# Questions tagged [f-test]

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

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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 ...
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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: ...
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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 ...
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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 ...
18 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 ...
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### F-test and T-test [duplicate]

if the f-test for my dependent variable is significant. however, the t-test for my independent variable is insignificant. Does that mean I reject the null hypothesis? my hypothesis: is if hiv is found ...
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### 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 ...
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### Relationship between F (Fisher) and R^2

Could you give me the demonstration with all algebraic steps of the relationship $$F=(R^2/(p-1))/((1-R^2)/(n-p))?$$
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### 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 ...
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1 vote
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### 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 ...
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### 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 ...
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### 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 ...
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### Should I pick a linear model that has a higher F-Value or lower number of variables used?

My first model: ...
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### 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 ...
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### 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. ...
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### How is F_test calculated in causality in R

As you know there are several packages in R that we can detect the presence of Granger causality between two time series. I am using the causality package which gives me the value of F_test, df1, df2, ...
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### How to compare variances of multiple independent variables (to themselves) pre vs post treatment to determine treatment efficacy?

I have 10 different subjects and observations of their blood pressure before and after treatment. Treatment occurred at different times and at different ages in the subjects lives. I'm interested in ...
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### Understanding FE explanatory power

I am trying to understand what is going on in terms of the additional variation explained by my fixed effects. The set up is as follows. I have a a data set of roughly 3929 firm acquisition events ...
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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 ...
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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://...
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### Is it fair to compare variance across two different datasets?

I'm working with two data from two studies where weights were measured in two types of mice A and B. Group A's mean weight is about 20g vs 40g for Group B. Group B has a larger standard deviation/...
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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 ...
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### Interpretation of default Type III Sums in Squares in R

Many posts (i.e. here and here) discuss how the Type III sums of squares produced by car::Anova() in R are incorrect or nonsensical under R's default model parameterization, "contr.treatment"...
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### Chi square test negative difference

I am currently running a chi square test and my values from the hypothesised model are 65.387 on 24 df and I want to compare the results to another nested model which values are 28.535 on 8 df (28.535-...
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### Linear regression: F-test for lack of fit (using ANOVA to test regression model) - intuition?

This is the data set: https://raw.githubusercontent.com/FlorinAndrei/misc/master/stackexchange_attach/normtemp.csv I'm looking at a simple linear regression. The data is quite trivial. ...
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### F-test and Wald test in time series

Assume we have the time series $X_{1,t}$ and $X_{2,t}$ where $X_{i,t}=(x_{i,1},...,x_{i,T})$. We build two models as (Assume the time series are weakly stationary): \begin{align} X_{1,t}=\sum_{\...
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### F-test and violated assumptions

I am researching the effect of parameters on energy consumption. To determine the effect of parameters, I want to use the R Studio's F-test. In this way I want to investigate if the model with the ...
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### Interpreting test statistic from testing $\sigma_1^2 = \sigma_2^2$

I am running through a past test paper; The question (simplied) goes as follows - the university has had a number of 10-pin bowling ball games over the years. Participants Jeremy and Jonathon want to ...
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### Is the F test in ANOVA a likelihood ratio or Wald's one?

I'm trying to figure out, if the F test in ANOVA is the Wald's test or LRT? I learned, that the LRT compare nested models and "assess" the reduction in residual variance. This would justify ...
1 vote
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### How to compute minimum sample size of a simple linear regression model with given statistics values

Suppose the statistics values are given as follows: $\sum_{i=1}^{n}x_i, \sum_{i=1}^{n}y_i, \sum_{i=1}^{n}x_iy_i, \sum_{i=1}^{n}x_i^2,\sum_{i=1}^{n}y_i^2$ Firstly, we can compute the regression ...
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### ANOVA table in R: F-value does not "match the math"

I was playing around with a simple linear models when I noticed that, in the ANOVA table, the ratio MSreg/MSres does not exactly correspond to the F-value. Indeed, the two values are very similar but ...
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### F-test value in significance test for Linear Regression; what is the value when R^2 is equals 1?

What is F-test value in significance test for Linear Regression when $R^2$ is equals 1?
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### Significance test if R-squared ($R^2$) is significantly different from 1 (or some number very close to 1)

I am trying to find a way to test if a R-squared value that is high (>90%, on a small sample of c30 observations) is not significantly different from 1 (or at least from a number very close to 1, 0....
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### Different tests for model fit

I saw that in linear regression models one often uses a hypothesis z- or t-test for $R^2$ or for effect sizes. A z-Test is only useful if the standardized $R^2$-values are standard normally ...
1 vote
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### Are partial F test and student test the same for one parameter?

In the context of a multiple linear regression, is applying a partial F-test on the significance of a single parameter equivalent to applying a student test on this parameter?
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### Non-parametric joint difference in means between groups

Background: I want to test the difference in means between two groups along multiple variables. The approach I know is to run a regression where the group variable defining the populations is the ...
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### Correctly specify nested error structure for a split-plot ANOVA

I would like to check we are thinking about an approriate model structure for an experiment we have run, and whether I have specified this correctly in R. I have data from an experiment using plants ...
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### p-value adjustment/correction on main effects & interactions (F-tests / ANOVA)

I performed 8 ANOVAs on the same subjects with different dependent variables. We tested the significance of each term & interactions using F-tests (ANOVA). A reviewer asks us if we have applied ...
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### Is there such a thing as a paired-samples F-test?

I have paired data (from a pre/post-test) for which I assume that the variance differs between groups (again between pre/post). Visually, this assumption appears to check out and there is less ...
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### Comparing nested regression models on multiple data sets

Suppose we have two nested models $M_1(p_1)$ and $M_2(p_2)$ where $p_1$ and $p_2$ are the parameter sets of the models. Consider that $M_1$ is a restricted version of $M_2$ so $p_1$ set is a special ...
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### Test for overall significance of regression when the variance of errors is known

Say we want to test the overall model adequacy in a multiple linear regression model: $$H_0: B_1 = B_2 = ... = 0$$ $$H_1: B_j \neq 0 \text{ for at least one j}$$ the random errors $\epsilon$ are ...
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### How to know which group out of multiple has higher variance?

I am looking at different species of plants are established in different locations with different environmental variables. I want to see if some species are established in locations with wider values ...
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### Checking whether improvement is significant

I am looking to compare if there is a significant improvement between two test trials. As a background: some time ago as a practise I created a simple app aimed at improving pressure force accuracy. ...
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### Derivation of Distribution for the Robust F-statistic

This question is motivated by the question here. That question asked about the formula for a robust F-statistic. I am aware of the formula. My question is how to prove the distribution of the test ...
1 vote
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### Negative F-test value comparing two nested models

I am comparing two non-linear nested models - let me call them model A and model B. Model B has one parameter more than model A, i.e. model A can be obtained as a special case of model B. These two ...
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### Appropriate statistical test: 2 groups, 2 measures, one measure in common

Group 1 does measure A and measure B. Group 2 does measure A and measure C. A, B, and C are all on the same scale (say 1-100). What's the appropriate test if I want to compare means on A, B, and C? I'...
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### Unclear if my p-value from my ANOVA analysis makes sense

I am working with a sample of data for three different groups, and the times they spent in a line at Store B. The groups are A, B, and C, and I want to determine if those three groups' mean time spent ...
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### Distribution of the F-statistic of a Wald test

On the Wikipedia page for the Wald test, there is a derivation for the test statistic under multiple hypotheses. The derivation ends in an F-distribution. I am curious about the final step in that ...
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### F - test to compare two nested models [duplicate]

I want to fully understand how F test is used to compare two nested models. Every information I found about it, is only standard use i.e. to compare model with model containing no variables. How I ...
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Let's imagine that we have three variables - $Y, X_1$ and $X_2$, where $Y$ is dependent continuous variable, $X_1$ is continuous variable and $X_2$ is discrete variable with two factors - $0$ and $1$. ...