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.MethodologyThe following table shows the banking data collected:Table 1BalanceATMServicesDebitInterestCityRank (Balances)17561340123874892101815011010012718311040134116221460143218861730114474063003715931081013011696400417212518600251155412610329147412710124191365001451218103101181006124001122215203104561377200321675400433437200142557207104602276154103571494112011262144173003531995107002481053841031415268401228112086103151838751134217461120023716161041123119586210246634271046580410015132045101201675671023478984004101735127013361784115001391326168003212051144104491044751011318851061124317901140134076543004916456901433322000311266117004198907101111220414500255240916800259133814410222207612510250170813310135213818501452237512400258145595113231487841042511256410216198912301247215614510254In 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 2The person did not own a debit card.The person owned a debit cardBalanceRankBalanceRank321634613727488167310441334341053145805112015740711251676591218187891013202089011133822100612145523116917147424126619148725132621155429149426159330150127161631152628167534162232170835164533183842173536188543174637195846175638205149178439207650179040215654183141221556188644227657191345255760198947199548212551213852214453220455237558240959Hypothesis“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 RuleAt ? = .
05 level of significance, the two-tail critical value is , which yields the decision ruleReject if z > 1.960 or z < – 1.960.Otherwise, do not rejectCalculation of the Test StatisticThe 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 andThe 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 cardRank Sum= 1010Rank Sum= 820Sample Size= 34Sample size= 26Mean Rank= 29.71Mean Rank= 31.54Since the samples are large ( and ), we can use a z test. The test statistic isDecisionAt ? = .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 rejectThe 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.ReferencesDoane 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.