How do I figure an effect size for a data set? Ok the data is this
A manager of a small store wanted to discourage shoplifters by putting signs around the store saying "Shoplifting is a crime!" However, he wanted to make sure this would not result in customers buying less. To test this, he displayed the signs every other Wednesday for 8 weeks, for a total of 4 days displayed. He recorded the store's sales for those four Wednesdays and then recorded the store's sales for the four alternate Wednesdays, when the signs were not displayed. On the Wednesdays with the sign, the sales were 83, 73, 81, and 79. On the Wednesdays without the sign, sales were 84, 90, 82, and 84.
Research: Whether or not sales will be effected by placing a sign that states "Shoplifting is a crime!".
Hypothesis: Sales will Not be affected by displaying the "shoplifting" sign.
Null Hypothesis: Sales will be effected by displaying the "shoplifting" sign.
Find the means of the two groups: 83+73+81+/ M1
84+90+82+/ M2
Figure each samples variance: , 73-79= -6, ,
Sum of deviations for P1= 12/4= 3 variance of the mean
84-85= -1, 90-85= 5, 82-85= -3, 84-85= -1
Sum of deviations for P2= 0/ variance of controlled mean
Find the squared deviation score for each sample:
, , , 56 is the sum of the squared deviation scores P1
-1= 1, , -3= 9, 30 is the sum of the squared deviation scores P2
Divide the sum of squared deviation scores to the number of samples to find how spread out the scores are: 56/4= 14, 30/.5 which indicates that P1 is more spread out than P2.
Do these results suggest that customers buy less when the signs are displayed? (Use the .05 significance level.)
a. Use the five steps of hypothesis testing.
b. Sketch the distribution involved.
c. Figure the effect size.
d. Explain what you did to a person who is familiar with the t test for a single sample but is unfamiliar with the t test for independent means.