Questions tagged [f-distribution]

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

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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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Asymptotic distribution of intraclass correlation

Consider the random effects ANOVA model below (notation based on Snijders and Bosker, 1999), where $j$ represents a group and $i$ an individual: $$ Y_{ij} = \mu + U_j + R_{ij}, \qquad var(Y_{ij}) = \...
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Ratio of Standard Deviations from a Normal Distribution to an F Distribution

Apologies if the title is confusing, I couldn't think of a more apt title. I have that $W_i$s are iid $N(\mu_a,\sigma_a^2)$ and independent of $Z_i$s which are iid $N(\mu_b,\sigma_b^2)$. This means $...
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Convergence of F distribution

I am trying to solve the following exercise: Let $W = (X/Y)((p-k)/k) \sim F_{k,p-k}$, where $X$ and $Y$ are distributed as chi-squared with $k$ and $p-k$ degrees of freedom, respectively. Suppose ...
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Why does G*power calculate the noncentrality parameter in this way?(different from formula)

I'm calculating the power of some F-family tests and I found the key to the power was the noncentrality parameter (ncp). So I'm trying to calculate the ncp $\lambda$. However, I got different results ...
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ratio of 2 chi square to get f-distribution

How can I use two chi square functions to make a f function? I only see invchisquare functions in some languages when I need to use an inv f-dist to get the exact binomial CI. So, looking to figure ...
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$F$-test with a variance being $C$ times as large as the other

I am familiar with $F$-tests in which the alternative hypothesis is defined as $H_a=\{\sigma^2_1/\sigma^2_2>C\}$ (the sign "$>$" can be either "$<$" or "$\ne$" as well), where $C=1$. If I ...
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How to interpret $F > F_{\rm crit}$, but $p > \alpha$

My F is greater than F critical, while P-Value is 0.99 greater than alpha (0.05) which one should I consider the P value or F statistic, rejecting the Ho: I am confused. Edit: $$ \begin{array}{ccc} \...
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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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What is Cov(X,Y) when X,Y is a F-distribution (a,b) and (c,d) ,in case X,Y Not independent [closed]

I want to know Covariance of random variable between $X$ and $Y$ when $X$ is a F-distribution with degree of freedom $a$ and $b$ and $Y$ is a F-distribution with degree of freedom $c$ and $d$,in case $...
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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 ...
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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 ...
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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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Tail bounds for F-distribution (not using $\chi^2$ bounds)

Are there any sharp tail bounds for an $F_{p,q}$ distribution? That is, if $X \sim F_{p,q}$, then for a $t_1,t_2 > 0$, what are the sharpest $\delta_1$ and $\delta_2$ known such that $$P(X > ...
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298 views

Simulate CDF of sum of i.i.d. F distributions

I have trouble on simulating the CDF of a random variable Y, where $Y = \sum_{i=1}^{12} X_i$, and $X_i$ are i.i.d. F-distribution. I am doing this in MATLAB, the problem is that small instance of Y ...
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Finding value of F distribution without special calculator or table?

When performing a t-test, the calculation of p-values related to this are given as: Is there a way to find $F(.)$ using a t-distribution table or a normal distribution table? (i.e. without a special ...
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Distributions of variance and mean

I am adding this again with details as suggested The following questions were asked. State if true The test statistic for the difference of population variance follows an F-distribution The test ...
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Inverse of a (singly) non-central F variable

It is known that if $X \sim F_{\nu_1,\nu_2}$ (F distribution with degrees of freedom $\nu_1$ and $\nu_2$), then $X^{-1} \sim F_{\nu_2,\nu_1}$. Is there any known similar result for $X \sim F_{\nu_1,\...
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How does one calculate the F-value-threshold used to evaluate an F-test?

I am studying Response Surface Methodology (by Myers, Montgomery, and Anderson-Cook). When introducing the significance testing for regression parameters, an $F$-test is introduced but only partially ...
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Convergence of F(n,n) distribution to normal

Suppose that $X \sim F(n,n)$, an F distribution on $n$ and $n$ degrees of freedom. I'm trying to figure out why some literature state that $X$ converges in distribution to a normal distribution. My ...
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What do you do if your degrees of freedom goes past the end of your tables?

The degrees of freedom in my F table don't go up high enough for my big sample. For example, if I have an F with 5 and 6744 degrees of freedom, how do I find the 5% critical value for an ANOVA? What ...
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F-Distribution formula

How did we get this formula? Can you explain it with visualization if possible? $$\text{Using properties of f distribution } f_{(1-\alpha), (\nu_1,\nu_2)} = \frac 1 {f_{\alpha, (\nu_2,\nu_1)}}$$
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A question about Two-Sample poisson test [closed]

I read this paper: "Experiment Size and Power Comparisons for Two-Sample Poisson Tests", Wei-Kei Shiue and Lee J. Bain, Journal of the Royal Statistical Society. Series C (Applied Statistics), Vol. ...
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Confusion about greater variance in the numerator for F ratio

I am studying about F ratio and how, as a random variable, it follows F Distribution. So let me explain what confuses me. This is what the theory says -- We draw two random samples $sample_x$ and $...
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Compute a quantile of F distribution?

I'm looking for the meaning of this definition of $q$, found in a chapter on non-linear regression. "$q=q_{1-\alpha}^{F_{p,n-p}}$ is the $(1-\alpha)$ quantile of the $F$ distribution with $p$ and $n-...
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Proof that F-statistic follows F-distribution

In light of this question : Proof that the coefficients in an OLS model follow a t-distribution with (n-k) degrees of freedom I would love to understand why $$ F = \frac{(\text{TSS}-\text{RSS})/(p-1)...
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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 $\eta^2$)....
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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 ...
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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, ...
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How can one produce many `p-values` in regression analysis?

In order to understand ANOVA and regression better, I read this: http://www.theanalysisfactor.com/why-anova-and-linear-regression-are-the-same-analysis/ It seems to make sense for the most part. The ...
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What could the null hypotesis be in the case of a $F-$test for two $\chi^2$s coming from two fits of the same data?

I report one of the definiton of Fisher's $F$ Suppose that $\chi^2_A$ has the chi-square distribution with $\nu_A$ degrees of freedom and $\chi^2_B$ has the chi-square distribution with $\nu_B$...
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Udacity claims that the F-distribution peaks at 1, but Wikipedia has counterexamples. Which is true?

Here's a transcript of the first minute, though you may watch the video here: The F distribution is positively skewed, meaning it peaks on the left side and is stretched off to the right side. ...
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What is the null distribution of the between-group variance?

Scenario From a population, we randomly sample $n$ individuals, measure the normally distributed random variable $X$ and compute the total variance $V_T$ of $X$ in this sample. Then, we randomly ...
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How do I find the expected value of F(isher)-distribution

$E(F)=\int xf_{k,m}dx$ where $f_{k,m}(t) = \Gamma(t)=\frac{\Gamma((k+m)/2)}{\Gamma (k/2)\Gamma(m/2)}k^{k/2}m^{m/2}t^{k/2 - 1}(m+kt)^{-(k+m)/2}$. How do you find $E(F)$? Say you have to convert $x*f(k,...
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Does the F-test for multivariable regression work with non-normal residuals but large sample size?

Suppose I am building a multiple regression model, perhaps with 5 explanatory variables. Suppose the residuals are not normally distributed (based on a Q-Q plot and a D'Agostino test, due to kurtosis)....
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If we were given differences in variances, and power, find n?

If we have a given difference in the variances x and 80% power, how would you find the sample size needed to detect the difference in variances equal to x? I know that power = 1-P(type II error) but I ...
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Why is F used for an unspecified distribution?

I'm taking a linear regression course in university right now, and my professor often uses the notation F to refer to a generic, unspecified distribution with the given mean and variance. For example, ...
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CDF of the ratio of two correlated $\chi^2$ random variables

It is well known that the sum of a series $m$ of squared standard independent normal random variables follows a $\chi^2$ dstribution with $m$ degrees of freedom. It is also true that the ratio of two ...
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How to Calculate F distribution given R squared? [duplicate]

After some research, I find that the relationship between $R^2$ and the F distribution is as follows: $$ R^2 = 1 - (1 + F \cdot \frac{p-1}{n-p})^{-1} $$ But I am not sure what the $p$ and $n$ values ...
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For F-distribution, find df1 and df2 given mode of PDF and height of PDF at mode?

Are there closed form equations to find the degrees of freedom of an F-distribution (df1 and df2), given the mode of the PDF and the height of the PDF at the mode? We can assume df1 > 2. If the ...