Quantitative Methods
ANOVA & Chi-Square Tests
Module Goals
After completing this module, students will be able to do the following:
⦁ Scrutinize the variances of two independent populations.
⦁ Analyze the means and variances of more than two populations.
⦁ Exhibit understand of chi-square test.
⦁ Develop contingency tables for chi-square test.
Overview
Module 7 discusses ANOVA and Chi-Square test. In Chapter 10, section 5 the one-way Analysis of Variance will be discussed. For the one-way Analysis of Variance, the sum of squared differences around the overall mean can be divided into two other sums of squares that add up to the total sum of squares.
One of these measures differences among the means of the groups and thus is called sum of squares among groups (SSA), while the other measures the differences within the groups and is called the sum of squares within the groups (SSW).
Since the variance is a sum of squares divided by degrees of freedom, a variance among the groups and a variance within the groups can be computed by dividing each sum of squares by the corresponding degrees of freedom. The terminology used in the Analysis of Variance for variance is Mean Square, so the variances computed are called MSA, MSW, and MST. This will lead to the development of the F statistic as the ratio of two variances. The ANOVA summary table will be used when solving problems.
Chapter 11 discusses Chi-square testing for both one-sample and two samples. For Chi-square testing are used to determining whether the results are statistically significant. Chi-square tables will be used to compute the expected frequencies of the items of interest and items not of interest.
Assignment:
You are working as a statistician with the Boston Police department. You were given this case to work on to see if there is enough data to support an arrest warrant.
Kristen Gilbert started working at the VAMC as a nurse in 1989. A proficiency report obtained by the Boston Police Department, which described her as “highly skillful”, calm, and compassionate. She organized charity drives, collections for the needy, and organized a memorial service for a colleague who died of cancer (CBS News, Killer Nurse Gets Life, 2009).
However, Gilbert did tend to be nearby when patients died. Coworkers sometimes referred to her as the “angel of death”. Eventually her fellow nurses grew suspicious. Gilbert’s coworkers stated to raise concerns about an increase in medical emergencies (codes) and deaths in Ward C between August 1995 and February 1996. A criminal investigation was launched in February and Gilbert left her job shortly after learning she was the target of the investigation.
The search warrant of hospital records showed that on Ward C between January 1, 1995 and February 19, 1996 Gilbert was present or on duty for 40 codes which ended in death.
As the statistician for this case answer the following question
⦁ What information would you need to see if there is an association between Gilbert being on duty and code/death rates?
⦁ What other explanations might there be for why Gilbert had more deaths on her shifts?
⦁ What type of statistical test would you use for this case to see if there is an association?
⦁ What are your null hypotheses and alternative hypotheses?
