and can't seem to find answers online... I have a factorial response variable of habitat type of a species ...
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42 views

Why is normality assumption so important (even for large N) for Chi-square test for the Variance

In my textbook i found the note that for a Chi-square test ($\chi = \frac{(n-1) \cdot s'^2}{\sigma^2}$) the assumption of a normal distribution in the population is very important - and much more ...
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75 views

Optimizing parameter estimates by minimizing chi^2 in iterative procedure

I need to minimize my Chi^2 (bottom-left in figure 1) by adjusting parameter-values in a MLE-procedure (or something alike). The chi^2 (red) is a goodness-of-fit measure. It expresses how well the ...
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13 views

Chi square test of independence with multivariate nominal data

I used a list-type open-ended question to collect responses, in which respondents can list up to 6 items. After coding the items, I have the multivariate nominal data. I want to check if my IV ...
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1answer
39 views

Chi-square test on a sample from population having an unequal distribution

I got a sample with an unequal gender distribution ($30$ males to $200$ female). This distribution is quite "representative" for the population the sample is taken from. Nevertheless, in a paper, ...
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46 views

Uncorrelating correlated $\chi^2$ distribution

This question is related to my previous question in here So I was trying to simulate correlated $\chi^2(1)$ random variables given the desired co-variance matrix. However, it seems like the only ...
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1answer
22 views

Outliers and chi-squared goodness of fit

Do outliers lead chi-squared tests of goodness of fit to fail?
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11 views

Comparing proportion of categories in samples of different sizes

Maybe this is a very simple procedure, but I have been trying to find the appropriate method and I am getting confused. I have data from two different surveys. In the first survey (s1) there were ...
2
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1answer
34 views

Chi squared goodness of fit test

I have a dataset and I want to show that it has lognormal distribution by using estimated logmu and logsd of it by MLE. I have read about making dat into bins by using predetermined intervals, but I ...
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1answer
50 views

Power analysis on chi-squared test with low cell counts

I am hoping to perform a chi-square test of independence on data in a 2x2 contingency table with the following values: ...
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16 views

Goodness-of-fit test by Pearson's chi-squared test for bimodal normal distribution

Consider I have estimated the following parameters for two modes inside a vector of numbers: m1,s1 m2,s2 m is mean s is standard deviation I want to use ...
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Should I split my independent variable into 2 groups?

I want to study if atheists/non-believers are having a harder time gaining results from 12-step facilitation treatment for alcohol dependence. My hypothesis is that a higher degree of belief in ...
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17 views

Taking into account population size differences in chi-squared test

I have a group of patients who live in London. They come from the 33 London local authorities and I want to know whether there is any significant variation in where they live. In other words, I want ...