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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%