Assignment: T-tests & ANOVA 1.
Recall again that Rind & Bordia (1996) investigated whether or not drawing a happy face on customers' checks increased the amount of tips received by a waitress at an upscale restaurant on a university campus. During the lunch hour a waitress drew a happy, smiling face on the checks of a random half of her customers. The remaining half of the customers received a check with no drawing.
The tip percentages for the control group (no happy face) are as follows: 45% 39% 36% 34% 34% 33% 31% 31% 30% 30% 28% 28% 28% 27% 27% 25% 23% 22% 21% 21% 20% 18% 8% The tip percentages for the experimental group (happy face) are as follows: 72% 65% 47% 44% 41% 40% 34% 33% 33% 30% 29% 28% 27% 27% 25% 24% 24% 23% 22% 21% 21% 17%
This time, you are to perform a "hypothesis test" using the tip data, answering each of the questions below. For short-answer questions, be brief. However, you must give enough detail to justify your answers. Single-sentence responses will generally not suffice, but do not exceed a paragraph for any given answer.
a. What type of hypothesis test (i.e., statistical procedure) is most appropriate for this research scenario? Briefly (in a sentence or two) explain why you chose the test you did.
b. Prior to conducting the study, what magnitude of effect size (i.e., small, medium, or large) would you argue is important in this context? In other words, how large of an effect would you have to see before you felt that the results would have some "practical significance" to the waitresses in this population? Thoroughly explain your rationale, as this involves a value judgment on your part.
c. If you were conducting the study above, would you perform a one- or a two tailed test? Why?
d. Write null and alternate hypotheses that correspond with your answer to question #c. If you decided to perform a one-tailed test, make sure and specify which of the two groups you predict will be higher/lower.
e. Staying with convention, you will perform your hypothesis test using an alpha level of .05 (5%). Suppose you had to explain this significance criterion CJI 703 Applied Statistics I-Revised Winter 2016 10 to someone who has little experience with statistics. Explain how alpha is used to make a decision (reject or retain) regarding the null hypothesis.
f. Recall that one of the assumptions of the independent t-test is homogeneity of variance. If you had to explain this assumption to someone with little statistical expertise, how would you explain it?
g. Calculate the appropriate test statistic (i.e., z-test, t-test) using the descriptive statistics below. Note: you should check your work using the SPSS printout below. If your answer does not match either you 1) made a mistake in your calculations, or 2) entered the data incorrectly. N Mean Std. Dev. Control 23 27.78 7.78 Treatment 22 33.05 13.95
h. Enter the data above into SPSS. You will enter in two variables for each restaurant patron: 1) which experimental group they belonged to (1 = no happy face, 2 = happy face) and 2) the tip percentage left.
i. Obtain the appropriate test statistic. From the SPSS menus choose Analyze and Compare Means, followed by the appropriate test.
j. Using the descriptive statistics from the SPSS printout, calculate the F-Max statistic. Also, examine the p-value (i.e., significance level) for Levene's test. Based on the results of these two statistics, do you feel that the homogeneity of variance assumption has been violated? Explain.
k. What is the value of the t statistic and probability value on the SPSS printout. Note: You need to be consistent with your conclusion in question #10. Your choice of statistic on the printout should reflect whether or not you felt the assumption was violated.
l. Using the formula discussed in class, calculate Cohen's d effect size measure. Provide a brief interpretation of the statistic. Note: simply saying that the effect is "small", "medium", or "large" will not suffice.
m. Suppose you had to explain the probability value (i.e., significance level) on the printout to someone with limited statistical experience. Provide a brief interpretation of the p-value.
n. What is your decision concerning the null hypothesis? Did you reject or retain?
o. Considering both the probability value and effect size measure, what interpretations would you make about the findings? That is, what are your conclusions about the effects of leaving happy faces on checks?