Questions tagged [f-test]

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

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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 ...
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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 ...
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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 ...
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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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Are the level-level and log-log models nested?

In my Econometrics Textbook, It says that an F-test (RESET test in this case) can be used to check for misspecification in the following models: $$ Y = \beta_{0} + \beta _{1}x_{1} + \beta _{2}x_{2} + \...
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Comparison of two staircase test series means and standard deviations

In a staircase test, each specimen is tested in a sequential way. It starts by testing a first specimen at a first stress level to find if it fails before a certain number of test cycles. For the next ...
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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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3 votes
1 answer
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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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Testing whether dividing independent variable into groups is rational

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 $1$. ...
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How should I proceed to know relationship of a specific response variable with proposed multiple predictor variables?

For a research project I am working on I am trying to determine if there is a positive relationship between two predictors and a response. My current model is: Salary = B0 + B1 Cost + B2 SchoolType + ...
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1 answer
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Standard convention for test statistic for F-test?

According to my textbook, Mathematical Statistics with Applications 7th. Ed, they write the test statistic in a F-test, that compares variances of two different populations, so that the larger ...
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Is there an extension to the F-test?

I'm new to statistics but I come from a mathematical background. So while learning about the t-test, which compares sample means, and the f-test which compares variances is was wondering if there is ...
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How to see regression F-test as comparison of sample variances?

F-test is designed for comparison of variances of two samples. In one-way ANOVA, it can be simply interpreted like that: $$F = {\text{explained variance} \over \text{unexplained variance}}$$ I was ...
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Test if regression coefficients are equal between periods of time

I have multiple observations per year and I was asked to estimate an individual regression line for each year within a single model. My data has three years (1979, 1980 and 1981) and two independent ...
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Evaluating K-Means with Percentage Variance Explained on non-normal data

Hi have Poisson distributed data which I am running an unsupervised K-Means algorithm on. I was doing some research on this site, and found this page which discusses K-Means on non-normal data, ...
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F-test for time series

I have a problem and I'm not sure how should I approach it. So I have a time series with a autocorrelation, but without any seasonality. And I notice that standard deviation increases after some ...
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Are ANOVA/F-tests valid for time-series data?

All of this may be based on some really bad premises: Say for example I a continuous variable A that is a possible predictor of an event E occurring or not. I want to form a hypothesis that is useful ...
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Correct formulation for getting the F-test, p-value

I am reviewing some code that is used to calculate the efficiency of the elecitrical distribution companies in Denmark. In short, this method measures all the companies up against each other, and then ...
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When in the F-test the restricted and unrestricted regressions both have independent variables, must they be the same ones?

I've been given a task related to F-tests, in which I'm asked to explain why regression (1) is a restricted version of (2). However, the independent variables are transformed for regression b. As an ...
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Estimating the number of degrees of freedom for an F test

I have a question regarding how to estimate the number of degrees of freedom for an F-test as discussed in the following image. In this paper (https://rmets.onlinelibrary.wiley.com/doi/abs/10.1002/...

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