Design and Data Analysis in Psychology I School of Psychology Dpt. Experimental Psychology Design and Data Analysis in Psychology I Salvador Chacón Moscoso Susana Sanduvete Chaves

Relationships between two qualitative variables Lesson 10 Relationships between two qualitative variables

1. Chi square test When samples are independent. When both variables are nominal (although they also could be ordinal). Assumptions: N > 20 Expected value for each cell (E) ≥ 5 (in tables 2x2) E ≥ 5 in at leas 20% of cells (in tables higher than 2x2) When assumptions are violated, Fisher Exact test can be used (section 2).

1. Chi square test

1. Chi square test. Example A middle-school teacher was interested in determining if there was a relationship between math anxiety and gender among students at her school. The confidence level (CL) is 95%. The results are presented in the contingency table below. Gender Anxiety Male Female Low 12 32 Medium 22 14 High 9 6

1. Chi square test. Example *Expected value into brackets Gender ANXIETY Male Female ∑ Low 12 (19.9)* 32 (24.1) 44 Medium 22 (16.3) 14 (19.7) 36 High 9 (6.8) 6 (8.2) 15 43 52 95

1. Chi square test. Example The null hypothesis is rejected. There is relationship between math anxiety and gender.

2. The Fisher Exact test When samples are independent. When both variables are nominal (although they also could be ordinal). When both variables are dichotomous. When Χ2 assumptions are violated.

2. The Fisher Exact test 1 a b c d

2. The Fisher Exact test. Example We would like to test if an anxiety reduction program is effective to eliminate the post-intervention fear. The confidence level (CL) is 95%. The results are presented in the contingency table below. Fear GROUP Yes No Control 7 3 Experimental 2 8

2. The Fisher Exact test. Example Z=2.25 > Zα/2=1.96: The null hypothesis is rejected. The anxiety reduction program is effective to eliminate the post-intervention fear.

3.The McNemar test When samples are dependent. When both variables are nominal (although they also could be ordinal). When both variables are dichotomous. 1 A B C D

3.The McNemar test. Example A psychologist wanted to study if, the first day in the kindergarten, children started relationships mainly with adults, and after 6 months, mainly with other children (CL=95%). 6 months First day Child Adult 14 4 3

3.The McNemar test. Example The null hypothesis is rejected. Firstly, children in the kindergarten interact more with adults; in 6 months, with other children.