Question

D.Consider the following 2 x 2 contingency table for an experiment in which you sampled the number of instances of each of two different categories from two different data sets Data set 2 Data set 1 10 15 Category 1 Category 2 25 20 Calculate the appropriate x2 test statistic to determine whether these two data sets are the same.

Answer 1

Given Contigeny table, Sets Cat. 1 10 Cat 3 2 20 This is taken as observed value Before that, here are some values to be calmlaled 2 Row - Gati TOTAL N= a+b+c+d) a b atb. Cata c COLUMNA TOTAL d ctd. bedl N=a+b+c+d. Expected data table Cat 1 (a+b)(at) (a+b) Cord) Cata (arc) (c+d) (bxd) card) So far then given problem Experted N=10+15+ +20= 70 lat a 12.5 12.5 Cat 2 22.5 22.5

X²= 2 (observed - Expected ) ² Espected X? - (10-12.5)?+(15-12.5) + (25-22.5) 125 12.5 22.5 + (20-22.5)² 22.5 = 0.5 + 0.5 +0.28 +0.28 = 1.56 Degree of freedom = (ne of low-1) (no of Column-1) = (2-1) (2-) = 1 Now look into the chi square distribution takle, se ning some p-calculator we will get anurate p-value. p=0.2123 il p=21% is too ligh. Sine p is very large, il mull hypothesis is correct in There is no relationshup between two data sets. D =