SPSS Chi-square Test Analysis - Case Study Example

Chi-Square Test Name Number Course Tutor Date Chi-Square Test The Executive Director of the NBAA wanted to know if there were any differences among the various variables included in the sample data. Therefore, in this research study, several hypotheses were formulated based on the respective research questions. The Chi-square test was used to evaluate the differences among the tested variables. For all the statistical analyses, the alpha significance level is set at .05. Results The CAM combined data set (bogus) contains several variables. Included in the sample is the Position breakdown which was analyzed for differences in the distribution among the position type. The null hypothesis for the Chi-square test stated that there is no difference in the distribution of the position breakdown other than each of the position type occurs with equal frequencies. Table 1: Distribution of Position breakdown by position type Observed N Expected N Residual Pilot 124 136 -12.0 Maintenance 131 136 -5.0 Other 153 136 17 N 408 The chi-square test for independence showed that there is no significant difference in the distribution of the Position breakdown among the position type, χ2(2) = 3.368, p = .186; at alpha level of significance .05. Therefore, we fail to reject the null hypothesis. Furthermore, the difference in the distribution of the expected against the observed counts for the Aviation degree was analyzed. 70% was the expected distribution for having an Aviation degree while 30% was the expected distribution for not having an Aviation degree. The null hypothesis for the Chi-square test stated that there is no difference in the distribution of expected against the observed counts for the Aviation degree. Table 2: Distribution of the expected and observed counts for Aviation degree Observed N Expected N Residual No 147 122.4 24.6 Yes 261 285.6 -24.6 N 408 The chi-square test showed that there is a significant difference in the distribution of expected against the observed counts for the Aviation degree (Yes/No), χ2(1) = 7.063, p = .008; at alpha level of significance .05. Therefore, reject the null hypothesis. Subsequently, the differences in Formal Education based on Position Breakdown were analyzed. The null hypothesis stated that there is no difference in Formal Education based on the Position Breakdown. The frequency statistics for the distribution of the Formal education among the Position types were as follows: Table 3: Distribution of Formal Education based on Position Breakdown Observed N Expected N Residual Pilot Associates 14 41.0 -27.0 Bachelors 74 41.0 33.0 Graduate 35 41.0 -6.0 N 123 Maintenance Associates 56 43.7 12.3 Bachelors 49 43.7 5.3 Graduate 26 43.7 -17.7 N 131 Other Associates 20 50.0 -30.0 Bachelors 78 50.0 28.0 Graduate 52 50.0 2.0 N 150 The Chi-square test results for the evaluation of the differences in the distribution of Formal Education based on Position Breakdown were as follows; Formal Education among the Pilot (χ2(2) = 45.220, p = .000), Maintenance (χ2(2) = 11.282, p = .004) and Other (χ2(2) = 33.760, p = .000). The differences in Formal Education based on the three Position Breakdowns were all statistically significant. Hence, their corresponding null hypotheses were rejected. In addition, the differences in Position Breakdown based on Aviation Degree (Yes/No) were analyzed. The null hypothesis stated that there is no difference in Position Breakdown based on the Aviation Degree (Yes/No). The frequency statistics for the distribution of the Position Breakdown based on Aviation Degree (Yes/No) were as follows: Table 4: Distribution of Position Breakdown based on Aviation Degree (Yes/No) Aviation Degree Observed N Expected N Residual No Pilot 45 49.0 -4.0 Maintenance 52 49.0 3.0 Other 50 49.0 1.0 N 147 Yes Pilot 79 87.0 -8.0 Maintenance 79 87.0 -8.0 Other 103 87.0 16.0 N 261 The empirical results for the evaluation of the differences in the distribution of Position Breakdown based on Aviation Degree (Yes/No) were as follows; Position Breakdown among the examinees without Aviation Degree (χ2(2) = 0.531, p = .767) and examinees having Aviation (χ2(2) = 4.414, p = .110). The differences in Position Breakdown based on the Aviation Degree (Yes/No) were not statistically significant. Hence, we fail to reject the corresponding null hypotheses. Discussion The objective of this case study was to compare and evaluate the differences between the variables included in the CAM exam sample data. Hence, Chi-square tests were used to determine and evaluate the difference among these variables. The frequency distributions of the position types for Position Breakdown were compared. The Chi-square test for the distribution of the Position Breakdown by position type yielded χ2(2) = 3.368, p = .186. Thus, the difference between the observed distribution of the position type and the expected equal distribution of each position type is not statistically significant because the corresponding p-value [.186] is greater than the significance value. Therefore, the observed distribution of the position type is not significantly different from the expected equal frequency distribution for each position type. Subsequently, the difference in the distribution of the expected against the observed counts for the Aviation degree was analyzed. 70% was the expected distribution for having an Aviation degree while 30% was the expected distribution for not having an Aviation degree. The Chi-square test for the difference between the observed and expected distribution of the Aviation Degree (Yes/No) yielded χ2(1) = 7.063, p = .008. Thus, the difference between the observed and the expected distribution of the Aviation Degree (Yes/No) is statistically significant because the corresponding p-value [.008] is less than the significance value. Therefore, the observed distribution of Aviation Degree (Yes/No) differs significantly from the expected frequency distribution of 70% for those with aviation degree and 30% for those without aviation degree. Furthermore, the differences in Formal Education based on Position Breakdown were analyzed. It was found that the differences in Formal Education based on the three position types were all statistically significant. The results are also practically significant since they indicate that the level of formal education significantly determines the position held by an employee of a company. The differences in Position Breakdown based on Aviation Degree (Yes/No) were also analyzed. The Chi-square test indicated that the differences in Position Breakdown based on Aviation Degree (Yes/No) were not statistically significant for both the examinees with and without an aviation degree. This implies that an aviation degree does not significantly determine the position held by an employee for the population from which the sample data was drawn. Conclusion and Recommendations The CAM combined data set (BOGUS) contains several variables which could provide insightful information when analyzed. As established the observed distribution of the Position Breakdown does not differ significantly from the expected equal frequency distribution for each position type. However, the difference between the distribution of the observed and expected counts of 70% for those having Aviation degree and 30% for those without Aviation degree is statistically significant. In addition, it was established that the differences in Formal Education based on the Position Breakdown were all statistically significant. However, the differences in Position Breakdown based on Aviation Degree (Yes/No) were not statistically significant. This implies that Formal Education significantly determines the position held by an employee in a company, but an aviation degree does not significantly determine the position that an employee will hold in a company. Therefore, when hiring employees, a company should consider the Formal Education of an individual when determining the position to be held by an employee. Read More