Comparing Two Population Means (Dependent Samples): Apply It 1

  • Complete a two-sample [latex]t[/latex]-test for dependent population means from hypotheses to conclusions

Hand Sanitizer

A 2011 study[1] measured the effectiveness of alcohol-based hand sanitizer on volunteers’ hands artificially contaminated with the bacteria Escherichia coli in the presence of dirt and cooking oil. The researchers wanted to study whether or not hand sanitizer effectively reduced the number of bacteria in the presence of dirt.

Suppose you want to replicate the study. You collect bacteria from the hands of eight randomly selected people who had dirt applied to their hands, and then you collect bacteria from their hands after they apply an alcohol-based sanitizer. You want to compare the amount of bacteria found on their hands before and after they apply the sanitizer.

The results are presented in the following table.

Participant Number of Colony-forming Units (CFU) before Sanitizer Number of Colony-forming Units (CFU) after Sanitizer
1 11.8 12.1
2 10.8 12.0
3 9.1 3.8
4 14.6 10.1
5 8.2 6.3
6 14.1 11.1
7 13.0 7.2
8 14.0 13.7
When comparing two means in dependent samples, we analyze the differences in each participant or subject. The last column of the following table shows the difference between the bacteria on participants’ hands before and after they apply the sanitizer. Although the order does not matter, it is important to be clear about the order selected. 
The order of subtraction is defined as: 

(number of CFU before applying sanitizer) – (number of CFU after applying sanitizer)

  1. Pickering, A. J., Davis, J., & Boehm, A. B. (2011, September). Efficacy of alcohol-based hand sanitizer on hands soiled with dirt and cooking oil. Journal of Water and Health, 9(3), 429–433. DOI: 10.2166/wh.2011.138 ↵