Chi Squared Test - Step by step of how to do the chi square test PDF

Preview

Summary

Step by step of how to do the chi square test...

Description

Chi Squared test Chi Squared test of association  Looking for an association between variables  Variables are categorical  Non Parametric  Compare observed with expected frequencies  Widely used test  When you want to measure a difference in proportions between 2 categories.  2 independent samples  Mutually exclusive categories  Nominal data  Compares E (Expected) with O (Observed)  Significant departure from the E leads us to accept the difference between the two categories.

Coffee and exam example. Hypotheses – H0- no difference. Same number of students in the two categories. Two tailed test. Observed: Yes= 40 No= 10

1) Calculate the expected frequencies. (40 + 10) / 2 = 25 2) 25 and 25 Sum of ((40-25)sq) / 25 = 9 Sum of ((10-25)sq) / 25 = 9 Step 3) Sum the 2 values measured for the 2 categories to find X squared. 9+9= 18 Significance Degrees of freedom = K-1 (K= number of cells) 2-1=1

To be significant the X sq value must equal or exceed the critical value at the sig level (p < 0.05) The calculated values of X sq (18) is above the critical value 3.84 Xsq (1) = 18, p < 0.05

2 X 2 Chi squared test Drunk Coffee Pass

50 39

Didn’t drink coffee 10 21

Fail

15 26

25 14

65

35

60 40 100

Row total X column total / grand total 60 x 65 / 100 = 39 60 x 35 /100 = 26 40 x 65 / 100 = 21 40 x 65 / 100 = 14 50 – 39 = 11 11 sq = 121 121 / 39 = 3.10 (10-21) sq / 21 = 5.76 (15-26) sq / 26 = 4.65 (25-14) sq / 14 = 8.64 x2 = 22.5

Step 1) Calculate the total for each row/column Step 2) Calculate the grand total (rows+columns) Step 3) Row total x column total / grand total four times. Step 4) Calculate xsq using the original formula – xsq= Sum of ((o-e)sq) / e...