Question

Happy face: interaction. Researchers at Temple University wanted to know the following: If you work waiting tables and you draw a happy face on the back of your customers' checks, will you get better tips? To study this question, they enlisted the cooperation of two servers at a Philadelphia restaurant. One was male, the other female. Each server recorded his or her tips for their next 50 tables. For 25 of the 50, following a predetermined randomization, they drew a happy face on the back of the check. The other 25 randomly chosen checks got no happy face. The response was the tip, expressed as a percentage of the total bill. The averages for the male server were 18% with a happy face, 21% with none. For the female server, the averages were 33% with a happy face, 28% with none.

a. Regard the dataset as a two-way ANOVA, which is the way it was analyzed in the article. Name the two factors of interest, tell whether each is observational or experimental, and identify the number of levels.

b. Draw an interaction graph(Including R code). Is there evidence of interaction? Describe the pattern in words, using the fact that an interaction, if present, is a difference of differences.

Answer 1

Solution:

The way of analysis was a randomized experiment in which 50 tables were randomly assigned equally to male and female servers. The two factors of interest was gender of the server and whether there is a happy face drawn at the back of check. The gender of server is obervational as there was no treatment applied to this factor. Happy face drawn is experimental as it has a treatment associated with it whether a happy face is drawn or not.

Level of gender of Server - Male , Female

Level of happy face drawn at back of check - Yes, No

b.

The interaction graph is,

As, the lines for "Happy face drawn Yes" and "Happy face drawn No" cross each other in the interaction graph, so there is interaction between Gender of server and Happy face drawn yes or no. As, we can also see in the graph, the tip % for male server reduced from 21 to 18, when happy face is drwan but the tip % for female server increased from 28 to 33 when a happy face was drawn. So clearly there is an intercation between Gender of server and Happy face drawn yes or no.

Difference in tip for male server at two levels of happy face = 18 - 21 = -3

Difference in tip for female server at two levels of happy face = 33 - 28 = 5

Difference in differences of tip = 5 -(-3) = 8

So, if a happy face is drawan , the tip % will increase by 8 for female server as compared with male server.