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 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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Sample size and power for an F-test with more than 2 samples
There is a known formula for calculating the minimum sample size for t-test:
$$n = \frac{\sigma^2 z^2}{m^2}$$
where $\sigma$ is the (expected) standard deviation in the population, $m$ the margin or ...
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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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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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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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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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Where do the degrees of freedom in the F-test come from?
In the context of a linear regression, say
\begin{align}
y_{i} & = \beta_{0} + \beta_{1}x_{1i} + \beta_{2}x_{2i} + \ldots + \beta_{k}x_{ki} + \epsilon_{i}
\end{align}
the F-test is
\begin{align}
...
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Why does overall-F-test is considering right tailed only?
I've seen this overall F-test several times, and when they compare F-statistics or $\alpha=5$% with its p-value always use right tailed, whereas the hypothesis is formualed as
$$H_0:\beta_0=\beta_1=\...
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Test to compare 5 subgroups with population parameter
I have 5 subgroups , A,B,C,D,E each have their own mean and standard deviation.
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Very confused by residual degrees of freedom in REML
I am trying to estimate a LMEM model with three fixed effects (two regressors and their interaction) and one random effect (a by-subject random intercept). Both regressors are dichotomous.
I'm using R'...
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Why is the sphericity assumption sufficient for the $F$ test in RMANOVA?
To the best of my knowledge, a one-way RMANOVA is typically formulated as
$Y_{ij}=\mu+\alpha_i+\beta_j+\epsilon_{ij}$
where $Y_{ij}$ is the response variable, $\alpha_i$ is the fixed time effect, $\...
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Is there an established way to quantify the number of parameters in a random forest?
I'm interested in applying an F-test to random forest regression models I've trained. The formula for calculating an F-statistic (found here: https://en.wikipedia.org/wiki/F-test) requires values for $...
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Repeated Measures ANOVA Tests of Within-Subjects Contrasts
Using the MIXED procedure and a set of repeated measures data of vertical format, I obtained the results of fixed effect estimates and related t-tests for orthogonal polynomial linear and quadratic ...
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Significance test testing whether one variance is larger than the other
I feel like I am missing a key link and this tasks is quite easy:
I am given the following averages and standard deviations:
$\bar{x}_1 = 971$, $s_1 = 42$, $n_1 = 1000$
$\bar{x}_2 = 983.9$, $s_2 = 60....
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Can a partial F test test a contrast
Suppose I have a model
$$y_i = \beta_0 + \beta_1 x_{1i} + \beta_2 x_{2i} + \beta_3x_{3i} + \epsilon_i \qquad (1)$$
Now I want to test $$H_0: \beta_2 = \beta_3$$
I know that I can use a Wald-type test ...
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Test statistic for regression analysis with robust standard errors
I am looking for the test statistic for a regression analysis (using lm in R) with robust standard errors. As far as I understood the F-statistic from the original model is invalid but I was wondering ...
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Regression power analysis: R's `pwr::pwr.f2.test` R2 deviation from zero vs. R2 increase (vs. G*Power)?
This question is about the difference between R's pwr::pwr.f2.test and G*Power regarding the ...
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Why we use the number of params as degree of freedoom in the F test for regression?
In a linear regression, we can assume that
$\frac{(SSD_y - SSR)/p-1}{SSR/(n-p-1)}$ have a $F$ distribution if the null hypothesis $Ho$ is true, with $SSR$ being the sum of residues of the regression ...
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Interpretation of p-values in a factor with multiple levels (summary.lm)
Here is a regression of a continuous response variable on a factor (religion) with 8 levels in R. I am wondering if any conclusions could be drawn from those p-values that are greater than $0.05$?
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If the omnibus F-test for testing is not significant, is it still possible for the pairwise comparison for testing to be significant?
Continuous outcome data are collected for three independent groups of equal size (i.e., all group n’s are equal). A linear regression analysis is performed to model the group means. More specifically, ...
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Significance test for the difference in Simpson's Diversity Index values?
I've taken several samples of categorical data and calculated the spread of each using Simpson's Diversity Index. I would now like to perform a significance test to see if these spreads are similar or ...
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what is the ratio of a ratio of two variances
I know that the ratio of two variances leads to an F-test but what of the ratio of two variance ratios? Is there are simple comparable result? Essentially I'm looking for the analogue of an ...
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