# Questions tagged [f-distribution]

The F distribution is a continuous probability distribution which is commonly used in statistical testing procedures.

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### Connection between t and F distributions [duplicate]

We have: $Z\sim N_{0,1}$ (standard normal distribution) , $U\sim X^2_{k}$ ($X^2$ distribution, with k df) with $Z \bot U$ Then $X = \frac{Z}{ \sqrt{U /k} } \sim t (k)$ (t-distribution, with k df) I ...
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### In an F distribution, when would the first parameter, d1, ever be greater than the second parameter, d2?

It seems that when running an ANOVA, the degrees of freedom of the mean sum of squares between groups (SS_b) will always be less than or equal to the degrees of freedom of the (summed for all groups) ...
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### Confidence interval bounds for BIN(1,p)

Consider the confidence interval bounds (p L , p u ) for BIN(1, p). In this caseT =ΣXi ~ BIN(n, p) is sufficient for p. To apply the cdf pivoting method, solve pbinom(t; n, p U) = α/2 1 − pbinom(t −...
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### Does Hotelling's T-Squared test assume multivariate normal or all marginally normal?

Does doing hotelling's t-squared test assume our data is multivariate normal or just all the variables themselves are marginally normal? Thanks!
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### F-Distribution: difference between the expected value for a random variable and the expected value of its inverse?

It is known that the expected value of the F-Distribution depends only on the degrees of freedom associated with the Chi-square random variable in the denominator. In other words, E[1/X] does not ...
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### Expected value of the F-Distribution dependent on the degrees of freedom associated with the Chi-square random variable in the denominator?

0 The F-Distribution has a Probability Density Function that can be defined as: with an expected value of: What would be a logical explanation for why the expected value only depends on the ...
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### F distribution definition with gamma function or square root [closed]

On wikipedia (https://en.wikipedia.org/wiki/F-distribution) I see the pdf of F distribution defined using squared root function, while other places I see the pdf defined with the gamme function. E.g ...
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### Korn and Graubard Confidence Intervals for complex survey data

NHANES has posted a tutorial for recommendation of analysing their data. They suggest using the Korn and Graubard confidence limits and provide the equations below.(The hyperlink to the NHANES ...
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### Finding cumulative probability for F distribution

If Degrees of Freedom is 2 & 27, what would be cumulative probability for finding F-statistic higher than 1? Below are possible options. Option 1: 0.456 Option 2: 0.852 Option 3: 0.762 Option ...
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### t-student or f-distribution?

I am reading 'Applied multivariate statistical analysis' by Richard Johnson and I do not understand that first to explain this test, talks about the t-student distribution. And then out of nowhere he ...
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### Relationship between an F-distribution random variable and its invert regarding the power calculation

I am reading something about the sample size calculation and have a question about the relationship between an F-distribution random variable and its invert: For X ~ F(n, m), and 1/X ~ F(m, n), why ...
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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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### From expected value of R2 in Regression to expected value of partial eta squared in ANOVA

In general, $R^2$, the estimator of "multiple correlation coefficient" in regression, is known to be positively biased. Given $K$ predictors, and $N$ total sample size, Johnson, Kotz, & ...
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### Derive the distribution of the ANOVA F-statistic under the alternative hypothesis

Say we have $k$ samples of data, where sample $i$ is of size $n_i$ and we write it as $x_{i1}, ... , x_{in_i}$. Let the total sample size be $N$. The ANOVA model is $X_{ij} \sim N(\mu_i, \sigma^2)$ ...
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