In: Statistics and Probability
SSHA score
Survey Study Habits and Attitude (SSHA) is a psychological test designed to measure motivation, habits and attitudes towards learning among college students in the United States. The scores on the SSHA range from 0 to 200. In a study at an American college, The SSHA, SPSS file is attached below with the number SPSS FILE 1 AND 2..
1- Give a descriptive description of the SSHA score, with mean, median, standard deviation and any other descriptive targets that can describe this data.
2- Are the SSHA slots normalized?
The study also indicates whether you are female (sex = 0) or male (sex = 1).
3- Provide a 95% confidence interval for the average for women and men individually.
4- Show that confidentiality ranges for women and men are overlapping.
A researcher of you claims that the impossible can be statistically significant difference between the SSHA scores as long as the confidence intervals are (partially) overlapping. What do you mean about this claim?
5- Test the hypothesis that the SSHA scores are equal for men and women. What is the conclusion? Be sure to check the assumptions that lie behind the test
6- Summarize the conclusion in point 5 to what you got in point 4, and what can you tell your alleged researcher?
SPSS FILE 1.
Score
154
109
137
115
152
140
154
168
101
103
126
126
137
165
165
128
180
148
108
140
114
91
175
115
126
92
169
146
109
132
75
88
113
151
70
115
169
104
SPSS FILE 2.
SEX
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
Result:
1- Give a descriptive description of the SSHA score, with mean, median, standard deviation and any other descriptive targets that can describe this data.
Statistics |
||
SSHA score |
||
N |
Valid |
38 |
Missing |
0 |
|
Mean |
129.21 |
|
Median |
127.00 |
|
Std. Deviation |
28.774 |
|
Minimum |
70 |
|
Maximum |
180 |
2- Are the SSHA slots normalized?
The plot shows the data are not approximately normal.
The study also indicates whether you are female (sex = 0) or male (sex = 1).
3- Provide a 95% confidence interval for the average for women and men individually.
95% CI for female= (127.73, 150.94)
95% CI for male= (105.75, 134.45)
Descriptives |
|||||
sex |
Statistic |
Std. Error |
|||
SSHA score |
female |
Mean |
139.33 |
5.500 |
|
95% Confidence Interval for Mean |
Lower Bound |
127.73 |
|||
Upper Bound |
150.94 |
||||
5% Trimmed Mean |
139.20 |
||||
Median |
138.50 |
||||
Variance |
544.471 |
||||
Std. Deviation |
23.334 |
||||
Minimum |
101 |
||||
Maximum |
180 |
||||
Range |
79 |
||||
Interquartile Range |
34 |
||||
Skewness |
-0.100 |
0.536 |
|||
Kurtosis |
-0.903 |
1.038 |
|||
Male |
Mean |
120.10 |
6.858 |
||
95% Confidence Interval for Mean |
Lower Bound |
105.75 |
|||
Upper Bound |
134.45 |
||||
5% Trimmed Mean |
119.83 |
||||
Median |
114.50 |
||||
Variance |
940.726 |
||||
Std. Deviation |
30.671 |
||||
Minimum |
70 |
||||
Maximum |
175 |
||||
Range |
105 |
||||
Interquartile Range |
50 |
||||
Skewness |
0.305 |
0.512 |
|||
Kurtosis |
-0.681 |
0.992 |
4- Show that confidentiality ranges for women and men are overlapping.
A researcher of you claims that the impossible can be statistically significant difference between the SSHA scores as long as the confidence intervals are (partially) overlapping. What do you mean about this claim?
95% CI for female= (127.73, 150.94)
95% CI for male= (105.75, 134.45)
The two 95% confidence intervals are overlapping. There for there is no statistically significant difference between the SSHA scores of males and females at 95% level..
5- Test the hypothesis that the SSHA scores are equal for men and women. What is the conclusion? Be sure to check the assumptions that lie behind the test
Group Statistics |
|||||
sex |
N |
Mean |
Std. Deviation |
Std. Error Mean |
|
SSHA score |
female |
18 |
139.33 |
23.334 |
5.500 |
Male |
20 |
120.10 |
30.671 |
6.858 |
Independent Samples Test |
||||||||||
Levene's Test for Equality of Variances |
t-test for Equality of Means |
|||||||||
F |
Sig. |
t |
df |
Sig. (2-tailed) |
Mean Difference |
Std. Error Difference |
95% Confidence Interval of the Difference |
|||
Lower |
Upper |
|||||||||
SSHA score |
Equal variances assumed |
1.287 |
0.264 |
2.156 |
36 |
0.038 |
19.233 |
8.919 |
1.145 |
37.322 |
Equal variances not assumed |
2.188 |
35.080 |
0.035 |
19.233 |
8.791 |
1.388 |
37.079 |
To test the equality of variance of males and females, calculated Levene's Test for Equality of Variances F=1.287, P=0.264 which is > 0.05 level. The assumption of equality of variance is not violated.
To test the equality of means of males and females, calculated t=2.156, P=0.038 which is < 0.05 level. We conclude that the means of males and females are different.
6- Summarize the conclusion in point 5 to what you got in point 4, and what can you tell your alleged researcher?
The hypothesis test shows there is a significant difference and confidence intervals result shows that there is no difference of means. By considering the no normality of the distribution of the data, nonparametric method of comparison of means of males and females are recommended.