Comparison of Experts Perception of Age Bands Regarding Motor and Household Fraudsters - Research Paper Example

Comparison of Experts Perception of Age Bands Regarding Motor and Household Fraudsters Methodology Selection of Sample We selected 46 participants (experts) for the present study. These participants were selected by random sampling method. Each participant was provided a questionnaire where they rated their perception for a fraudster falling in a particular age band. The question asked was -“please assign a percentage to the age groups you think fraudsters most commonly fit into?’.They were asked the same question twice on their perception of probable age group of Motor fraudsters and Household fraudsters. During final tabulation comments of 43 experts were analyzed as because the response data of 3 experts were missing. Further actual age data of different fraudsters with respect to motor fraudsters and household fraudsters were collected. The total number of respondents was 63 in case of motor fraudster category while 78 were in case of household fraudster category. Since the response data from 3 individuals for both categories were missing, so the final calculations were done with 60 individuals and 75 individuals from motor fraudster category and household fraudster category respectively. The age bandings selected for perception ratings were as follows: Group 1= 17-21 years of age Group 2= 22-26 years of age Group 3= 27-31 years of age Group 4 = 32-36 years of age Group 5= 37-41 years of age Group 6= 42-46 years of age Group 7= 47-51 years of age Group 8= 52-56 years of age Group 9= 57-61 years of age Group 10= 62 years of age or older Principle The perceptions of the experts were compared with actual findings from the crime department and legal cells. Each participant assigned a particular percentage against a specific age band. On the other hand random profile of 60 motor fraudsters and 75 household fraudsters were collected and was segregated according to the age bands for the reason of comparison. The data was analyzed by common statistical tests of inference (Healy, 2009) The study was conducted to explore 3 questions in particular and they were: i. Do experts hold accurate perceptions of fraudster ages? ii. Is there any significant difference in fraudsters with respect to their total numbers either in household category or motor category? iii. Do experts differentiate between fraudster types when perceiving age? Statistical Tests and Hypothesis Testing Chi square test was undertaken as the statistical test of significance to assess both of our evaluation. The test was so selected because our study dealt with qualitative variables (perception) and also the sample size may not represent either the expert population or the fraudster population and hence we concluded to perform the chi-square test for independence (Corder & Foreman, 2014). The chi-square test that was used in this study was Pearson’s Chi-square test. In this test the observed frequencies of an event or a variable is taken in one column while the expected frequencies of happening of such events or variables are taken in the second column (Corder & Foreman, 2014). The test compares whether there is either a significant association between the observed and expected frequencies or there is no significant association between them and the observed and expected frequencies are considered independent of each other. Chi-square test establishes such significances or non-significances if the relationships are either very strong or very weak between the expected and observed frequencies, the sample size or the number of observations is large, or the numbers of two associated values are large. The tabulation of chi-square test is represented as percentages or frequencies so the total values of observed and actual percentages or frequencies are 100 and 1 respectively. Further if in any category of variables the observed or actual percentage or frequency is less than 5, Yate’s correction is applied to adjust the data, to get valid results (Corder & Foreman, 2014). The experimental hypothesis contended the association of variables under consideration. This means that the perception of experts and the actual age bands were significantly associated with each other and it can be concluded that the experts are capable to predict the fraudsters age according to age band. The experimental hypothesis was to be accepted if the probability value of the “Computed Chi-square” was more than the probability value at the chosen level of significance (which was considered 0.05 levels). This meant that out of 100 observations, more than 5 observations regarding the perceptions of experts with regard to the actual age group of either motor or household fraudsters are dependent and are significantly associated (Greenwood,1996) (Bagdonavicious,2011). The rejection of experimental hypothesis was based on the independence of variables under consideration. This means that the perception of experts and the actual age bands are independent of each other and it can be concluded that the experts are unable to predict the fraudsters age according to age band. The experimental hypothesis was rejected if the probability value of the “Computed Chi-square” was less than the probability value at the chosen level of significance (0.05 levels). This meant that out of 100 observations, 5 observations regarding the perceptions of experts with regard to the actual age group of either motor or household fraudsters are dependant which is considered too low (Greenwood, 1996) (Bagdonavicious,2011). The chi-square analysis was also done similarly to evaluate whether the perceptions according to the age bands differ with regard to the fraudster categories (Motor fraudster versus Household Fraudster). The experimental hypothesis contended the independence of variables under consideration. This means that the perception of experts and with regard to age bands of motor fraudsters and household fraudsters are independent, which means experts do differentiate between fraudster types when perceiving age. The experimental hypothesis was to be accepted if the probability value of the “Computed Chi-square” was less than the probability value at the chosen level of significance (which was considered at 0.05 levels). This means that out of 100 observations, less than 5 observations regarding the perceptions of experts with regard to the actual age group of fraudsters are same for both categories which considered too low and this indicates that in majority of the observations experts do differentiate between fraudster types when perceiving age (Greenwood, 1996) (Bagdonavicious,2011). The rejection of experimental hypothesis in this case contended the similarity of variables under consideration. This means that the perception of experts with regard to age banding were similar in case of both motor fraudsters and household fraudsters. The logic of rejection of experimental hypothesis was based on probability value of the “Computed Chi-square” more than the probability value at the chosen level of significance (which was considered at 0.05 levels). This means that out of 100 observations, more than 1 or 5 observations regarding the perceptions of experts with regard to the actual age group of fraudsters are similar and hence it can be concluded that in majority of the observations experts do not differentiate between fraudster types when perceiving age (Greenwood, 1996) (Bagdonavicious, 2011). The chi-square analysis was also done similarly to evaluate whether there is significant difference in actual fraudster profile (Motor fraudster versus Household Fraudster) with regard to age band category. The experimental hypothesis contended the independence of variables under consideration. This means the category of fraudsters according to actual age bands significantly differ from each other. The experimental hypothesis was to be accepted if the probability value of the “Computed Chi-square” was more than the probability value at the chosen level of significance (which was considered at 0.05 levels). This means that out of 100 observations, less than 1 or 5 observations regarding the age groups with respect to 2 different categories are same while in rest of the observations the two groups significantly differ from each other (Greenwood, 1996) (Bagdonavicious, 2011). The rejection of experimental hypothesis contended that there is no significant difference in age bands according to fraudster profiles. This means that the category of fraudsters according to actual age bands do not significantly differ from each other and it can be concluded that age categories of motor and household fraudsters are similar. The rejection of experimental hypothesis was based on the fact, that the probability value of the “Computed Chi-square” was less than the probability value at the chosen level of significance (which was considered at 0.05 levels). This means that out of 100 observations, more than 5 observations of actual age of fraudster according to the two groups were similar (Greenwood, 1996) (Bagdonavicious, 2011). Results & Discussion Descriptive Statistics: Participants perception of Motor Fraudster’s age   17-21 22-26 27-31 32-36 37-41 42-46 47-51 52-56 57-61 62 and above Mean 7 17 21 17 14 13 4 3 2 2 SD 9.44 15.95 14.87 16.73 17.14 21.21 4.52 3.56 3 3.05 Range 0%-36% 0%-100% 0%-75% 0%-100% 0%-100% 0%-100% 0%-20% 0%-10% 0%-10% 0%-13% Table 1: Represents that the mean percentages of motor fraudsters in different age groups as perceived by experts and the most perceived percentage fraudsters are in the age band of 27-31 years. Fig 1: The table 1 is represented as a pie diagram which reflects that the most perceived age band is 27-31 years in case of motor fraudsters as it bears the highest percentage (21%). Descriptive Statistics: Participants perception of Household Fraudster’s age   17-21 22-26 27-31 32-36 37-41 42-46 47-51 52-56 57-61 62 and above mean 4 10 14 23 20 12 9 4 2 2 sd 5.72 9.26 10.18 19.99 19.89 11.04 15.33 4.33 3.26 3.97 Range 0%-25% 0%-35% 0%-40% 0%-100% 0%-100% 0%-50% 0%-100% 0%-15% 0%-10% 0%-20% Table 2: Represents that the mean percentages of household fraudsters in different age groups as perceived by experts and the most percentage fraudsters are perceived to be in the age band of 32-36 years. Fig 2: The table 2 is represented as a pie diagram which reflects that the most perceived age band is 32-36 years in case of household fraudsters as it bears the highest percentage (23%). Actual Mean Age  Actual mean age Motor Fraudsters Household fraudsters Mean :38.74 Mean:40.46 SD: 11.08 SD:10.68  Range: 20 to 66 years  Range: 20-64 years Table 3: Represents the mean of actual age of motor and household fraudsters with their respective standard deviations.  Motor Fraudsters Age Band Perceived% Actual % 17-21 7 3 22-26 17 7 27-31 21 22 32-36 17 17 37-41 14 15 42-46 13 10 47-51 4 12 52-56 3 5 57-61 2 7 62 and above 2 2 Total % 100 100 Table 4. Represents the perception percentages of experts to the actual percentages with regard to the age band of the Motor fraudsters. A chi square test was done with the above tabulation between the perceived and actual percentages of motor fraudsters. The chi square value at (df=9, N=43) was 25.77 after Yate’s correction with p < 0.05 (p =0.0022). Hence it can be concluded that the perception of experts with regard to actual percentage of Motor fraudsters are not significantly associated and are independent. This will cause rejection of experimental hypothesis and it can be concluded that the experts are unable to predict the motor fraudsters age according to their age and respective age bands.  Household fraudsters Age Group Perceived% Actual % 17-21 4 3 22-26 10 8 27-31 14 9 32-36 23 16 37-41 20 20 42-46 12 16 47-51 9 13 52-56 4 8 57-61 2 4 62 and above 2 3 Total % 100 100 Table 5: Represents the perception percentages of experts versus the actual percentages with regard to expert’s prediction of the age band of the Household fraudsters. A chi square test was done with the above tabulation between the perceived and actual percentages of household fraudsters. The chi square value at (df=9, N=43) was 10.27 after Yate’s correction with p > 0.05 (p =0.328). Hence it can be concluded that the perception of experts with regard to actual percentage of Household fraudsters are significantly associated and the experimental hypothesis will be retained. This will cause retention of experimental hypothesis and it can be concluded that the experts are unable to predict the household fraudsters age according to their age and respective age bands.   Motor Household   Perceived% Perceived% 17-21 7 4 22-26 17 10 27-31 21 14 32-36 17 23 37-41 14 20 42-46 13 12 47-51 4 9 52-56 3 4 57-61 2 2 62 and above 2 2 Total % 100 100 Table 6: represents the perception percentages of experts with regard to age band of the Household fraudsters and Motor Fraudsters. A chi-square test was conducted between perceptions of age of motor and household fraudsters. The chi square value (df=9, N=43) after Yate’s correction was 14.216 with p > 0.05 (p =0.114) and hence it can be concluded that the perception of experts with regarding age and age band of motor and household fraudsters does not significantly differ from each other which causes rejection of the experimental hypothesis and it can be concluded that experts do not differentiate between fraudster types when perceiving age at least in the case of motor and household fraudsters. The reason for rejection of experimental hypothesis is because more than 5 observations out of 100, experts perceive that motor and household fraudsters’ falls under same age category.   Motor Household Age band Actual % Actual % 17-21 3 3 22-26 7 8 27-31 22 9 32-36 17 16 37-41 15 20 42-46 10 16 47-51 12 13 52-56 5 8 57-61 7 4 62 and above 2 3 Total % 100 100 Table 7: represents the actual percentages with regard to age band of the Household fraudsters and Motor Fraudsters. A chi-square test was done between the actual percentages of motor and household fraudsters from the above tabulation. The chi square value (df=9, N=43) after Yate’s correction was 13.9 with p >0.05(p=0.12). Hence it can be concluded that the actual percentage of household fraudsters and motor fraudsters do not significantly differ from each other and the experimental hypothesis is rejected. This means that the actual age bands of the two categories of fraudsters do not significantly differ from each other. From the above analyses it becomes evident that although experts cannot predict the actual age group of motor fraudsters, however they hold correct perceptions of age groups of the household fraudsters. Further we conclude there was no significant difference in the mean actual age of motor and household fraudsters that were evaluated in this study. Finally, our study also revealed that experts did not held significant different perceptions of age bands according to fraudster categories while differentiating between motor and household fraudsters. References Bagdonavicius, V. & Nikulin, M.. (2011) "Chi-squared goodness-of-fit test for right censored data". The International Journal of Applied Mathematics and Statistics, p. 30-50 Corder, G.& Foreman, D.(2014). Nonparametric Statistics: A Step-by-Step Approach. Wiley, New York. ISBN 978-1118840313 Greenwood, P. & Nikulin, M. (1996) A guide to chi-squared testing. Wiley, New York.  Green, P. (2006). Lying, Cheating, and Stealing: A Moral Theory of White Collar Crime. Oxford University Press. Healy, J. (2009). The Essentials of Statistics: A Tool for Social Research (2nd ed.). Belmont, CA: Cengage Learning. pp. 177–205 KPMG Report Corporate Fraud in Latin America 2008-10, published in 2011. Nigrini, M.(2011). Forensic Analytics- Methods and techniques for forensic Investigations. Hoboken, NJ: John Wiley & Sons Inc. ISBN 978-0-470-89046-2. Podgor, E.(1999). Criminal Fraud, Vol, 48, No. 4 American Law Review 1999. Appendix-1 (Chi-square outputs) Reference: http://www.quantpsy.org/chisq/chisq.htm Chi-square: degrees of freedom: p-value: Yates chi-square: Status: Yates p-value: 0.00220351 Chi-square output for table 4 Chi-square: degrees of freedom: p-value: Yates chi-square: Status: Yates p-value: 0.328451 Chi square output for table 5 Chi-square: degrees of freedom: p-value: Yates chi-square: Status: Yates p-value: 0.12592 Chi square results for table 7 Chi-square: degrees of freedom: p-value: Yates chi-square: Status: Yates p-value: 0.1148468 Chi square results for table 6 Read More