如题所述
From last time we know t-test is used for comparing the mean of 2-level categorical variable and ANOVA is used for comparing the mean value of a 3-level categorical variable or more.
Question:
However, there is a question bugs me, why both T-test and ANOVA are comparing the mean value, but** one P-value comes from the t-test and the other P-value is derived from the F-test**?
Pexels / Pixabay[/caption]
I did a bit research into this and discussed with little Rain, then we found out the key relation to answer is the equivalence of F and t-test.
The hidden reason is when pair of the sample are normally distributed then the ratios of variance of sample in each pair will always follow the same distribution . Therefore, the t-test and F-test generate the same p-values.
We want to know if the blood pressure medication has changed the blood pressure for 15 patients after 6 months.
As we can see the F-test and t-test have the same P-value = 0.0127.
I used SAS to generate a graph:
Except for , I summarized a table for F-test and t-test.
The mean value of the two groups are the same.
The mean value = n0.
The mean value of three or more groups are the same.
N1=N2=N3…
The Standard deviation is not known and Sample size is small.
F-test Features:
The variance of the normal populations is not known.
1.Compare mean value of two groups.
2.Compare mean value of a group with a particular number.
