Questions tagged [f-distribution]
The F distribution is a continuous probability distribution which is commonly used in statistical testing procedures.
94
questions
-1
votes
1answer
42 views
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
0
votes
0answers
7 views
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 ...
0
votes
0answers
10 views
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. ...
-2
votes
1answer
34 views
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 ...
1
vote
2answers
65 views
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 ...
2
votes
1answer
178 views
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 ...
3
votes
2answers
119 views
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 ...
0
votes
0answers
29 views
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:
...
4
votes
4answers
153 views
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 ...
asked Sep 7 '20 at 5:15
user1205901 - Reinstate Monica
10.7k22 gold badges73 silver badges148 bronze badges
1
vote
0answers
22 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
248 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) ...
1
vote
1answer
46 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
48 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
168 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
1k 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
75 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 ...
2
votes
0answers
32 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:
$$
Y_{ij} = \mu + U_j + R_{ij}, \qquad var(Y_{ij}) = \...
0
votes
1answer
96 views
Ratio of Standard Deviations from a Normal Distribution to an F Distribution
Apologies if the title is confusing, I couldn't think of a more apt title.
I have that $W_i$s are iid $N(\mu_a,\sigma_a^2)$ and independent of $Z_i$s which are iid $N(\mu_b,\sigma_b^2)$. This means
$...
0
votes
1answer
244 views
ratio of 2 chi square to get f-distribution
How can I use two chi square functions to make a f function? I only see invchisquare functions in some languages when I need to use an inv f-dist to get the exact binomial CI. So, looking to figure ...
1
vote
1answer
22 views
$F$-test with a variance being $C$ times as large as the other
I am familiar with $F$-tests in which the alternative hypothesis is defined as $H_a=\{\sigma^2_1/\sigma^2_2>C\}$ (the sign "$>$" can be either "$<$" or "$\ne$" as well), where $C=1$.
If I ...
2
votes
1answer
62 views
How to interpret $F > F_{\rm crit}$, but $p > \alpha$
My F is greater than F critical, while P-Value is 0.99 greater than alpha (0.05) which one should I consider the P value or F statistic, rejecting the Ho:
I am confused.
Edit:
$$
\begin{array}{ccc}
\...
5
votes
2answers
127 views
Why is this statistic F-distributed?
A book I'm reading claims that the statistic:
$\frac{(RSS_0 - RSS_1) / (p_1 - p_0)}{RSS_1 / (N - p_1 - 1)}$ has an F distribution. Why is this? I know that an F distribution is something like $\frac{\...
1
vote
0answers
27 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-...
5
votes
1answer
137 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
881 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
168 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
26 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
6k 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
119 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
137 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 > ...
0
votes
0answers
30 views
Link between Fisher and Chi-squared
I am fairly new to statistics, and during practice, i used this link between Chi-squared and F-statistics where F equals to ration between 2 Chi squared distributions. Can someone elaborate more on ...
2
votes
1answer
394 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
78 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
32 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
147 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,\...
1
vote
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 ...
0
votes
1answer
144 views
Can you perform an inverse F-test on two datasets with the same degrees of freedom?
Stats newbie here.
Is there any meaning to the critical F value if the two samples have the same degrees of freedom?
For example, I have 2 sets of data, each with the same number of degrees of ...
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
8k 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
87 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)}}$$
2
votes
1answer
396 views
A question about Two-Sample poisson test [closed]
I read this paper: "Experiment Size and Power Comparisons for Two-Sample Poisson Tests", Wei-Kei Shiue and Lee J. Bain,
Journal of the Royal Statistical Society. Series C (Applied Statistics),
Vol. ...
0
votes
1answer
238 views
Confusion about greater variance in the numerator for F ratio
I am studying about F ratio and how, as a random variable, it follows F Distribution. So let me explain what confuses me.
This is what the theory says -- We draw two random samples $sample_x$ and $...
0
votes
0answers
722 views
Compute a quantile of F distribution?
I'm looking for the meaning of this definition of $q$, found in a chapter on non-linear regression.
"$q=q_{1-\alpha}^{F_{p,n-p}}$ is the $(1-\alpha)$ quantile of the $F$ distribution with $p$ and $n-...
25
votes
2answers
8k views
Proof that F-statistic follows F-distribution
In light of this question : Proof that the coefficients in an OLS model follow a t-distribution with (n-k) degrees of freedom
I would love to understand why
$$ F = \frac{(\text{TSS}-\text{RSS})/(p-1)...
2
votes
0answers
298 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
54 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
210 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 ...
3
votes
0answers
359 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
56 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, ...
