Testing the difference between two means, independent samples.
+Setting H0 and H1:
+
+
Test statistics:
+
+
Confidence Interval, for (μ1 - μ2):
+
+
Test statistics:
+
Where
+
+
Confidence Interval, for (μ1 - μ2):
+
+
Test statistics:
+
+
Confidence Interval, for (μ1 - μ2):
+
+
For checking the validity of the equal variance assumption
+
for a two-sample t-test.
++
Setting H0 and H1:
+
+
Test statistics:
+
assuming
+
+
Critical value in the rejection region is based on 2 degrees of freedom, each n - 1
+So,
+
+
Setting H0 and H1:
+
+
Test statistics:
+
Where
+
and
+
+
Confidence Interval, for μd:
+
+
ANalysis-Of-VAriance table could test the Difference among three or more means.
+Setting H0 and H1:
+H0: all populations means are equal.
+H1: at least one μ differs.
++
|
+ Variation + |
+
+ DF + |
+
+ Sum of Squares + |
+
+ Mean Square + |
+
+ F + |
+
|
+ Treatment + |
+
+  |
+
+  |
+
+  |
+
+  |
+
|
+ Error + |
+
+  |
+
+  |
+
+  |
+ |
|
+ Total + |
+
+   |
+
+  |
+
+ + |
+
N is overall sample size.
+k is the number of groups.
+