Lecture 8: Paired Data

In class we discussed the importance of analyzing differences when the data are paired because it uses the information efficiently and greatly increases your power to detect statistical differences.

You can either create a column containing the differences and analyze it with a 1-sample t-test or Minitab now has a paired-sample t-test in its menu options.

We also discuss the two non-paramteric alternatives, the simple sign test and the more powerful signed rank test.

The following data were originally from Kacprzak and Chvojka (1976). I found them in Rice's: Mathematical Statistics and Data Analysis.

Fish SelectiveReduction Permanganate
1 .32 .39
2 .40 .47
3 .11 .11
4 .47 .43
5 .32 .42
6 .35 .30
7 .32 .43
8 .63 .98
9 .5 .86
10 .60 .79
11 .38 .33
12 .46 .45
13 .20 .22
14 .31 .30
15 .62 .60
16 .52 .53
17 .77 .85
18 .23 .21
19 .30 .33
20 .70 .57
21 .41 .43
22 .53 .49
23 .19 .20
24 .31 .35
25 .48 .40