Questions tagged [f-distribution]
The F distribution is a continuous probability distribution which is commonly used in statistical testing procedures.
85
questions
1
vote
0answers
21 views
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 ...
1
vote
1answer
29 views
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) ...
0
votes
0answers
9 views
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 −...
0
votes
0answers
4 views
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!
1
vote
1answer
37 views
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 ...
1
vote
1answer
36 views
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 ...
1
vote
0answers
59 views
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 ...
0
votes
0answers
20 views
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 ...
0
votes
0answers
388 views
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 ...
1
vote
1answer
51 views
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 ...
0
votes
0answers
12 views
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 ...
2
votes
0answers
19 views
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:
$$
Y_{ij} = \mu + U_j + R_{ij}, \qquad var(Y_{ij}) = \...
0
votes
1answer
52 views
Ratio of Standard Deviations from a Normal Distribution to an F Distribution
Apologies if the title is confusing, I couldn't think of a more apt title.
I have that $W_i$s are iid $N(\mu_a,\sigma_a^2)$ and independent of $Z_i$s which are iid $N(\mu_b,\sigma_b^2)$. This means
$...
0
votes
0answers
130 views
Convergence of F distribution
I am trying to solve the following exercise:
Let $W = (X/Y)((p-k)/k) \sim F_{k,p-k}$, where $X$ and $Y$ are distributed as chi-squared with $k$ and $p-k$ degrees of freedom, respectively.
Suppose ...
0
votes
1answer
106 views
ratio of 2 chi square to get f-distribution
How can I use two chi square functions to make a f function? I only see invchisquare functions in some languages when I need to use an inv f-dist to get the exact binomial CI. So, looking to figure ...
1
vote
1answer
21 views
$F$-test with a variance being $C$ times as large as the other
I am familiar with $F$-tests in which the alternative hypothesis is defined as $H_a=\{\sigma^2_1/\sigma^2_2>C\}$ (the sign "$>$" can be either "$<$" or "$\ne$" as well), where $C=1$.
If I ...
2
votes
1answer
54 views
How to interpret $F > F_{\rm crit}$, but $p > \alpha$
My F is greater than F critical, while P-Value is 0.99 greater than alpha (0.05) which one should I consider the P value or F statistic, rejecting the Ho:
I am confused.
Edit:
$$
\begin{array}{ccc}
\...
1
vote
0answers
21 views
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-...
4
votes
1answer
120 views
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, & ...
2
votes
1answer
524 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 $X_{ij} \sim N(\mu_i, \sigma^2)$ ...
2
votes
0answers
157 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 $...
1
vote
0answers
24 views
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 ...
3
votes
2answers
4k 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 ...
3
votes
2answers
103 views
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 ...
3
votes
0answers
95 views
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 > ...
2
votes
1answer
328 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 ...
1
vote
0answers
71 views
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 ...
1
vote
0answers
31 views
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 ...
1
vote
1answer
131 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,\...
0
votes
1answer
2k 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 ...
5
votes
1answer
1k 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 ...
11
votes
1answer
5k views
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 ...
-2
votes
1answer
81 views
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)}}$$
2
votes
1answer
302 views
A question about Two-Sample poisson test [closed]
I read this paper: "Experiment Size and Power Comparisons for Two-Sample Poisson Tests", Wei-Kei Shiue and Lee J. Bain,
Journal of the Royal Statistical Society. Series C (Applied Statistics),
Vol. ...
0
votes
1answer
147 views
Confusion about greater variance in the numerator for F ratio
I am studying about F ratio and how, as a random variable, it follows F Distribution. So let me explain what confuses me.
This is what the theory says -- We draw two random samples $sample_x$ and $...
0
votes
0answers
532 views
Compute a quantile of F distribution?
I'm looking for the meaning of this definition of $q$, found in a chapter on non-linear regression.
"$q=q_{1-\alpha}^{F_{p,n-p}}$ is the $(1-\alpha)$ quantile of the $F$ distribution with $p$ and $n-...
21
votes
2answers
7k views
Proof that F-statistic follows F-distribution
In light of this question : Proof that the coefficients in an OLS model follow a t-distribution with (n-k) degrees of freedom
I would love to understand why
$$ F = \frac{(\text{TSS}-\text{RSS})/(p-1)...
2
votes
0answers
209 views
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 ...
1
vote
0answers
45 views
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?
3
votes
0answers
189 views
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 ...
2
votes
0answers
301 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 $\eta^2$)....
1
vote
1answer
53 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 ...
3
votes
1answer
1k 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, ...
5
votes
1answer
103 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 ...
2
votes
1answer
98 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
$\nu_B$...
5
votes
1answer
360 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. ...
1
vote
0answers
324 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 ...
3
votes
1answer
1k views
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,...
3
votes
1answer
853 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)....
0
votes
1answer
18 views
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 ...
