Questions tagged [f-distribution]
The F distribution is a continuous probability distribution which is commonly used in statistical testing procedures.
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Power Analysis with Noncentral F distribution
I'm looking to replicate a power analysis for binary data using an MRMC analysis (details found here). The data looks like this, where Score is a binary variable.
...
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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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1answer
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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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141 views
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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137 views
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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2answers
1k views
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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432 views
Cook's Distance Cutoff based on F(p,n-p)
I am struggling to understand (or find) justification for using certain Cook's Distance cut offs for identifying outliers. I've looked around Cross Validated here and here specifically, but haven't ...
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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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1answer
226 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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1answer
62 views
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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1answer
983 views
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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1answer
650 views
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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1answer
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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)}}$$
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1answer
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A question about Two-Sample poisson test [closed]
I read this paper: "Experiment Size and Power Comparisons for Two-Sample Poisson Tests", Wei-Kei Shiue and Lee J. Bain,
Journal of the Royal Statistical Society. Series C (Applied Statistics),
Vol. ...
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1answer
83 views
Confusion about greater variance in the numerator for F ratio
I am studying about F ratio and how, as a random variable, it follows F Distribution. So let me explain what confuses me.
This is what the theory says -- We draw two random samples $sample_x$ and $...
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Compute a quantile of F distribution?
I'm looking for the meaning of this definition of $q$, found in a chapter on non-linear regression.
"$q=q_{1-\alpha}^{F_{p,n-p}}$ is the $(1-\alpha)$ quantile of the $F$ distribution with $p$ and $n-...
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2answers
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Proof that F-statistic follows F-distribution
In light of this question : Proof that the coefficients in an OLS model follow a t-distribution with (n-k) degrees of freedom
I would love to understand why
$$ 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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227 views
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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1answer
46 views
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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1answer
678 views
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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1answer
91 views
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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1answer
72 views
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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1answer
276 views
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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259 views
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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1answer
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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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1answer
354 views
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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1answer
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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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1answer
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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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551 views
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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1answer
161 views
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 ...
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1answer
10k views
Relationship between F and Student's t distributions
According to Wikipedia, $Y\sim F_{1,v}$ has an F-distribution if $Y=X^2$ and $X\sim t(v)$ has a Student's t distribution. The proof of this makes sense to me. But I don't understand the relationship ...
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2answers
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F-distribution of data in Matlab
I have F = 1x44100 vector in Matlab. Based on how this was calculated, we have predicted that this fits the F-distribution with 16 degrees of freedom for both numerator and denominator.
I am really ...
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2answers
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Probability that one sum of squared standard normals is greater than a constant times another such sum
Let $Y_1,Y_2,..., Y_n$ $i.i.d$ $\mathcal{N}(0,\sigma^2)$ random variables and $n>4$. Find the probability $\mathbb{P}\{Y_3^2 + Y_4^2+ ... + Y_n^2 \geq \alpha ( Y_1^2 + Y_2^2)\}$ for $\alpha >0$....
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1answer
401 views
Why do we make a F-Test rather than a Beta-Test in ANOVAs?
When one performs an ANOVA, (s)he always end up calculating the observed F-ratio and comparing it to the appropriate F-distribution. From this post, I discovered that the coefficient of correlation $r^...
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1answer
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Which distribution should I use when building a GAM in R?
What type of distribution would you consider this data to be? My first thought is an f-distribution, but I suppose it could also be a poisson distribution. I am trying to build a generalized additive ...
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1answer
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What is a “log-F” distribution?
Recently I have encountered the Wiener-Granger causality test. The statistic which is used is the logarithm of the ratio of two residual variances. It is well known that the ratio of two such (...
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1answer
241 views
“Under the ANOVA null, within group and between group sample variance are both estimates of the pop. variance” — why only under the null?
In Statistical Methods by Snedecor and Cochran, it states something to the effect of "the within-group variance is an estimate of overall variance given the null hypothesis"
and this point is used to ...
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1answer
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Using R to calculate qt (t-dist) using qf(f dist) help?
I am having quite some trouble using R to calculate, say, qt(0.975,6) using qf instead of qt. I know the relationship between the t-distribution and the f-distribution which I understand as follows:
/...
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1answer
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Find the degrees of freedom of a F distribution given its 97.5th percentile
Let's suppose I have a F distribution $f$ with unknown degrees of freedom $df_{numerator}=df_{denominator}=df$.
If I know the 97.5th percentile $f_{0.975}$ such that $P(f>f_{0.975})=0.025$, is it ...
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3answers
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In ANOVA, if the null hypothesis is true is the expected value of F guaranteed to be 1?
By null hypothesis is true I mean that the means of each group is the same at population level.
I am wondering whether the expected value would depart from 1 in the case that the variances of the ...
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0answers
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Computing the F-ratio under null hypothesis
Statistical model for a Completely Randomized Design:
$$y_{ij}=\mu+\tau_{i}+\epsilon_{ij}\quad i=1,2,\ldots,a;
j=1,2,\ldots,n$$
where,
$y_{ij}$ is the $j$th observation of $i$th treatment effect
$...
