You volunteer some of your spare time to your local fire dep

You volunteer some of your spare time to your local fire department and have been asked by an assistant chief to analyze data on firefighters who applied for promotion. The assistant chief wants to ensure that gender bias is not a concern in the promotion of firefighters. Shown below is data for 50 firefighters who applied for promotion and the results of a chi-square analysis of the data.

What factors should the assistant chief consider in determining the presence of gender bias in firefighter promotion?

Is the promotional status of recently promoted firefighters independent of their gender?

What reasons should the assistant chief convey to the fire chief to justify the absence of gender bias in the most recent class of firefighters who were promoted?

How might the presence of gender bias in promotions impact the fire department?

Solution

The assistant manager should consider the total number of applicants for promotion and the number of females and males promoted from those applicants. This will give the view of data such as odds ratio, proportion of promoted males and females.

A Chi-Square test gives the result of goodness of fit in other words dependence of one variable over the other. The Null Hypothesis in this case is that the dependence is significant and the alternate hypothesis is that the dependence is insignificant.

As the result has P-value greater than 0.05, so we will fail to reject the null hypothesis and conclude that the dependence is significant at 95% level of significance.

However at 99% level of significance, the dependence is insignificant as the p-value is then smaller than 0.01. So, null hypothesis will be rejected.

Hence, the assistant manager should report that at 99% level of significance, the result shows no dependence of promotion over the gender. So, there is no biasness.