Hello,

Given students grades in test 1 and 2
Test1 - Test2
100 - 80
99 - 79
98 - 78
97 - 77
96 - 75
95 - 73

Pearson, Spearman and Kendall correlation all produce value of almost 1 with p-value <0.001 . To show/measure that students grades in test 1 are different than test 2 , I can use t-test with paired two sample.

Assume that test-2 grades were similar to test 1
Test1 - Test2
100 - 100
99 - 99
98 - 98
97 - 98
96 - 95
95 - 93

To show that the 2 tests are similar , should I first show that there is no significance difference between 2 tests and then show that they have high correlation?