Goodness of Fit and Independence Testing †MyAssignmenthelp.com

Question: Discuss about the Goodness of Fit and Independence Testing. Answer: Introduction: The analysis focuses on relation between income levels and confidence levels. It is generally being believed that people who are more confident about local police can work more efficiently and therefore, they earn more. The fact will be tested with Chi square test procedure. Data has been collected on relevant variables and categorized according to requirement. Data management with the sub divisions are depicted through Pie chart. The dataset is about relation between confidence levels on local police and peoples income levels. Confidence levels are divided into 4 divisions. The divisions are: no confidence at all, not very much confident, quite a lot of confidence, a great deal of confidence. Income levels are divided into 6 broad groups. The groups are like: less than $30k, $30k to less than $60k, $60k to less than $90k, $90k to less than $120k, $120k to less than dollar $150k, $150 k or more and dont know the income or refused to state income. Data are arranged in a contingency table or cross table and frequency for each cross group is noted. Frequency table and Pie chart: There are two variables named confidence levels and income levels and the pie charts are being constructed one for each variable. Table 2: Frequency table for confidence levels. C1-How much confidence do you have in the local police in your area? Frequency No confidence at all 68 Not very much confidence 398 Quite a lot of confidence 1244 A great deal of confidence 656 It shows the percentage of confidence levels of police department. The levels are being divided into four sub-groups. Four groups are no confidence at all, not very much confidence, Quite a lot of confidence and a great deal of confidence (Lipsitz et al. 2015). Frequency of people with low confidence is the minimum and frequency of people with great confidence is maximum. People with not very much confidence and Quite a lot of confidence have medium frequency. Table 2: Frequency table for Distribution of income: INCOME Frequency Less than $30k 337 $30k to less than $60k 516 $60k to less than $90k 427 $90k to less than $120k 277 $120k to less than $150k 119 $150k or more 146 Don't know/Refuse 544 Income levels are depicted in this pie chart. Levels are being divided into 7 groups like less than $30k, $30k to less than $60k, $60k to less than $90k, $90k to less than $120k, $120$ to less than $150k, and division who refused to show their income (Farg and Khalil 2015). The charts shows that people with income in $120k to less than $150k are least in number. Highest frequency lies in the group of $60k to less than $90k. Rest of the income group has frequency in the middle of them. Chi-Square Test: A chi-square test has been carried to check whether income levels and confidence levels are dependent (Sharpe 2015). Requires hypothesis is: H0: income level and confidence levels are independent vs. H1: Income level and confidence intervals are dependent management. Required test statistic: - Chi-stat: {displaystyle chi ^{2}} , where O is observed frequency and E is expected frequency (Gaboardi et al. 2016). Calculation results: Table 3: Calculated values for Chi square test. Calculations Value a 0.05 df 18 c2 20.88 p-value 0.29 c2-crit value 28.87 Sig No The test is being made at 5% level of significance. It can be seen that p-value 0.05 and also, tabulated chi-square calculated chi-square. Therefore, the null hypothesis will be rejected and it can be said that income levels and confidence levels are independent. Conclusion: It can be concluded from the test that income levels and confidence levels are independent. Data are being collected here on different income levels and tallied. Confidence levels are also being marked in four categories. With a chi square test, it has been seen that the two levels are not at all related. References: Farg, M.H.M. and Khalil, F.M.H., 2015. Statistical Analysis of Academic Level of Student in Quantitative Methods Courses by Using Chi-Square Test and Markov Chains-Case Study of Faculty of Sciences and Humanities (Thadiq)-Shaqra University-KSA.Transition,20(2), p.1. Gaboardi, M., Lim, H.W., Rogers, R.M. and Vadhan, S.P., 2016. Differentially private chi-squared hypothesis testing: Goodness of fit and independence testing. InICML'16 Proceedings of the 33rd International Conference on International Conference on Machine Learning-Volume 48. JMLR. Lipsitz, S.R., Fitzmaurice, G.M., Sinha, D., Hevelone, N., Giovannucci, E. and Hu, J.C., 2015. Testing for independence in J K contingency tables with complex sample survey data.Biometrics,71(3), pp.832-840. Sharpe, D., 2015. Your chi-square test is statistically significant: Now what?.Practical Assessment, Research Evaluation,20.