# Questions tagged [chi-squared]

Use this tag for questions about (1) distributions of a sum of squares of independent standard normal random variables or (2) statistical hypothesis tests with such a sampling distribution if the null hypothesis is true.

187 questions
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### Test goodness of fit for weighting samples

There are N samples $x_1, x_2, ...,x_N$ for random variable $X$. I know Pearson's chi-squared test can be used to figure whether X follows uniform distribution. First, discretize the range of $X$ ...
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### What is an intuitive explanation for how the t-distribution, normal distribution, F-distribution and Chi-square distribution relate to each other?

What is an intuitive explanation for how the t-distribution, normal distribution, F-distribution, and Chi-square distribution relate to each other? Could anyone explain this clearly with a sensible ...
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### Making chi-square distribution out of unknown CDF [duplicate]

Suppose that the random variables X1,..., Xn are independent, and each random variable Xi has a continuous c.d.f. Fi. Also, let the random variable Y be deﬁned by the relation Y = −2∑(i=1~n) log Fi(...
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### Deriving the Chi-squared distribution using characteristic functions

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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### Can we conclude that the advertising technique has an impact on sales?

The impact of three different advertising techniques is being studied by a marketing firm. Sales, in thousand dollars, categorized in four groups are shown for each advertising technique for 200 ...
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### $\chi^2$-test for smoothing splines: degrees of freedom

Suppose we are given raw data, e.g. raw mortality rates $\widetilde{q_x}$, which are graduated by a smoothing (cubic natural) spline $S$. That is, we obtain smoothed rates by setting $q_x:=S(x).$ Let ...
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### sub-exponential property of a linear transformation of independent random variables

I need to use a Bernstein-type bound to a random variable $y^Ty$, where $y^Ty= Qx$ is a linear transformation of independent variables $x$. I don't consider $y$ to be an independent variable. So to ...
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### Changing the null hypothesis: Chi-Square test for Independency/ Homogeneity on a g x 2 table

My Goal is summarize the prerson statistic (Goodness-of-fit, Homogeneity and Independency). I want to know how and why the test works. For this I've read a lot of papers, including the original paper ...
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### How to proper determinate the number of degrees of freedom using the Pearson Chi-Square test?

Introduction and notation My Goal is summarize the prerson statistic (Goodness-of-fit, Homogeneity and Independency). I want to know how and why the test works. For this I've read a lot of papers, ...