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Questions tagged [f-test]

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

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The F-test and the t-test reject the null hypothesis while the KS test and the Chi-Squared test do not

This is a follow-up question to How can the F-test reject the null hypothesis while the KS test does not?. Let's consider I perform the following tests: Two-sample Kolmogorov-Smirnov test (KS-test), ...
Ommo's user avatar
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Where can I find a Kolmogorov-Smirnov critical value table for an F-distribution? [closed]

I have developed an Excel model for a one-sample Kolmogorov-Smirnov test for an F-distribution. I have the K-S test statistic, but no CV to compare it to. If anyone knows of an online table of ...
Jim Robison's user avatar
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Can descriptive statistics of three ordered groups be converted into a correlation?

I know that a one-way ANOVA with two groups can be converted into a Standardized Mean Difference (SMD), that can, in turn, be converted into a Pearson correlation. Anyway, with two group means and ...
Federico Tedeschi's user avatar
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Using ANOVA for model comparison with a different ratio, how does it differ?

When we compare two models with ANOVA then we typically compute an F-score like $$F = \frac{\left(\frac{RSS_1-RSS_2}{p_2-p_1}\right)}{\left(\frac{RSS_2}{n-p_2}\right)}$$ where subscripts refer to the ...
Sextus Empiricus's user avatar
3 votes
1 answer
64 views

Using F-test for restricted model vs unrestricted, wrong answer

studying Econometrics I come across this question for which I cannot find the right answer: Assuming a percentage of household's expenses on food is linearly dependent on the total expenditure and ...
Aleksei P's user avatar
2 votes
2 answers
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F test to compare variances. How is ncp calculated to obtain the F distribution under the alt hypothesis?

Recently I needed to do a power analysis for a comparison of variance with a F test. In the past I used the OC curves from Edwin Crow's "Statistics Manual" Chart VIII to get beta. https://...
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Prove Wald statistic = number of linear restrictions times F statistics

I'm considering $F[J,n-k]= \displaystyle \frac{(e_{*}^{'}e_{*}-e'e) \backslash J}{e'e\backslash (n-k)}$, where $J$ stands for number of restrictions. I want to prove $W=(Rb-q)'(Rs^2(X'X)^{-1}R')^{-1}(...
Chang Henry's user avatar
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Is it possible to conduct an F test without fitting a restricted model?

Say I'm fitting the following regression: $$ Y = \beta_0 + \beta_1X_1 + \beta_2X_2 + \beta_3X_3 + \beta_4X_4 $$ If I was interested in testing the hypothesis that $\beta_2 = 0$, I know I can do things:...
mle_in_paris's user avatar
1 vote
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Help needed in recreating ANOVA test results from study

I am aiming to recreate ANOVA tests as part of Study 1 from the following research paper related to some psychological factors: https://doi.org/10.3389/fpsyg.2021.738447 There are altogether 80 ...
Fluellen's user avatar
6 votes
2 answers
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F-test for equality of variance for truncated normal distributions

I am fairly new to hypothesis testing. I read that the F-test for equality of variance doesn't work well for distributions that aren't normal. Does this test work for truncated normal distributions ...
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Relationship between f test and t -test [duplicate]

I am working on a problem where I should derive the t test statistic from an f test given an ANOVA table (below). From my understanding, when we conduct an f-test we are using the variance to ...
Harry Lofi's user avatar
4 votes
3 answers
410 views

Why do we use an F distribution instead of just chi-squared when testing multiple hypotheses from regression?

After estimating a multiple-regression using ordinary least squares (OLS), the classical test for joint significance of multiple variables is to run an F test using restricted and unrestricted ...
midnightGreen's user avatar
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F-statistics and paired t-test

I want to create a synthetic data set with $n = 3$ replicates for each of $a = 3$ groups such that the overall F - test rejects $H_0: µ_1 = µ_2 = µ_3$ at the $\alpha = 0.05$ level, but all three ...
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Can I use Breusch-Pagan test to a data that need correlation test later? or should I transform the data?

I did a homogeneity test using Levene test and the result said : "warning : in anova. lm(lm(resp~group)) ANOVA F-test on an essential perfect fit are unreliable" I want to test my data with ...
Nimas Pertiwi's user avatar
4 votes
1 answer
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Regression model not significant, but the predictor significant

I'm testing the hypothesis that variable $x$ predicts the variable $y$ AND that it predicts it when adjusted for other variables that have been shown to predict $y$ in the literature ($z_1$ to $z_5$). ...
CagYuk's user avatar
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1 answer
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Testing for a difference in $R^2$ with the same model but two different (equally sized) datasets

I have two datasets of the same size, $\{\vec{Y}_{1},\vec{X}_1\}$ and $\{\vec{Y}_{2},\vec{X}_2\}$. I fit the same regression model to both datasets and calculate the coefficient of determination from ...
Pablo's user avatar
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4 votes
1 answer
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Test if two curves have the same shape

I have a gene expression measured for 5 humans (7 different layers each: L1, L2, L3, L4, L5, L6, WM) and 4 chimpanzee (7 different layers each: L1, L2, L3, L4, L5, L6, WM). What I want to do is to ...
Claptar's user avatar
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11 votes
3 answers
555 views

What are the benefits of classical ANOVA F compared to Welch's F?

Is there a reason to report classical ANOVA F values (Fisher's F), instead of Welch's F-tests? I know Welch's F test is corrected, so that it's robust against heterogeneity of variance. This leaves me ...
foggy's user avatar
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Number of classes, and number of observations per class in ANOVA

Let's say we do a classical ANOVA F-test to reject or not reject the hypothesis: H0: $µ_1 = µ_2 = ... = µ_k$ with $k$ classes, and $n$ observations per class Are there ranges of $k$, $n$ for which the ...
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Why the F test is NA in R package Fect?

I am a new learner of Fect package in R, see https://yiqingxu.org/packages/fect/fect.html. I try to use method to do counterfactual analysis of my DiD. I use unbalanced panel data, and the Matrix ...
StarRiver's user avatar
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T-test vs. ANOVA [duplicate]

With two groups I can either perform ANOVA or T-test. Additionally I can have one-sided test, if I want to make sure I get the same conclusion from both tests and for t-test I choose alpha=0.05, I ...
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1 answer
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Difference between F-test and confidence intervals on variance estimates

Given n samples from a normally-distributed variable X, we estimate variance as $s^2=\frac{1}{n-1}\sum{(x_i - \bar{x})^2}$. We can also get a confidence interval for such a variance estimate as: $$...
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7 votes
4 answers
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Null hypothesis for ANOVA for regression

Context: I know the "classic" ANOVA framework: we have $n$ groups and $k$ measurements of a variable $X$ for each group. Let $µ_1$, $µ_2$, ..., $µ_n$ be the mean of $X$ in each group. ...
Basj's user avatar
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2 votes
1 answer
32 views

Calculate F test when restricting intercept term

Restrict the intercept term, i.e. In this case, I want to calculate F-test. The formula is as follows: How can I calculate SSR for restricted version? What is its formula? Thank you.
1190's user avatar
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1 vote
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F-Test J linear restriction

I am referring to the question here: Determining the Number of Restrictions in an F-test. But I want to derive a more general rule than counting the equality signs. If I denote the null hypothesis in ...
Marlon Brando's user avatar
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42 views

Understanding degrees of freedom of F-statistic in Linear Regression

I was reviewing linear regression and I wanted to dig deeper into the F test that many software suites provide. I am aware that many sources comment on the degrees of freedom, but I haven't really ...
rusiano's user avatar
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Got some wacky numbers doing a Student's t-test

For context, I am currently enrolled in a Quantitative Analysis course for chemistry at my university. We've been focusing on errors and statistical analysis to determine whether the random error is ...
WillAlmy's user avatar
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Comparison of variances: symmetric F-test is likelihood ratio test?

Suppose $X_i\stackrel{IID}\sim N(\mu,\sigma^2)$ for $i=1,...,n$, where $\mu$ is known. We want to apply the likelihood ratio test to decide between the hypotheses $$ H_0: \sigma=\sigma_0 \\ H_1: \...
No-one's user avatar
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2 votes
0 answers
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How to realise a two-sided Student's t-test for a slope coefficient (b)(raster) in R? [closed]

For a project, I have to analyse NDVI trends over times (between 2001 and 2020). My teacher asked me to use the same method as presented by Leroux et al. (2017) ( https://doi.org/10.1016/j.rse.2017.01....
Céline's user avatar
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1 vote
1 answer
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Can the F-test be used when comparing 2 groups? Why not use the t-test?

I recently read a paper and the authors run a survey experiment that had 4 groups, including a control group. The author writes the following: "The treatment about better responding to economic ...
chunguc1004's user avatar
3 votes
1 answer
124 views

Linear regression testing under constraints

Consider the following regression: $$Y_i = \alpha + \beta X_i + \epsilon_i.$$ I have to test the following hypothesis: $$H_0: \alpha = \beta = 0;$$ $$H_1: \alpha \geq 0, \; \beta \geq 0, \quad \alpha \...
Residual Claimant 's user avatar
3 votes
0 answers
35 views

Power analysis of a chunk test

I set up following chunk test in R: restricted Model <- DV ~ IV1 unrestricted Model <- DV ~ IV1 + IV2 + IV3 anova(restricted Model, unrestricted Model) ...
crobo's user avatar
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3 votes
1 answer
476 views

F-statistic decreases when adding variables

When adding control variables to my regression, the F-statistic decreases. Furthermore, when I add an interaction term, the F-statistic is reduced further. How do I interpret these regression results?
ines's user avatar
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How to make decision on a hypothesis if the p-values of t-test and F-test are not similar

I have to variables X (continuous) and Y (binary with two value 0 and 1). When I ran the t-test and F-test with critical value of 0.05, I got the following results ...
Nemo's user avatar
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1 vote
0 answers
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How to account for multicollinearity in a partial F-Test?

I am trying to setup a model in R. I want to test if strategies picked by different agents have a joint significant effect on the outcome. My idea was to create a partial F-Test: ...
crobo's user avatar
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1 answer
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Should you bootstrap when doing F-test on small sample

I want to conduct an F-test on a linear model with 5 groups each with around 20-25 samples. I know I could perform an anova() in R, but the residuals aren't quite normally distributed. If I perform a ...
Yeet's user avatar
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0 answers
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One-tailed hypothesis test of the difference between two population variances

My hypothesis is that the difference between two population variances is greater than X. Please note that I am not asking if the difference is equal to zero. The solution should also apply to the ...
Jim Robison's user avatar
1 vote
2 answers
93 views

Do we always use F test in multiple linear regression?

Since the F test deals with testing multiple categories/features/independent variables, do we always use a F test in determining if the independent variables are significant in multiple linear ...
Katsu's user avatar
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0 votes
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40 views

F test for model selection other than linear regression

I have tried googling this, but all results lead me to F-tests for model selection specifically for linear regressions (or even other non-model selection F-tests). Maybe I'm missing the right ...
Rafael's user avatar
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2 votes
1 answer
176 views

Relationship between F (Fisher) and R^2

Could you give me the demonstration with all algebraic steps of the relationship $$F=(R^2/(p-1))/((1-R^2)/(n-p))?$$
Bibi's user avatar
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3 votes
1 answer
186 views

How does variance-inflation factor creep into a chunk test?

In this question, the OP runs a “chunk test” and has a linear relationship between a variable in the restricted model and the variables in the chunk. If this were a chunk of just one variable, that ...
Dave's user avatar
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1 vote
1 answer
104 views

Can an F-test for Full vs. Reduced Model Always Be Trusted?

I am trying to compare two models: Costs = Income + Education1 + ... + Education10 and Costs = Income From the ANOVA table using anova() in conjunction with the corresponding lm() objects, I get that ...
Code Ike's user avatar
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3 votes
2 answers
100 views

Why is $R(X'X)^{-1}R'$ in the $F$-test for OLS coefficients invertible?

Let $b$ denote the OLS estimator, and assuming normality of the errors we get $b \sim \mathop{\mathcal N}\left(\beta, \sigma^2\left(X'X\right)^{-1}\right)$, where $X\in\mathbb R^{N\times K}$ is of ...
Zugzwang14's user avatar
2 votes
1 answer
473 views

How to calculate F-statistic given only coefficient, standard errors and confidence intervals in R [closed]

My output is a table of coefficients, together with standard errors and 90 % confidence intervals, nothing else. I miss the degrees of freedom but I do have the number of observations. How can I ...
Irazall's user avatar
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0 votes
1 answer
98 views

Should I pick a linear model that has a higher F-Value or lower number of variables used?

My first model: ...
Antonio's user avatar
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2 votes
0 answers
146 views

F-test for multiple directional alternative hypotheses?

Suppose we have the linear model for Y, with X1, X2 and X3 being continuous independent variables: Y = b0 + b1 * X1 + b2 * X2 + b3 * X3 + e To test H0: b1=b2=0 against H1: b1 or b2 or both are ...
BenP's user avatar
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1 vote
1 answer
202 views

Finding critical value for F statistic

I am performing a hypothesis test and therefore intersted in finding the F critical value for my F statistic. Below is the anova output when I compare two models. ...
Zhi Hao's user avatar
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0 votes
1 answer
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Notations in the statistical analysis of experimental research

I am very new to experimental setup and have recently started to learn about designing experiments and analyzing the results. In the papers that I read there are notations that I am unfamiliar with. I ...
amiref's user avatar
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6 votes
1 answer
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What exactly do Anova sums of squares represent in lmer models?

In a lme4::lmer model, the anova function returns an sequential analysis of variance table. As explained on page 34 of http://...
mjandrews's user avatar
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0 votes
1 answer
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Need equality of variance test between control and experimental conditions on a within subjects with replication dataset

I have some proteomics data of 16 biological replicate samples split between 8 control and 8 knockdown. One of the tests I wanted to do was to see if the knockdown impacts the variance of the protein ...
Fat Moe's user avatar

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