Often in businesses, we come across situations that cannot be understood without the use of statistical analysis. There are various statistical tools then, that can be applied to datasets and appropriate conclusions can be drawn according to them. The aim of this paper is to apply Mann-Whitney Test (Non-Parametric Test) on the Banking dataset. The Mann-Whitney test is a nonparametric test to compare two populations, utilizing only the ranks of the data from two independent samples. It does not require normality, but does assume equal variances. The conclusion will be based upon the results derived from the testing.

In this paper, centrality of the account balances of the people using an ATM card is the same as the centrality of the account balances of the people not using an ATM card will be checked using Mann-Whitney Test. In other words, the account balances of the people in two datasets differ or do not differ will be checked.

Methodology

The following table shows the banking data collected:

Table 1

Balance

ATM

Services

Debit

Interest

City

Rank (Balances)

1756

13

4

0

1

2

38

748

9

2

1

0

1

8

1501

10

1

0

0

1

27

1831

10

4

0

1

3

41

1622

14

6

0

1

4

32

1886

17

3

0

1

1

44

740

6

3

0

0

3

7

1593

10

8

1

0

1

30

1169

6

4

0

0

4

17

2125

18

6

0

0

2

51

1554

12

6

1

0

3

29

1474

12

7

1

0

1

24

1913

6

5

0

0

1

45

1218

10

3

1

0

1

18

1006

12

4

0

0

1

12

2215

20

3

1

0

4

56

137

7

2

0

0

3

2

167

5

4

0

0

4

3

343

7

2

0

0

1

4

2557

20

7

1

0

4

60

2276

15

4

1

0

3

57

1494

11

2

0

1

1

26

2144

17

3

0

0

3

53

1995

10

7

0

0

2

48

1053

8

4

1

0

3

14

1526

8

4

0

1

2

28

1120

8

6

1

0

3

15

1838

7

5

1

1

3

42

1746

11

2

0

0

2

37

1616

10

4

1

1

2

31

1958

6

2

1

0

2

46

634

2

7

1

0

4

6

580

4

1

0

0

1

5

1320

4

5

1

0

1

20

1675

6

7

1

0

2

34

789

8

4

0

0

4

10

1735

12

7

0

1

3

36

1784

11

5

0

0

1

39

1326

16

8

0

0

3

21

2051

14

4

1

0

4

49

1044

7

5

1

0

1

13

1885

10

6

1

1

2

43

1790

11

4

0

1

3

40

765

4

3

0

0

4

9

1645

6

9

0

1

4

33

32

2

0

0

0

3

1

1266

11

7

0

0

4

19

890

7

1

0

1

1

11

2204

14

5

0

0

2

55

2409

16

8

0

0

2

59

1338

14

4

1

0

2

22

2076

12

5

1

0

2

50

1708

13

3

1

0

1

35

2138

18

5

0

1

4

52

2375

12

4

0

0

2

58

1455

9

5

1

1

3

23

1487

8

4

1

0

4

25

1125

6

4

1

0

2

16

1989

12

3

0

1

2

47

2156

14

5

1

0

2

54

In table 1, we convert the account balances into ranks by sorting the combined samples from lowest to highest account balances, and then assigning a rank to each account balance. If values are tied, the average of the ranks is assigned to each.

The dataset in table 1 will be divided into two separate datasets: people possessing a debit card and people not possessing a debit card, as shown in table 2. We will treat these two datasets as independent populations. The distinguishing factor between the two populations is the field ‘Debit’. The ‘Debit’ field ‘0’ indicate that the person did not own a debit card and ‘1’ indicate that the person owned a debit card.

Table 2

The person did not own a debit card.

The person owned a debit card

Balance

Rank

Balance

Rank

32

1

634

6

137

2

748

8

167

3

1044

13

343

4

1053

14

580

5

1120

15

740

7

1125

16

765

9

1218

18

789

10

1320

20

890

11

1338

22

1006

12

1455

23

1169

17

1474

24

1266

19

1487

25

1326

21

1554

29

1494

26

1593

30

1501

27

1616

31

1526

28

1675

34

1622

32

1708

35

1645

33

1838

42

1735

36

1885

43

1746

37

1958

46

1756

38

2051

49

1784

39

2076

50

1790

40

2156

54

1831

41

2215

56

1886

44

2276

57

1913

45

2557

60

1989

47

1995

48

2125

51

2138

52

2144

53

2204

55

2375

58

2409

59

Hypothesis

“The median of the account balance of the people possessing a debit card is not equal to the median of the account balance of the people not possessing a debit card.”

Assuming that the only difference in the populations is in location, the hypotheses for a two-tailed test of the population medians would be:

(No difference in account balance)

(Account balance differs for the two datasets)

Using the above hypothesis, the Mann-Whitney test to compare two populations will be carried out.

The Decision Rule

At ? = .05 level of significance, the two-tail critical value is , which yields the decision rule

Reject if z > 1.960 or z < – 1.960.

Otherwise, do not reject

Calculation of the Test Statistic

The ranks are summed for each column to get = 1010 and = 820.

The sum + must be n( n + 1)/2 where n = + = 34 + 26 = 60.

Since n(n + 1)/2 = (60)(61)/2 = 1830 and

The sample sums are + = 1010 + 820 = 1830, our calculations check.

Next, we calculate the mean rank sums and . If there were no difference between groups, we would expect – to be near zero.

The person did not own a debit card.

The person owned a debit card

Rank Sum

= 1010

Rank Sum

= 820

Sample Size

= 34

Sample size

= 26

Mean Rank

= 29.71

Mean Rank

= 31.54

Since the samples are large ( and ), we can use a z test. The test statistic is

Decision

At ? = .05, rejection in a two-tailed test requires z > +1.960 or z < ?1.960, so we would not reject the Null hypothesis that the population medians are the same.

Decision: do not reject

The Mann-Whitney test carried out on the Banking dataset at the 95% confidence level provides strong evidence for the fact that the account balance of the people not possessing a debit card does not differ to the account balance of the people possessing a debit card. This suggests that possession of a debit card does not account for a higher account balance.

The results of the test at 95% significance level, proposes that there is no significant difference in the centrality of the account balance of the people who do not possess a debit card as against those who possess a debit card. This leads to the suggestion that the possession of a debit card does not increase the account balance. In simple banking terms, the following conclusion can be drawn: the debit card does not increase the account balances for the customers since it does not serve its purpose of money withdrawal, which may be later re-deposited by the customers.

References

Doane D.P. & Seward L.E. (2007). Applied Statistics in Business and Economics. New York: McGraw-Hill/Irwin.

Nathan, J. (1995). Statistical Inference. Chicago: Delton Publishers Inc.

Walpole, R. E. (2002). Introductory Statistics. Los Angeles: Kraft Publishers.

Weiss, N. A. (1984). Introductory Statistics, 5th Edition. New York: CRC Press.