We can calculate the p-value from the test statistic in an F-test using the scipy.stats.f module. Let’s say we are performing a one-way ANOVA test. The test statistic, in this case, follows the F-distribution. So, ANOVA is also an F-test.
Let’s say there are three distinct groups of students. Each group consists of 20 different students. Each group of students is subjected to a teaching method. And then, a test is conducted for each group of students. After the tests, the mean marks obtained by each group of students are compared. We perform a one-way ANOVA test to determine whether the difference in the mean marks obtained by each group of students is statistically significant. Here,
dfn = degrees of freedom while calculating the estimate of variance of numerator and dfd = degrees of freedom while calculating the estimate of variance of denominator
We know that in a one-way ANOVA test, dfn = (total number of groups – 1). And dfd = (total number of observations – total number of groups). So, in our case, dfn = (3 – 1) = 2 and dfd = (3×20 – 3) = 57.
Let’s also assume that after the one-way ANOVA test, we get the test statistic to be 1.3906585540443808.
So, we can use the following Python code to calculate the p-value from the f-score.
from scipy.stats import f # F-statistic: 1.3906585540443808 dfn = 2 dfd = 57 f_statistic = 1.3906585540443808 p_value = f.sf(f_statistic, dfn, dfd) print("p-value: ", p_value)
Here, we are using the f.sf() function from the scipy.stats.f module to calculate the p-value. The f.sf() function is the survival function and is equivalent to (1 – cdf), where cdf is the cumulative distribution function. The f.sf() function is sometimes more accurate than (1 – cdf) and hence, it is recommended to use the f.sf() function to calculate the p-value from the f-score.
The output of the above program will be like the following:
p-value: 0.2572274003795069






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