# Evaluate statistical significance of difference between outcomes of tests

I have 400 patients and I apply 4 tests to all of them. This gives me a number of positive and negative for each test. I want to compare the tests 2 by 2 to find out if there is any statistically significant difference between them.

Test  Pos   Neg
1     100   300
2     150   250
3     160   240
4     200   200


What statistical test I can use to determine this? I'm very new to the field so I appreciate any pointers.

## 4 Answers

McNemar's test is the two by two comparison. NB You want to record for tests #1 & #2 how many patients tested +ve in both #1 & #2, how many +ve in #1 but -ve in #2, how many -ve in #1 but +ve in #2, & how many tested -ve in both #1 & #2.

I was going to suggest the chi-squared test, but I think that your suggestion of McNemar's test would be better. A related topic would be the Fisher's exact test: https://en.wikipedia.org/wiki/Fisher%27s_exact_test.

• From the example it looks like McNemar is what I need, but I'll keep Fisher in my mind too. There are just too many similar tests for a beginner to comprehend :) – rslite Apr 8 '13 at 23:25

Perform a McNemar test for independence in a 2x2 table

Paired proportions have traditionally been compared using McNemar's test but an exact alternative due to Liddell (1983) is preferable.

Useful links:

• www.statsdirect.com/help/default.htm#chi_square_tests/mcnemar.htm
• freesourcecode.net/matlabprojects/68089
• jech.bmj.com/content/37/1/82.abstract
• There is an exact version of McNemar's test. – gung - Reinstate Monica May 14 '15 at 4:37