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

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27 views

What distribution has this non-central Chi-Squared -like moment generating function?

I'm new here so please criticize errors! My moment generating function looks like this (after some tidying): $E[e^{wY(t)}] = \frac{1}{\left(1-2\theta(t) w\right)^{k/2}} ...
2
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1answer
16 views

Describing the target audience for a set of movies

I have several observations with both categorical and numerical variables relating to the personal details of surveyed individuals (such as age, gender, education and region inside the country they ...
3
votes
1answer
63 views

How to test for a statistically significant difference between 3 percentages?

I have samples of stories from three newspapers, all testing for the same proportion of stories with a certain characteristic. The data I have is: np1=16.34%, np2=14.00%, np3=18.29%. I want to ...
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0answers
13 views

How do I check whether my data fits exponential or lognormal or weibull using chi square and ks tests in R?

I'm a newbie to R language and I need to quickly find whether a set of data I have in a CSV file fits the three distributions Generalized exponential, log normal and Weibull. I need to test it using ...
2
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0answers
21 views

G-test vs Pearson's chi-squared test

I'm testing independence in an $N \times M$ contingency table, I don't know which of the G-test or Pearson's chi-squared test is the best ? The sample size is in the hundreds but there are some low ...
3
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2answers
50 views

Understanding the direction & strength of a correlation, & causal status, from a chi-squared test

I am analyzing Stack Overflow Posts. So I have a database with 1000000 questions, their current score (upvote or downvote) and a flag, that there is a source code part in the question (or not). So I ...
0
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0answers
17 views

how to use the likelihood ratio test for model selection in the study with several subjects

In my study, I have 30 subjects, for each subject, I use likelihood ratio test to compare two models (nested logistic regression), and I get a chi-squared value and a p value like the result shown ...
0
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1answer
43 views

constant $times$ distribution

I know that if $U\sim\chi^2(k)$ then $aU\sim \Gamma(k/2,2a)$ for $a>0$. But i read about the estimator and its distribution $$\hat{\sigma}_k^2=\frac{1}{2k}\sum_{i=1}^k ...
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1answer
38 views

Moment-generating function (MGF) of non-central chi-squared distribution

I need to compute the moment-generating function of the non-central chi-squared distribution, but I have no idea where to begin.
2
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1answer
42 views

When doesn't the chi-squared statistic follow the chi-squared distribution?

When we do a chi-squared test (to test goodness of fit or the dependence of two variables), we assume that the the chi-squared statistic follows the chi-squared distribution. Shouldn't we first ...
0
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0answers
41 views

Z-test and confidence intervals for mutual information

Given two discrete random variables $X,Y$, I would like to obtain confidence intervals for the Mutual Information $I(X;Y)$ and a p-value for the null-hypothesis that $X,Y$ are independent. I would ...
3
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1answer
49 views

Deegrees of freedom of Student's distribution

I'm trying to figure out the distribution of this statistic: $$S=\frac{\frac{\overline{X}-\mu_0}{\sigma / \sqrt{n}}}{\sqrt{\hat{\sigma}^2/\sigma^2}}$$ Where: $\overline{X}=\frac{1}{n} \sum_{i=1}^n ...
10
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0answers
143 views

Degrees of freedom of $\chi^2$ in Hosmer-Lemeshow test

The test statistic for the Hosmer-Lemeshow test for goodness of fit of a logistic regression model is defined as follows: the sample is split into $d=10$ deciles, $D_1, D_2, \dots , D_{d}$, per ...
0
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1answer
24 views

Chi Square Statistic - Which variable should be defined as the dependent variable?

I am stuck with this very basic question which I need to answer using SPSS for the problem set pasted in cursive below. Any pointers in the right direction would be very much appreciated. Thank you. ...
1
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1answer
29 views

How does the $\chi^2$ test tests the overall fit of a structural equation model?

I understand the $\chi^2$ test tests the model fit based on the comparison between the observed and null covariance matrices. Can someone explain to me how to compute the null matrix?
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20 views

Chi-square approximation in homogeneity

I am interested in testing homogeneity in mixture of Gaussians (testing no mixture vs. 2 populations) given that we know the weights of the two distributions. We can first use MLE to estimate the mean ...
1
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1answer
14 views

determining significance between counts in a chi square test?

I wish to know if there is a statistically significant difference between generational cohorts (Boomers, Gex X, Gen Y) using the frequency in which subjects selected a particular leadership quality as ...
2
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0answers
23 views

Comparing means of two samples, one with 2million+ samples, other with only 200

I have two sets of data and a metric associated with each of them, I want to see if one category of data (e.g. males) have a tendency to have ahigher metric associated with it than the other category ...
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0answers
27 views

Chi-square/G-test/Fisher exact with replicates

I want to use Fisher exact or G-test/Chi-squared (the choice depends on the numbers of observations in a particular case) to test difference in species frequencies between and within replicated groups ...
0
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0answers
21 views

Finding the Significant Differences (with p-values) in a 4x2 Chi-Square Table Using SPSS

In short, I would like to learn how to discover where the significant differences lie within a 4x2 Chi-Square table and report the significant findings with a p-value, preferably using SPSS. Setup: ...
1
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1answer
47 views

Find confidence interval via pivotal quantity?

Suppose $X_1, X_2, ..., X_n$ is a random sample from a population with pdf $$f(x|\theta) = \dfrac{1}{2\theta}e^{-|x|/\theta},x\in \mathbb{R}$$ The pivotal quantity is $\frac{2}{\theta}\sum_{i=1}^n ...
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0answers
12 views

Post-Hoc Chi-Sq test - conclusions drawn from comparing individual categories

My question is very similar to this one: (Post hoc $\chi^2$ test with R), but I'm still confused, and tried to provide as much detail as possible. I have two categories of students: Domestic and ...
0
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0answers
14 views

Pearsons Chi Squared and z-score question [duplicate]

1) I have a list of who is short or not in a group(by using binary 0,1).I also have a list of where each case is located in region. If I do crosstabs for the calculate the percentage of short(1) in ...
0
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0answers
27 views

Pearsons Chi Squared and z-scores question

1) I have a list of who is short or not in a group(by using binary 0,1).I also have a list of where each case is located in region. If I do crosstabs for the calculate the percentage of short(1) in ...
0
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0answers
16 views

How is the confidence interval of variance component calculated?

How is the confidence interval of variance component calculated ? As far I know , confidence interval of variance is calculated as : ...
0
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1answer
39 views

Quick reality check: using correlation and Chi-square for hypotheses testing

I have two ordinal values on a 5 point Likert scale, let's say "Would you like flowers?" and "Would you like to go out to dinner with me?". My hypotheses is that there is a relationship between the ...
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0answers
10 views

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 ...
3
votes
1answer
40 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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1answer
26 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. ...
0
votes
1answer
15 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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0answers
16 views

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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0answers
29 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 ...
0
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1answer
52 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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0answers
32 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 ...
0
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0answers
27 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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0answers
17 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 ...
0
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1answer
25 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 ...
1
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0answers
12 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 ...
0
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0answers
49 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 ...
1
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1answer
80 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 ...
1
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1answer
20 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 ...
1
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1answer
35 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 ...
0
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0answers
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 ...
0
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0answers
9 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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0answers
11 views

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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2answers
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
32 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). ...
3
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2answers
174 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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4answers
83 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?
2
votes
2answers
62 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: ...