How does fsrftest calculate the p-value?

I am trying to understand how the fsrftest works in MATLAB. From the documentation, I understand that it uses an F-Test to test a null hypothesis and alternative hypothesis. Subsequently the p-value is used to determine the importance of the feature. From my understanding the p-value is also not compared with a significance level and as such this function does not actually reject/accept either hypothesis but rather just uses the p-value to rank features.

My question is regarding how is the p-value calculated? Is the process the same as ANOVA?

Answer 1

[Ive J]

At the end of doc you can see it uses -log(p) to rank features, so there is no significance level here. And yes, it's same as ANOVA (to be precise, it's a GLM), note that NumBins argument is used to bin continuous features.

n = 100; % sample size
data = table;
data.BMI = randi([18, 50], n, 1);

% bin BMI into two categories
med_bmi = median(data.BMI);
idx = data.BMI > med_bmi;
data.BMI(idx) = 1; 
data.BMI(~idx) = 0;

data.Sex = randi([0, 1], n, 1);
data.Target = randn(n, 1);

mdl_bmi = fitlm(data(:, ["BMI", "Target"]))

mdl_bmi = 
Linear regression model:
    Target ~ 1 + BMI

Estimated Coefficients:
                   Estimate       SE        tStat      pValue 
                   _________    _______    ________    _______

    (Intercept)      0.04267    0.13963     0.30559    0.76056
    BMI            -0.067441    0.19746    -0.34153    0.73343


Number of observations: 100, Error degrees of freedom: 98
Root Mean Squared Error: 0.987
R-squared: 0.00119,  Adjusted R-Squared: -0.009
F-statistic vs. constant model: 0.117, p-value = 0.733

mdl_sex = fitlm(data(:, ["Sex", "Target"]))

mdl_sex = 
Linear regression model:
    Target ~ 1 + Sex

Estimated Coefficients:
                   Estimate      SE        tStat      pValue 
                   ________    _______    ________    _______

    (Intercept)    -0.10768    0.14984    -0.71864    0.47407
    Sex             0.20462    0.19847       1.031    0.30509


Number of observations: 100, Error degrees of freedom: 98
Root Mean Squared Error: 0.983
R-squared: 0.0107,  Adjusted R-Squared: 0.000635
F-statistic vs. constant model: 1.06, p-value = 0.305

[~, sc] = fsrftest(data, "Target", "NumBins", 2);
p = exp(-sc)

p = 1×2

0.7334 0.3051