# Questions tagged [f-distribution]

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

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### Asking about the meaning of abbreviation f(1, 78)

Please I have a thesis defense and I wrote from this article this number f(1, 78) but I don't know what it refers to Can anyone clear it up for ME? THANK YOU
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### Why we use the number of params as degree of freedoom in the F test for regression?

In a linear regression, we can assume that $\frac{(SSD_y - SSR)/p-1}{SSR/(n-p-1)}$ have a $F$ distribution if the null hypothesis $Ho$ is true, with $SSR$ being the sum of residues of the regression ...
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### How to produce operating characteristic curve for ANOVA using Python Scipy?

I am not very proficient in statistics so the problem I am currently having can be possibly a trivial one. I would like to reproduce operating characteristic curves for ANOVA from Douglas C. ...
1answer
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### how to understand the logic of null distribution

In a statistics textbook I read the following about comparing two population variances by using independent samples: If a null hypothesis (stating that the ratio of two population variances is 1) is ...
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### F test for linear regression - why only upper tail

In linear regression when considering the f test for slopes be it MLR or SLR, we only consider the upper tail probability for the p value. Here's a video for reference: link. Why is that? EDIT: as ...
1answer
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### Prove that $Z = \frac{X_1}{X_2}$, has an F-distribution

Let $X_1, X_2$ be independent random variables following density law $f(x) = e^{-x} , 0 < x < \infty$, Show that $Z = \frac{X_1}{X_2}$, has an F-distribution. I thought of solving this by ...
2answers
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### Prove that $P(X \le a) + P\{Y \le \frac{1}{a}\} = 1$

Prove that if $X$ has the F-distribution with $(m, n)$ d.f. and $Y$ has the F-distribution with $(n, m)$ d.f., then for every $a > 0$, $$P(X \le a) + P\left\{Y \le \frac{1}{a}\right\} = 1$$ I ...
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### Why do we get different f-statistics for the ANOVA of two models in R if we add third model

For example, using the mtcars built-in dataset. A two-model ANOVA: ...
4answers
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### Why doesn’t a $F$-statistic of 1 result in a $p$-value of about 0.5?

I’ve been presented with the following chain of reasoning. In an ANOVA, if the null hypothesis is true the F-statistic is expected to be about 1. A p-value is the probability of obtaining test ...
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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 ...
1answer
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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) ...
1answer
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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 ...
1answer
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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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### 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 ...
1answer
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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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### The behaviour of the critical F per F distribution

I noticed that, for increasing degrees of freedom of the MSE (Mean square error / denominator in the F-ratio), the critical F declines. This is also the case for increasing degrees of freedom of the ...
2answers
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### When should an F-test be one sided vs two sided? [duplicate]

If we increase both numerator and denominator degrees of freedom of the F distribution, then the pdf narrows down on the value 1. This suggests that a two-sided test is reasonable: If we have high ...
2answers
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### What is the median of the non-central F ratio distribution

I am looking for a simple approximation to the median of the (simply) non-central F distribution with parameters dlnum, dldenominator, and ncp, the non-centrality parameter. Clearly, there is no ...
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### Help: Quantile tables and hypothesis testing

Information about the data For this study, I would like to statistically test how the total length of sparrows affects their survival. Consider here one of the characteristics of the sparrows ...
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### How to choose critical F value from statistical tables when the df is large? [duplicate]

For an F(2, 237) distribution, how should I determine a critical F value from a statistical table? Would I look up (2, 150) or (2, 300)? Should it simply be the closest degrees of freedom?
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### Prove f statistic in ANOVA multiple regression equals t statistic in linear regression

To clarify what I mean, let's say we have these two models fit.1<-lm(Output~Input1) fit.1.2<-lm(Output~Input1+Input2) Running ...
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### In inferential statistics, is the noncentrality parameter of the F-distribution simply the F-value 'in the population'?

I'm writing functions (in R) that allow working with the $\omega^2$ distribution (the effect size for analysis of variance; the less biased alternative to $\eta^2$)....
1answer
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### Why can I not see in the distribution functions that t^2=F?

I keep reading that $t_{(v)}^{2} = F(1,v)$. Given the context that a t value was computed for a parameter of a linear regression, I was under the impression that there are two possibilities to ...
1answer
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### How to manually calculate values to make an F-distribution Table?

I'm kind of stats noob, so appreciate any help. I'm writing a program in iOS (Swift) to work out ANOVAs and I want to know if values from the F-Distribution tables could be calculated manually, ...