Iycee Charles de Gaulle Summary Mann-Whitney Test: Century National Bank Essay

Mann-Whitney Test: Century National Bank Essay

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:

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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.