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Histological Data: Test for Correlation in Correlated Categorical Data

The original data contains brain tumor data on 30 individuals, with two sets of 5 histological measures recorded for each person. We are interested in determining if there is any correlation among these measurements. In this example we will use the second set of five measurements. The data are given below.

Individual

Histological Measurements

Individual

Histological Measurements

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15

 2 0 0 0 0 4 3 4 3 2
3 4 2 3 0 5 5 5 4 4
2 1 0 0 0 4 4 5 4 2
3 1 1 0 0 3 3 4 3 2
1 3 1 3 0 4 4 4 3 3
2 4 2 3 0 5 4 5 3 3
2 3 0 2 0 5 4 5 4 3
3 3 0 2 0 4 4 3 3 1
2 4 2 1 0 4 4 4 3 2
2 3 1 0 0 5 5 4 3 2
3 3 1 1 0 4 4 4 3 3
2 2 1 0 0 4 4 4 3 2
1 2 0 0 0 2 2 3 2 1
3 3 3 2 0 4 4 4 3 3
2 3 2 0 0 3 3 3 3 2
 16
17
18
19
20
21
22
23
24
25
26
27
28
29
30 		2 3 2 1 0 5 4 4 3 3
3 4 1 0 0 5 5 4 4 3
3 4 2 3 2 4 4 4 3 3
2 2 1 0 0 4 4 5 4 3
3 2 2 0 0 4 3 4 4 3
3 2 0 1 0 4 4 5 5 4
3 3 1 0 0 4 4 4 4 2
2 3 1 0 0 4 4 4 4 3
3 3 1 0 0 4 4 5 4 3
1 2 2 0 0 4 4 4 3 3
3 3 1 1 1 3 3 4 3 3
3 3 3 0 0 4 3 4 4 3
2 3 2 0 0 4 3 4 3 3
3 4 2 0 0 5 4 5 4 3
3 2 0 0 0 4 3 4 4 3

The values of the five measurements are coded into a dichotomous variable such that:

Analysis of the recoded data using StatXact 7 gives the following results:

Conclusion: notice that the exact p-value of 0.01517 indicates a significant correlation, among measurements within clusters.
 

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