Testing Statistical Hypotheses And Regression Analysis

Research Design

Discuss about the Testing Statistical Hypothese Regression Analysis.

One of the largest networks in the world in retail electronic payments is operated by the company Visa Inc. The company is also one of the most recognized brands in financial services across the world. The company provides a lot of facilities to the global commerce. These facilities include information and value transfer within some financial institutions, consumers, businesses, merchants and government entities management” href=”https://#”>government entities management.

There are a lot of types of fraud cases that are going on in the world nowadays. The most frequent fraud case that is happening now is credit card fraud. This type of card fraud is happening online as well as offline. Thus, this credit card company Visa Inc. is running this research to identify some specific issues and reduce the frequency of card fraud.

The primary objectives of this research are discussed as follows.

• To identify whether the number of card fraud is experienced differs across gender.
• To identify whether there is any difference across age group of people regarding card fraud.
• To determine whether the average time that is required to resolve the problem of card fraud is less than 12 hours or not.
• To determine the frequency of occurrence of online or offline card fraud.
• To determine whether there is any difference between the frequency of online and offline card fraud.
• To identify the influence of customers’ satisfaction scores of ‘response time’, ‘the level of advice’ and ‘the level of communication’ on the overall satisfaction with the credit card fraud resolution team.

In order to perform this research, data has to be collected. The data that is collected is on the experience of the customers in personal fraud. 2000 customers were selected randomly using the technique of simple random sampling. Among these 2000 customers who were selected to fill the questionnaire, 420 only responded. Thus, the success rate of the responses is only 21 percent.

            The ethical considerations that has to be kept in mind while collecting the data and doing the research are given below (Cacciattolo, 2015):

• The participants involved in the research should not be subjected to any types of harm.
• Respect and priority should be given to the dignity of the participants involved in the research.
• The participants should give full consent before participating in the study.
• The privacy of the participants taking part in the research must be assured.
• The data collected for the research purpose should be kept confidentially and must not be disclosed to anybody other than the individuals who are directly related to the research. .
• The participants of the survey must be assured that their identities will not be disclosed anywhere.
• The research aims and objectives must not be exaggerated.
• Any affiliations that are offered to the research or any sources from which the funding for the research are obtained must be mentioned at the time of the research.
• Communications that are necessary in doing the research must be done honestly and transparently.
• Information that are misleading to the research and biasness of the data in analysis and representation must not be done.

For the purpose of the research, the following hypothesis can be framed:

Is the number of card fraud experienced the same across gender?

Null Hypothesis (H₀₁): There is no significant difference between the card fraud experienced by males and females.

Alternate Hypothesis (H_A1): There is significant difference between the card fraud experienced by males and females.

Are there differences across age groups regarding card fraud?

Null Hypothesis (H₀₂): There is no significant difference across age groups regarding card fraud.

Alternate Hypothesis (H_A2): There is no significant difference across age groups regarding card fraud.

12 hours’ time significant as response time compared to what the customers have experienced before?

Null Hypothesis (H₀₃): There is no significant difference in the average response time from 12 hours

Alternate Hypothesis (H_A3): The average response time is less than 12 hours.

Question 4: Is the frequency of online card fraud more than that of offline card fraud?

Null Hypothesis (H₀₄): There is no significant difference in the frequency of online card fraud from offline card fraud.

Statistical Technique and Justification

Alternate Hypothesis (H_A4): There is significant difference in the frequency of online card fraud from offline card fraud.

Question 5: Do any of the customers’ satisfaction scores of ‘response time, ‘the level of advice’ and ‘the level of communication’ influence the overall satisfaction with the credit card fraud resolution team?

Null Hypothesis (H₀₅): The customers’ satisfaction scores of ‘response time, ‘the level of advice’ and ‘the level of communication’ do not influence the overall satisfaction with the credit card fraud resolution team

Alternate Hypothesis (H_A5): The customers’ satisfaction scores of ‘response time, ‘the level of advice’ and ‘the level of communication’ influence the overall satisfaction with the credit card fraud resolution team.

The hypothesis that has been stated above has to be tested using appropriate statistical techniques management. The techniques required to test the above stated hypothesis will be discussed here.

To test the first hypothesis, two sample t-test will be used. A two sample t test or an independent sample t test is the most appropriate test that can be used to compare the difference of the means of the two different groups of a single variable (Traitler, Coleman & Burbidge, 2017).

To test the second hypothesis, analysis of variance (ANOVA) test will be used as this the most appropriate test to compare the means of more than two groups of a single variable (Wiley & Pace, 2015).

To test the third hypothesis, a one-sample t-test will be used as this is the most appropriate test to compare the mean of one variable with a pre determined mean of the variable (Chachi, Taheri & Viertl, 2016).

To test the fourth hypothesis, two sample t-test will be performed as this is the most appropriate test that can be used to compare the difference of the means of the two different groups of a single variable.

To test the fifth hypothesis, regression analysis will be used as with the help of regression analysis only it is possible to find out whether there is any influence of the independent variables on the dependent variable (Draper & Smith, 2014).

It can be clearly observed that 34 percent of the respondents have not faced card fraud in the last 12 months. 66 percent of the respondents have experienced card fraud in the last 12 months. Thus, it can be said that most of the people around the world are now experiencing card fraud. The figures are given in table 5.1 and figure 5.1.

Two-Sample t-test

Table 5.1: Number of people who faced card fraud in last 12 months

Row Labels	Count of Question1
1	278
2	142
Grand Total	420

Thus, as shown before, out of 420 respondents, 278 have experienced card fraud. Now, the difference between the numbers of card frauds experienced by these 278 people across gender has to be tested. At first, the difference between the numbers of offline card frauds has been tested.

Table 5.2: Two-Sample t-test for difference in offline fraud

	Male	Female
Mean	4.40	4.24
Variance	23.44	23.64
Observations	126	152
Pooled Variance	23.55
Hypothesized Mean Difference	0
df	276
t Stat	0.262
P(T<=t) one-tail	0.397
t Critical one-tail	1.650
P(T<=t) two-tail	0.793
t Critical two-tail	1.969

Statistical Interpretation: From table 5.2, it is evident that t-calculated (0.262) is less than t-critical (1.969) and p-value is more than the significance level (5 percent level of significance), thus, we can accept the null hypothesis (H₀₁) that there is no significant difference between the offline card fraud experienced by males and females (p-value 0.793) at 5 percent level of significance.

The average number of times the females get card frauds offline does not differ much from the number of times the males get card fraud offline. Therefore, people should me much more careful so that nobody can fraud them.  

Table 5.3: Two-Sample t-test for difference in online fraud

	Male	Female
Mean	5.80	6.66
Variance	14.98	15.52
Observations	126	152
Pooled Variance	15.28
Hypothesized Mean Difference	0
df	276
t Stat	-1.818
P(T<=t) one-tail	0.035
t Critical one-tail	1.650
P(T<=t) two-tail	0.070
t Critical two-tail	1.969

From table 5.3, it is evident that t-calculated (-1.818) is less than t-critical (1.969) and p-value is more than the significance level (5 percent level of significance), thus, we can accept the null hypothesis (H₀₁) that there is no significant difference between the offline card fraud experienced by males and females (p-value 0.070) at 5 percent level of significance.

The average number of times the females get card frauds online does not differ much from the number of times the males get card fraud offline. Therefore, people should me much more careful while accessing their cards online so that nobody can fraud them.

Table 5.4: Summary Statistics for ANOVA on Offline Card Fraud
Groups	Count	Sum	Average	Variance
Less than 25 years	67	326	4.87	24.45
26-35 years	66	309	4.68	24.25
36-45 years	80	358	4.48	23.64
46-55 years	42	106	2.52	18.21
More than 55 years	23	100	4.35	24.15

Table 5.5: ANOVA Table on Offline Card Fraud
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	166.021	4	41.505	1.788	0.131	2.405
Within Groups	6335.753	273	23.208
Total	6501.773	277

Statistical Interpretation: From table 5.5, it is evident that f-calculated (1.788) is less than t-critical (2.405) and p-value is more than the significance level (5 percent level of significance), thus, we can accept the null hypothesis (H₀₂) that there is no significant difference between the offline card fraud experienced across different age groups (p-value 0.131) at 5 percent level of significance.

The average number of times the people of different age groups get offline card fraud has no significant difference. Thus, from here it can be said that people of all age groups has an equal chance of getting card fraud offline.

Table 5.6: Summary Statistics for ANOVA on Online Card Fraud
Groups	Count	Sum	Average	Variance
Less than 25 years	67	417	6.22	16.02
26-35 years	66	463	7.02	12.66
36-45 years	80	516	6.45	15.74
46-55 years	42	206	4.90	16.04
More than 55 years	23	141	6.13	16.66

Table 5.7: ANOVA Table on Online Card Fraud
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	118.112	4	29.528	1.943	0.104	2.405
Within Groups	4148.654	273	15.197
Total	4266.766	277

From table 5.7, it is evident that f-calculated (1.943) is less than t-critical (2.405) and p-value is more than the significance level (5 percent level of significance), thus, we can accept the null hypothesis (H₀₂) that there is no significant difference between the online card fraud experienced across different age groups (p-value 0.104) at 5 percent level of significance.

Analysis of Variance (ANOVA) test

The average number of times the people of different age groups get online card fraud has no significant difference. Thus, from here it can be said that people of all age groups has an equal chance of getting card fraud online as well as offline.

From table 5.8 given below, it can be seen clearly that the average time that can be lost by a customer suffering from online fraud is 13.65 hours.

Table 5.8: Descriptive statistics for amount of time lost (in hours) in resolving the most recent incident of credit card fraud
Mean	13.65
Standard Error	1.05
Median	1
Mode	1
Standard Deviation	17.562
Sample Variance	308.430
Kurtosis	-0.991
Skewness	0.844
Range	50
Minimum	0
Maximum	50
Sum	3795
Count	278

The company Visa Inc. has set a time-period of 12 hours. To test whether there will be any significant improvement to the response time; the following test has been done.

Table 5.9: One-Sample t-test for difference in service time from predefined mean

	Amount of time lost (in hours) in resolving the most recent incident of credit card fraud
Mean	13.65
Variance	308.43
Observations	278
Hypothesized Mean Difference	12
df	277
t Stat	1.568
P(T<=t) one-tail	0.059
t Critical one-tail	1.650
P(T<=t) two-tail	0.118
t Critical two-tail	1.969

From Table 5.9, it is evident that t-calculated (1.568) is less than t-critical (1.650) and p-value is greater than the significance level (5% level of significance), thus, we can reject that alternate hypothesis (H_A3) that the average service time in resolving the problem of online fraud is not less than 12 hours (p-value 0.059) at 5% level of significance.

The average service time (13.65 hours) is not less than 12 hours (value obtained from forecasting model). Therefore, the average service time should be used while advertizing for the company.

From table 5.10, it can be clearly understood that the average number of times an offline card fraud occurs is 4 and the average number of times an online card fraud occurs is 6.

Table 5.10: Descriptive statistics measures for the frequency of online and offline card fraud

	Offline Card Fraud	Online Card Fraud
Mean	4	6
Standard Error	0.29	0.24
Median	0	6
Mode	0	1
Standard Deviation	4.845	3.925
Sample Variance	23.472	15.403
Kurtosis	-1.896	-1.346
Skewness	0.292	-0.075
Range	10	12
Minimum	0	0
Maximum	10	12
Sum	1199	1743
Count	278	278

Table 5.11: Two-Sample t-test for difference in offline and online card fraud

	Offline Card Fraud	Online Card Fraud
Mean	4	6
Variance	23.47	15.40
Observations	278	278
Pooled Variance	19.44
Hypothesized Mean Difference	0
df	554
t Stat	-5.233
P(T<=t) one-tail	0.000
t Critical one-tail	1.648
P(T<=t) two-tail	0.000
t Critical two-tail	1.964

From table 5.11, it is evident that t-calculated (-5.233) is greater than t-critical (1.648) and p-value is less than the significance level (5 percent level of significance), thus, we can reject the null hypothesis (H₀₄) that there is no significant difference between the offline and online card fraud (p-value 0.070) at 5 percent level of significance.

The average number of times people get card frauds online is much more than the number of times the people get offline card fraud. Therefore, the company Visa Inc. must invest in the updated online security that will decrease the number of online card fraud while doing online transactions.

The following analysis has been performed to test the influence of the customers’ satisfaction scores of ‘response time’, ‘the level of advice’, and ‘the level of communication’ on the overall satisfaction with the credit card fraud resolution team

Table 5.12: Regression Statistics
Multiple R	0.80
R Square	0.65
Adjusted R Square	0.64
Standard Error	1.04
Observations	278

Table 5.13: ANOVA
	df	SS	MS	F	Significance F
Regression	3	536.252	178.751	166.415	0.000
Residual	274	294.310	1.074
Total	277	830.561

One-sample t-test

Table 5.14: Regression Coefficients

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	1.725	0.233	7.387	0.000	1.265	2.184
Response Time	0.246	0.058	4.271	0.000	0.133	0.360
Level of Advice	0.152	0.122	1.251	0.212	-0.087	0.392
Level of Communication	0.244	0.123	1.985	0.048	0.002	0.487

From table 5.14, it can be seen clearly that coefficients of the independent variables ‘response time’, ‘level of advice’ and ‘level of communication’ are not equal to zero. Thus, it can be said that the null hypothesis (H₀₅) is rejected. The variables ‘response time’, ‘level of advice’ and ‘level of communication’ does influence the overall satisfaction with the credit card fraud resolution team. 65 percent of the overall satisfaction can be explained by the variables ‘response time’, ‘level of advice’ and ‘level of communication’. The prediction equation can be given as follows:

Overall satisfaction = 1.725 + (0.246 * Response Time) + (0.152 * Level of Advice) + (0.244 * Level of Communication)

The average score of overall satisfaction can be predicted 65 percent correctly by the scores of response time, level of advice and the level of communication given by the customers. Since the correctness of the prediction is quite high, the company should try to improve these scores in order to maximize the overall satisfaction of the customers.

From the analysis conducted above, it has been stated clearly that the average number of card frauds (online or offline) do not differ across gender. It has also been stated that the average number of online and offline card frauds do not differ across different age groups. The average time required by the company Visa Inc is more than 12 hours which is not the claim the company has made. It has also been observed that the frequency of online card fraud is much more than that of offline card fraud. Thus, the company should take suitable measures of increasing security to reduce the frequency of card fraud during online transactions. Further, it has also been observed from the analysis that the overall satisfaction of the customers is influenced by the response time, level of advice and the level of communication of the card fraud resolution team.

The company Visa Inc. should take rapid measures on the account of customer security to reduce the frequency of card fraud that is taking place currently at the time of online transactions. The company should also develop the response time, level of advice and the level of communication of the card fraud resolution team in order to increase the overall satisfaction of the customers.

References

Cacciattolo, M. (2015). Ethical considerations in research. In The Praxis of English Language Teaching and Learning (PELT) (pp. 61-79). SensePublishers.

Chachi, J., Taheri, S. M., & Viertl, R. (2016). Testing statistical hypotheses based on fuzzy confidence intervals. Austrian Journal of Statistics, 41(4), 267-286.

Draper, N. R., & Smith, H. (2014). Applied regression analysis. John Wiley & Sons.

Traitler, H., Coleman, B., & Burbidge, A. (2017). Testing the hypotheses. Food Industry R&D: A New Approach, 227-247.

Wiley, J. F., & Pace, L. A. (2015). Analysis of variance. In Beginning R (pp. 111-120). Apress.