Enter the following data in SPSS. Using SPSS find the means and medians for the
ID: 3174189 • Letter: E
Question
Enter the following data in SPSS. Using SPSS find the means and medians for the two groups and use the parametric t test for independent groups to compare the two groups. Then compute a Mann-Whitney U test on the same data. Compare the results of the two tests. Explain any differences. Is there a difference between a parametric and a nonparametric test? What test would you use in this case and why?
Group A
Group B
30
36
31
37
32
38
33
39
35
40
35
41
82
44
Group A
Group B
30
36
31
37
32
38
33
39
35
40
35
41
82
44
Explanation / Answer
SPSS Output for Mean and Median
Case Processing Summary
Group
Cases
Valid
Missing
Total
N
Percent
N
Percent
N
Percent
value
Group 1
7
100.0%
0
.0%
7
100.0%
Group 2
7
100.0%
0
.0%
7
100.0%
Descriptives
Group
Statistic
Std. Error
value
Group 1
Mean
39.71
7.084
95% Confidence Interval for Mean
Lower Bound
22.38
Upper Bound
57.05
5% Trimmed Mean
37.90
Median
33.00
Variance
351.238
Std. Deviation
18.741
Minimum
30
Maximum
82
Range
52
Interquartile Range
4
Skewness
2.590
.794
Kurtosis
6.775
1.587
Group 2
Mean
39.29
1.017
95% Confidence Interval for Mean
Lower Bound
36.80
Upper Bound
41.77
5% Trimmed Mean
39.21
Median
39.00
Variance
7.238
Std. Deviation
2.690
Minimum
36
Maximum
44
Range
8
Interquartile Range
4
Skewness
.726
.794
Kurtosis
.385
1.587
Therefore, Mean and Median in the Group 1 = Mean 39.71, Median 33
Therefore, Mean and Median in the Group 2 = Mean 39.29, Median 39
Independent t test Result
Independent Samples Test
Levene's Test for Equality of Variances
t-test for Equality of Means
95% Confidence Interval of the Difference
F
Sig.
t
df
Sig. (2-tailed)
Mean Difference
Std. Error Difference
Lower
Upper
value
Equal variances assumed
3.850
.073
.060
12
.953
.429
7.156
-15.163
16.021
Equal variances not assumed
.060
6.247
.954
.429
7.156
-16.915
17.773
P value = 0.95 (Not Significant findings)
Mann Whitney
Ranks
Group
N
Mean Rank
Sum of Ranks
value
Group 1
7
5.00
35.00
Group 2
7
10.00
70.00
Total
14
Test Statisticsb
Value
Mann-Whitney U
7.000
Wilcoxon W
35.000
Z
-2.239
Asymp. Sig. (2-tailed)
.025
Exact Sig. [2*(1-tailed Sig.)]
.026a
a. Not corrected for ties.
b. Grouping Variable: Group
P value = 0.026 (Significant difference)
Inference: Parametric test which is based on the mean difference between two groups suggest that no statistical significant difference between two groups, however, non parametric test which is based on the median suggest there is statistically significant difference.
Test for normality suggest the data is not normally distributed.
Tests of Normality
Group
Kolmogorov-Smirnova
Shapiro-Wilk
Statistic
df
Sig.
Statistic
df
Sig.
value
Group 1
.456
7
.000
.550
7
.000
Group 2
.119
7
.200*
.967
7
.873
a. Lilliefors Significance Correction
*. This is a lower bound of the true significance.
In this case it is better to use the Mann-Whitney test as data is not normally distributed.
The Mann-Whitney U-test is a non-parametric method which is used as an alternative to the two-sample Student's t-test. Usually this test is used to compare medians of non-normal distributions X and Y (the t-test is not applicable because X and Yare not normal).
Case Processing Summary
Group
Cases
Valid
Missing
Total
N
Percent
N
Percent
N
Percent
value
Group 1
7
100.0%
0
.0%
7
100.0%
Group 2
7
100.0%
0
.0%
7
100.0%
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.