Question

A psychologist wanted to know if students in her class were more likely to cheat if they were low achievers. She divided her 60 students into three groups (low, middle, and high) based on their mean course-testings score on the previous three tests. She then asked them to rate how likely they were to cheat on an course-testings if the opportunity presented itself with very limited chance for consequences. The students rated their desire to cheat on a scale ranging from 1-100, with lower numbers indicating less desire to cheat.

2. Look at data set. Before running any statistical analyses, glance through the data. Which hypothesis will be supported?

DATA:

Achievement_Group	Gender	Cheat
1	0	20
1	0	40
1	0	49
1	0	50
1	0	51
1	0	51
1	0	52
1	0	53
1	0	58
1	1	42
1	1	48
1	1	48
1	1	52
1	1	55
1	1	55
1	1	56
1	1	59
1	1	67
1	1	80
1	1	79
2	0	19
2	0	25
2	0	20
2	0	29
2	0	24
2	0	32
2	0	25
2	0	27
2	0	30
2	0	55
2	1	40
2	1	25
2	1	27
2	1	35
2	1	42
2	1	30
2	1	30
2	1	34
2	1	40
2	0	27
3	0	60
3	0	65
3	0	69
3	0	78
3	0	79
3	0	80
3	0	80
3	0	90
3	0	95
3	0	50
3	1	55
3	1	55
3	1	60
3	1	69
3	1	70
3	1	70
3	1	88
3	1	90
3	1	90
3	1	91

Answer 1

Glancing the data showed we need to see if there is considerable difference in the Cheat scores for Achievement Group1, 2 & 3. If such difference exists, we can conclude that there is effect of Achievement on the student desire to cheat.

We have one categorical independent variable and one quantitative dependent variable. So we can perform one way Anova to see the difference among groups.

Hypothesis for this test would be

H0: The Cheat_Score means of all Achievement groups are equal

H1: The Cheat_Score mean of at least one Achievement group is different.

The below is the Anova test output.

Note: The data has been remodeled to perform Anova test

The p value (1.55E-15)<0.05 indicates the difference among the groups is significant.

But in this case we can only know whether there is difference among group means, we will not have pair wise comparison of groups(i,e comparison between means of Low and High Achievement groups). For getting that pair wise test, we can use "Tukey multiple pairwise-comparisons" Test.