Questions tagged [f-test]

Any hypothesis test in which the statistic has an F distribution under the null hypothesis.

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21
votes
2answers
2k views

How to test equality of variances with circular data

I am interested in comparing the amount of variability within 8 different samples (each from a different population). I am aware that this can be done by several methods with ratio data: F-test ...
16
votes
2answers
4k views

Why is F-test so sensitive for the assumption of normality?

Why is the F-test for difference in variance so sensitive to the assumption of normal distribution, even for large $N$? I have tried to search the web and visited the library, but none of it gave any ...
13
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3answers
51k views

Why do we use a one-tailed test F-test in analysis of variance (ANOVA)?

Can you give the reason for using a one tailed test in the analysis of variance test? Why do we use a one-tail test - the F-test - in ANOVA?
12
votes
2answers
16k views

Difference between selecting features based on “F regression” and based on $R^2$ values?

Is comparing features using F-regression the same as correlating features with the label individually and observing the $R^2$ value? I have often seen my ...
12
votes
1answer
1k views

Sample size formula for an F-test?

I am wondering if there is a sample size formula like Lehr's formula that applies to an F-test? Lehr's formula for t-tests is $n = 16 / \Delta^2$, where $\Delta$ is the effect size (e.g. $\Delta = (\...
11
votes
4answers
554 views

What is the relationship between ANOVA to compare means of several groups and ANOVA to compare nested models?

I've so far seen ANOVA used in two ways: First, in my introductory statistics text, ANOVA was introduced as a way to compare means of three or more groups, as an improvement over pairwise comparison, ...
8
votes
1answer
1k views

Mean comparisons following multiple imputation

I need to do some simple mean comparisons between groups (basic ANOVA F-tests) on data with missing values. I use the mice package in R for multiple imputation, but I can only pool results for the ...
7
votes
2answers
3k views

AR(q) model with F-test

I am wondering that if we have an AR($q$) model for time series: $$X_i=\beta_1X_{i-1}+..+\beta_{p}X_{i-p} + \beta_{p+1} X_{i-p-1} +...+\beta_{q} X_{i-q}+\epsilon_i,\epsilon_i \;\text{iid}\; N(0,\...
7
votes
2answers
16k views

How to interpret the confidence interval of a variance F-test using R?

I'm trying to understand the confidence interval returned by the function var.test() in R. More specifically, the confidence interval returned by var.test() is not the one I find when doing the ...
7
votes
2answers
1k views

“One-tailed” Levene Test

F-tests can be two-tailed (to test that $s_1^2 \ne s_2^2$) or one-tailed (to test that $s_1^2 > s_2^2$). How can I modify Levene/Brown-Forsythe to be "one-tailed", that is, to test $s_1^2 > s_2^...
7
votes
1answer
1k views

Big difference between a t-test and a F-test in a mixed model (anova vs summary in lmerTest)

While helping someone else with their analyses, I've run into a question regarding the difference between t-tests and F-tests for linear mixed models in lme4 for R, as provided by lmerTest. I'm aware ...
6
votes
3answers
29k views

Prove F test is equal to T test squared

I need to show that F test is equal to T test squared, when the T test is for 2 independent groups and assuming variances are equal. I know that $F=\frac{MSB}{MSW}=\frac{SSB/k-1}{SSW/N-K}$ and I know ...
6
votes
1answer
135 views

Comparison of variance between two samples with unequal sample size

The primary goal of my analysis is to compare the variability in the response variable, Blood Pressure, between sample1 and sample2. The secondary goal is to test for a difference in means. I do not ...
6
votes
1answer
3k views

Comparing two F-test statistics

I have two groups A and B, each of which consists of 5 samples. Each sample is described in a vector of length (>1000) of continuous numeric values (characteristics). I want to test if the sample in ...
5
votes
3answers
6k views

Calculating the $p$-value of an $F$- statistic

I am trying to implement an algorithm for calculating $p$-values of $F$-tests and I need this method to be highly precise. It is easy to implement this with $z$- or $t$- tables, however I don't know ...
5
votes
1answer
2k views

What is an F test?

What is an F test and what does it show? Also what is an alpha, and how do I evaluate the p-value?
5
votes
1answer
3k views

F-test formula under robust standard error

I am attempting to write a program that will (among other things) use the F-test in multivariate regression under standard robust errors. I am having trouble finding a specific formula for the F-...
5
votes
2answers
830 views

F-Test for Equality of Variances with Weighted Survey Data

I would like to use an F-Test for Equality of Variances on a variable to compare two groups. Normally, this would be done with an sdtest command in Stata or a ...
5
votes
1answer
461 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^...
5
votes
1answer
6k views

Heteroscedasticity-consistent F-test

Why is the F-test for overall significance (OLS regression analysis) invalid when residuals are heteroscedastic? Is there a way to calculate it in a consistent way under heteroscedasticity? Is there ...
5
votes
0answers
583 views

F-test to determine whether more than two sets of data differ

Here is the context for my question: I understand that you can fit the same model to two different datasets separately and then fit the model to the datasets pooled together as a way to discern ...
5
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0answers
745 views

When to use likelihood ratio test vs. incremental F-test in nested nonlinear model selection?

I have two nested nonlinear models and I want to know which provides a better fit to some data. I see descriptions of both the likelihood ratio test and of the incremental F-test (also called the ...
4
votes
4answers
4k views

Both t-test and F-test are significant, do I report both?

I undertook a large study (N about 200 in both control and treatment) in which one of the user ratings is significantly different (p < 0.0001). When I ran the unpaired t-test, the F-test also ...
4
votes
3answers
888 views

Does the p-value in the incremental F-test determine how many trials I expect to get correct?

I've implemented an incremental F-test program that evaluates the fit of an unrestricted model $M_{UR}$ against the restricted model $M_R$ using the F statistic $\frac{SSE_{R} - SSE_{UR}}{SSE_{UR}}\...
4
votes
1answer
357 views

Is an F-test for equality of variance appropriate for a very large dataset?

I have a dataset with about 500,000 subjects and I am trying to establish whether the variance is equal. I first performed an F-test but then I realised the data is slightly skewed with kurtosis. So ...
4
votes
2answers
923 views

One-tailed F-test with one restriction

I have a regression, e.g. $Y=a+b_1X_1+b_2X_2+c_1Z_1+c_2Z_2+e$. Is it possible test the one-tailed null $b_1+b_2\leqslant c_1+c_2$ against the alternative $b_1+b_2>c_1+c_2$? Notice that this is an $...
4
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1answer
254 views

Am I getting something wrong? A question about a paper on the F-test

First, I'm sorry for the long post, but I needed a second opinion from you, the experts, about this problem! I was reading a paper by Gallagher (2006), where he puts an example on "how one may ...
4
votes
1answer
342 views

Multivariate Bayesian Testing with an F-test

In Bayesian statistics a standard way to perform a Lindley significance test for the hypothesis $\theta=\theta_0$, where $\theta_0$ is the suggested value for $\theta$ at the $\alpha$ level of ...
4
votes
1answer
5k views

Is F test used for feature selection only for features with numerical and continuous domain?

The F-statistic/test can be used for feature selection, e.g. from http://scikit-learn.org/stable/modules/generated/sklearn.feature_selection.f_classif.html#sklearn.feature_selection.f_classif ANOVA ...
4
votes
1answer
8k views

ANOVA Omnibus F-Test

I ran an ANOVA test on some data. The Omnibus F-test comes back with a P-value of 0.3726. I was taught that this means that none of the individual variables would show as significant. But one of my ...
4
votes
1answer
1k views

Is AIC appropriate for model selection when the parameters are fitted by least-squares rather than MLE

I want to compare the fit of a linear model (M1) and nonlinear model (M2): M1: $y = b_0 + b_1x_1 + b_2x_2 + b_3x_1x_2 + \epsilon, \epsilon \sim N(0, \sigma^2)$ M2: $y = b_0 + b_1x_1 + b_2x_2 + b_1 ...
4
votes
1answer
2k views

Kendall's coefficient of concordance (W) for ratings with a lot of ties

I have read that Kendall W should be avoided when it comes to deal with non-rankings especially for rating scales which tend to have a lot of ties. Yet posts here seem to suggest it for ratings. As ...
4
votes
1answer
842 views

Regression model F test on different response variables?

I am comparing two different models (multiple linear model). Basically the explanatory variables remain the same while response variable are different. $Model\ 1 - Y_1 = X_1+X_2+X_3$ $Model\ 2 - ...
4
votes
0answers
69 views

How to modify the f-test null hypothesis in ANOVA

Normally the null hypothesis for a f-test in ANOVA is $H_0:\mu_1=\mu_2=...=\mu_m$ for a comparison of $m$ groups. How do I alter the f-statistic so that the null hypothesis is $H_0:\mu_1=\mu_2=...=\...
4
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0answers
235 views

Wild Bootstrap F-test

Is anyone aware of code for a wild bootstrap F-test? Namely, testing joint significance of several coefficients where the standard errors of each coefficient are computed using a wild bootstrap. The ...
3
votes
1answer
6k views

Adjusted $R^2$ & F test are not shown in regression with robust standard errors in Stata

The adjusted $R^2$ is not shown when a regression with robust standard errors is calculated in Stata. This is surprising to me since the value of the $R^2$ is unaffected in regressions with robust ...
3
votes
1answer
7k views

Effect of sample size in F-test?

Having worked hard to understand the t-test, I'm rapidly falling out of love with it. All that is required in the t-test to gain significance is increase sample size, which renders it close to ...
3
votes
1answer
10k views

F test and t test in linear regression model

F test and t test are performed in regression models. In linear model output in R, we get fitted values and expected values of response variable. Suppose I have height as explanatory variable and ...
3
votes
3answers
64 views

Relation between F test and T test. Are they mutually exclusive?

I am studying Statistics for data science since few months.. 1)I am learning that, when we have to compare multiple samples (>2) then a T test would be tedious and instead we go for ANOVA and ...
3
votes
2answers
2k views

Goodness of fit. How to evaluate if polynomial of order n+1 gives statistically better fit than polynomial of order n?

I fit polynomials with increasing order to some data. What is the best way to evaluate if the additional parameter of polynomial of order n+1 provides a statistically significant better fit than the ...
3
votes
2answers
7k views

Is a partial F-Test on a model reduced by only one variable valid?

For a recent project, I used multiple linear regression to model data. I attempted to choose between my initial full model and a reduced model by performing a partial F-test. The models used were the ...
3
votes
1answer
9k views

Not-significant F but a significant coefficient in multiple linear regression

I have a regression with two continuous predictors and one dichotomous predictor in Model 1 and two interactions of each of the continuous predictors with the dichotomous predictor in Model 2. The ...
3
votes
1answer
51 views

groups, levels and denominator dof in mixed effect models

I am trying very hard (I am not a statistician) to understand the concepts of "groups" and "levels" in mixed effect models. In particular, I am trying to understand this in the context of the ...
3
votes
1answer
16k views

P-value of F-test to compare two variances (var.test in R)

I am trying to understand where the p-value of a F-test comparing two variances comes from. More specifically, the p-value given by R's var.test function does not ...
3
votes
1answer
110 views

Chi Square vs F Tests for GLM Model Comparisons

I've been creating some models in R using glm() and rxGlm(). I'm experienced in building GLMs but my memory of some of the ...
3
votes
1answer
2k views

Breusch–Godfrey test under heteroskedasticity

Do I need to account for heteroskedasticity when performing the (vector) AR1-2 test? The Autocorrelation (AR) 1-2 test is defined as follows - often referred to as the Breusch–Godfrey test (Wiki link)...
3
votes
1answer
3k views

t test vs. F test

In linear regression, I have heard that the t test is more versatile than the F test because the t test can test the null hypothesis $H_0:{\beta_1}=k$ for $k$ a constant, whilst the F test can only ...
3
votes
1answer
1k views

F-test in Regression and Crossvalidation

I am wondering what is the better measure of predictive power in a multivariate regression setting. So an F-test for regression tests "the utility of the model", or exactly, if any of the $\beta$ ...
3
votes
1answer
2k views

F test for equality of variances

I know that the test statistic is $$F=S_1^2/S_2^2 $$ But I am looking at some example questions from my lecturer and some have confused me. For example: For a certain game, individual game scores ...
3
votes
1answer
754 views

Why are different answers obtained for a regression F-test when using SSE and R2 formulas?

I cannot understand what I'm doing wrong with an F-test for the regression - I get completely different answers using SSE and R2 formulas. Unrestricted model: Restricted model: 1 restriction is ...