Looking at the article by Anderson and Arvidson (2017) Childhood vaccine status and correlation with common non-vaccine-preventable illnesses, in a few pages paper focuse on the use of the chi-square test and:
The way the sample size was chosen for this study and if it was the appropriate sample size?
The way the chi-square test was used? The groups and variables evaluated?
The results of the chi-square test findings and it's meaning.