Questions tagged [f-test]

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

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29 views

anova from R: output and interpretation of F-Tests

These question have been asked in many different ways as you can see here or here; however much of this topic is still beyond my understanding. Let us consider a model having response variable $Y$, ...
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Test for equality of variances same as testing for equality of means under specific conditions

I stumbled on the quirk given below. I am working on two implementations, one to test for equality of means using the t-test and another testing for equality of variances using Brown-Forsythe's F-...
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Is an f-test the correct method for power analysis of my multivariate regression data?

I have been working on solving a problem that requires power analysis to be run in order to determine if the subset of data that we're running analysis on is sufficient before we do the analysis. I ...
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likelihood view of F-test

Suppose I observe independent $X, Y$ where $X/\sigma^2 \sim \chi^2(\nu_1,\delta)$ and $Y/\sigma^2 \sim \chi^2(\nu_2,0)$, where $\sigma^2$ is some nuisance parameter. (The notation $\chi^2(\nu,\delta)$ ...
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Understanding Relationship Within the F Test

When conducting a one-way ANOVA, the _______ the between-treatment variability is when compared to the within-treatment variability, the _______ the value of FDATA will be tend to be. a. smaller, ...
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Linear Regression: P-values of t-test of significance of regression coeficients are same as p-values of F-test about submodel

Suppose we have regression problem: $$Y = \beta_{0}+\beta_{1}X_{1} + \beta_{2}X_{2} + \epsilon \text{, } \epsilon \sim \mathcal{N}(0,1),$$ where $X_1 \sim U(0,1)$,$X_{2} \sim U(1,2)$, and we suppose ...
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488 views

How can the F-test reject the null hypothesis while the KS test does not?

Suppose I have two datasets, $\mathbf{a}$ and $\mathbf{b}$. I want to test whether the two datasets are different in a statistically significant way. To compute the F-test, I take the ratio of the ...
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hyp test: constant return to scale with Squared and interaction terms

I want to test if constant return to scale applies to my production function (modelA): log(y) = log(x1) + log(x2) + log(x1)^2 + log(x1)*log(x2) I have tried the following in r, but iam not sure if ...
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F-Test vs Independent Samples T-Test

If I have two samples from different populations and I would like to know if there is enough evidence to conclude that some particular relation. Ex. The IQ level is affected by the amount of fluoride ...
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101 views

Multiple linear regression, partial F-Test

I had seen many formulas out there and I hardly knew how to solve this exercise. Where it consists of: Enter link data set for the question I use $X_2,X_7\; and \;X_8$ Using the partial F test, ...
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Difference in Significance for a T and F test

After conducting a one way ANOVA, an F-test indicates that I should retain the null hypothesis (no two means differ), but the t-test (in line with the theory) tells me that the groups I tested are ...
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38 views

What good is an F-test and is using it as a test for significance of independent variable worth it?

An F-test may lead to the conclusion that a predictor is significant by an F-test low p-value. This is because while an independent variable like smoke (below) is statistically unimportant (high p-...
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31 views

Given two samples from N with known variances how to find probability that one sample's variance is two times larger than the other?

I have two samples with sizes 9 and 11 drawn from two independent normal distributions with variances 21 and 37 respectively. How can I find the probability that the variance of the first sample is ...
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23 views

Extremely High T-Test P-Value but Extremely Low F-Test P-Value

So I'm running a logistic regression on a binomial variable in R and came out with the following model. ...
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R-squared unbiased when F-test is biased in heteroscedasticity?

If R2 and F-statistic are in functional relationship, is it possible, that in case of heteroscedasticity F-test is biased but R-squared is not?
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When the linear term of a variable is insignificant, is it reasonable to use an F-test to state that they are jointly statistically significant?

I am running a multiple regression that takes the following simplified form (there are other variables not important to this question): $$Y_{it}=\beta_0+\beta_{1}X_{it}+\beta_{2}X_{it}^2+u_{it}$$ $Y_{...
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Do we use Sequential Sum of Squares or Adjusted Sum of Squares for Partial F test in Regression?

I would appreciate a detailed answer. Thank you.
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Clarification on equal variance vs unequal variance t-test

In unequal variance t-test (Welch t-test): $$H_0 = \text{No difference in means, but variance can differ}$$ $$H_1 = \text{Two sample means are significantly different}$$ I don't see the point of ...
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Testing joint-significance - no SSR

I am doing some revision for an exam in Econometrics...and I think I should possibly repeat as I am stumped on a past exam paper question, making we wonder if I learnt anything. It gives an equation ...
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Comparing means in bins of different sample sizes

Suppose I have the following 2 plots showing the mean of a variable on a 2-d spatial grid, as well as the occurrence histogram (see bottom). Is there a specific way to compare these means, even ...
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514 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 ...
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F test (joint significance) for two parameters

I want to test for the joint significance of two parameters (dcca1 and dccb1) estimated from a multivariate DCC GARCH model. does anyone know how to do it using R? any help is greatly appreciated.
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275 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 ...
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98 views

How do I compare the predictive power of two predictors within a single (logistic) regression?

I've read about how F-tests can be used to compare models and to decide whether an additional variable should be included in the regression. However, I want to test whether A vs. B are better ...
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59 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 ...
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In the F test, is a two-sided test mainly used?

I have a question about the F test. In R language, three parameters "two.side", "less" and "greater" can be specified as arguments of var.test (). However, I can not specify a one-sided test like "...
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21 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 ...
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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} \...
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F test, Model selection test

How to compare which of the following two models is a better fit: M1 $y$ = $\alpha$$X$ + $\epsilon$ M2 $ln(y)$ = $\alpha$$X$ + $\epsilon$ Can we run a test statistic to compare the two models? ...
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54 views

Two sample T test frequency table

I am struggling with a data analysis. I have made a survey and got the following answers in the first turn, I put them in a frequency table Don't agree at all: 8 Don't agree: 6 I don't know: 16 ...
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OLS: why is it possible to get insignificant F-test but resonably high adjusted R-squared?

I am estimating an OLS regression with 158 observations and about 140 regressors (some unstructured data features to personality measure). Below is the bottom output I get from OLS. Some of the ...
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Permutation F test for nested models

How can I do a permutation F test for testing if a larger model which contains a larger model is better? e.g. Model 1 : y ~ x1 + x2 Model 2 : ...
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I have an insignificant beta weight of a predictor, which the only predictor in a step with significant R-square change and significant F-value

I am running a hierarchichal multiple linear regression with 4 steps containing theoretically justifyable variables: Outcome: pain rating Step 1: demographic variables (age, gender) Step 2: Pain ...
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51 views

Interpreting ANOVA f-test for model comparison

In the book ISLR, there's a lab activity which compares the nested models. ...
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1answer
141 views

What is the point of a permutation F-test when all you need is one F-test for one-way ANOVA?

Say you have three groups, and each group has 5 observations. You can figure out if there is a significant difference between means with a simple one-way ANOVA. I read in my nonparametric book, one ...
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232 views

What is the difference between the residual, lack of fit and pure error In F test for Regression Analysis?

What is the difference between the residual, lack of fit and pure error and how to calculate each of them in ANOVA F test for nonlinear regression?
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1answer
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Is it possible to calculate F-value for a neural network regression model?

I trained a model using neural network regression and used the F-value equation that is used for calculating F-value for linear regression: F=(SUM(Ypredicted-Ymean)^2/p)/(SUM(Ypredicted-Yobserved)^2/...
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F-test in multiple linear regression

I'm currently reading Introduction to statistical learning. When trying to prove the collective significance of a regression linear model, we use the F-test with the following formula. $$F=\frac{(TSS-...
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1answer
29 views

Test for ratio of variances across multiple groups

I am looking for a statistical test for whether the ratio of variances vary significantly among groups. I have 100 groups, each with ~50 A individuals and ~50 B individuals (n varies somewhat between ...
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1answer
75 views

Alternative to Chow test in the case of heavy tailed residual distribution

I would like to check if two subpopulations of my data have the same parameters in a model. Model 1 is based on subpopulation 1 and Model 2 is based on subpopulation 2. Model 1: $y=x^\alpha + \...
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F test fails but t-test does not? [duplicate]

I'm a bit confused about this. I have a model with multiple variables trying to explain the dependent variable. When I use the F test, I don't pass the critical value. But when I seperate the ...
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1answer
169 views

Testing nested models with clustered errors

I have a simple linear model. $$Y_i = \beta_1X _{1i}+ \beta_2X_{2i}+\beta_3X_{3i}+\epsilon_i$$ I'd like to test if some of my model parameters ($\beta_2$ and $\beta_3$) are jointly different from ...
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What is the point in reporting the z statistic of a z-test?

In my field some authors report the z statistic of a z-test in a generalised linear model and others do not. Does reporting the z statistic serve any purpose if the p value of a z-test or of a post-...
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Can I mix and match F-test and T-test code when I implement a program for some statistical calculations?

I was told to rewrite an old java program that performs some statistical calculations. I was able to solve most of the problems until I ran into this one: The program compares two sets of data over ...
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140 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 ...
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Test the difference between average value of 2 random variables

I am doing an exercise on marketing analysis to determine the strategy that a brand should follow based on historical weekly data collected from supermarkets that sell the brand (let say brand1) and 4 ...
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Why is it possible to get insignificant F statistic (p>0.1) but significant regressor t-tests (p<0.1)? [duplicate]

My results show significant t-tests but an insignificant F-test. Is this possible or are my calculations wrong?
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Is this an appropriate way to compare simulated and measured data with small sample size, and are there alternatives?

I have a probably fairly basic question which I couldn't find an answer to on here or anywhere else. Would really appreciate any thoughts on this :) I am modelling the propagation of sound through a ...
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Can an F-Test be worse than the two single T-Tests? [duplicate]

Normally when conducting an F-Test one is hoping the F-Test of all variables is significant although the single T-Tests yield insignificant results. But can the reverse also be true? That is a worse ...
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Is the F-test (especially in stepwise regression context) problematic for huge datasets?

Let's say I have a huge dataset with 2000 observations. I want to test the significance of one predictor in a SLR Model. Then the F-statistic effectively becomes: F = $\frac{\frac{\sum{(\hat{Y_i}-\...

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