Question

A rapid serological test for the diagnosis of Helicobacter pylori infection is presented in the Journal of Tropical Pediatry of January 2006. It has been tested in 81 children, who also undergo the usual microbiological tests to determine whether or not they are infected. Use the 2 x 2 contingency table method and Association Chi square to know if the test is useful. The results are: (35pts)

Rapid test

Infection	+	-
+	24	1
-	3	53

Answer 1

Infection	+	-	total
+	24	1	25
-	3	53	56
Total	27	54

The Chi-square statistics compares the observed count in each table cell to the count which would be expected under the assumption of no association between row and column classifications.

the test is not useful, because the chi square value is negative. the chi square value can never be negative. the minimum value should be zero.

χ2 = n (bc-ad)²/ (a+b) (a+c) (b+d) (c+d)

     = 81 (1x3 – 24x53)²/ (24+1) (24+3) (1+53) (3+53)

     = - 64.2