ID Salary Compa Midpoint Age 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 60.3 27.2 35 61 47.7 76 41 21.5 74.3 23.6 24.8 66.1 41 22.1 24.6 47.1 69.6 35 24.9 34.2 74.4 51.4 23.4 56.4 25.1 23 42.5 75 79.9 48.8 24.1 27.4 60.6 27.3 24.4 22.7 22.5 58.9 34.5 24.3 42.6 24.8 75.7 64.4 48 61.3 62.9 66.3 60 67.2 1.058 57 31 31 57 48 67 40 23 67 23 23 57 40 23 23 40 57 31 23 31 67 48 23 48 23 23 40 67 67 48 23 31 57 31 23 23 23 57 31 23 40 23 67 57 48 57 57 57 57 57 34 52 30 42 36 36 32 32 49 30 41 52 30 32 32 44 27 31 32 44 43 48 36 30 41 22 35 44 52 45 29 25 35 26 23 27 22 45 27 24 25 32 42 45 36 39 37 34 41 38 0.878 1.129 1.070 0.993 1.135 1.026 0.933 1.109 1.025 1.078 1.159 1.026 0.963 1.069 1.177 1.221 1.130 1.081 1.104 1.110 1.070 1.018 1.176 1.093 0.999 1.063 1.120 1.193 1.017 1.047 0.885 1.063 0.882 1.062 0.985 0.977 1.033 1.114 1.055 1.066 1.078 1.130 1.130 1.000 1.076 1.103 1.163 1.053 1.179 Performance Service Gender Rating 85 80 75 100 90 70 100 90 100 80 100 95 100 90 80 90 55 80 85 70 95 65 65 75 70 95 80 95 95 90 60 95 90 80 90 75 95 95 90 90 80 100 95 90 95 75 95 90 95 80 8 7 5 16 16 12 8 9 10 7 19 22 2 12 8 4 3 11 1 16 13 6 6 9 4 2 7 9 5 18 4 4 9 2 4 3 2 11 6 2 5 8 20 16 8 20 5 11 21 12 0 0 1 0 0 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 0 1 1 1 0 1 0 1 0 0 1 0 0 0 1 1 1 0 1 0 0 1 1 0 1 0 0 1 0 0 Raise Degree Gender 1 5.7 3.9 3.6 5.5 5.7 4.5 5.7 5.8 4 4.7 4.8 4.5 4.7 6 4.9 5.7 3 5.6 4.6 4.8 6.3 3.8 3.3 3.8 4 6.2 3.9 4.4 5.4 4.3 3.9 5.6 5.5 4.9 5.3 4.3 6.2 4.5 5.5 6.3 4.3 5.7 5.5 5.2 5.2 3.9 5.5 5.3 6.6 4.6 0 0 1 1 1 1 1 1 1 1 1 0 0 1 1 0 1 0 1 0 1 1 0 0 0 0 1 0 0 0 1 0 1 1 0 0 0 0 0 0 0 1 0 1 1 1 1 1 0 0 M M F M M M F F M F F M F F F M F F M F M F F F M F M F M M F M M M F F F M F M M F F M F M M F M M Gr E B B E D F C A F A A E C A A C E B A B F D A D A A C F F D A B E B A A A E B A C A F E D E E E E E The ongoing question that the weekly assignments will focus on is: Are males and fe Note: to simplfy the analysis, we will assume that jobs within each grade comprise eq The column labels in the table mean: ID - Employee sample number Salary - Salary in thousands Age - Age in years Performance Rating - Appraisal rating (e Service - Years of service (rounded) Gender - 0 = male, 1 = female Midpoint - salary grade midpoint Raise - percent of last raise Grade - job/pay grade Degree (0= BS\\BA 1 = MS) Gender1 (Male or Female) Compa - salary divided by midpoint emales paid the same for equal work (under the Equal Pay Act)? qual work. employee evaluation score) Sal Compa 24 1.045 24.2 1.053 23.4 1.018 23.4 1.017 22.6 0.983 22.9 0.995 23.1 1.003 23.3 1.011 22.7 0.985 23.5 1.023 23 1.002 24 1.042 35.5 1.145 34.7 1.119 35.5 1.146 35.2 1.136 40.4 1.01 42.7 1.068 53.4 1.112 51.5 1.072 49.8 1.037 68.3 1.198 65.4 1.148 78.4 1.17 75.9 1.133 24 1.044 23.3 1.012 24.1 1.049 27.5 0.887 27.1 0.875 27.7 0.895 40.8 1.019 43.9 1.097 41 1.025 48.7 1.014 49.4 1.029 64.4 1.13 64.5 1.132 58.9 1.033 57.9 1.016 59 1.035 63.3 1.111 56.8 0.996 58 1.017 62.4 1.094 63.8 1.12 79 1.179 77 1.149 74.8 1.116 76 1.135 G 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Mid 23 23 23 23 23 23 23 23 23 23 23 23 31 31 31 31 40 40 48 48 48 57 57 67 67 23 23 23 31 31 31 40 40 40 48 48 57 57 57 57 57 57 57 57 57 57 67 67 67 67 Age 32 30 41 32 32 36 22 29 23 27 22 32 30 31 44 27 32 30 48 30 36 27 34 44 42 32 41 24 52 25 26 44 35 25 36 45 34 42 52 35 45 45 39 37 41 38 36 49 43 52 EES 90 80 100 90 80 65 95 60 90 75 95 100 75 80 70 90 100 100 65 75 95 55 90 95 95 85 70 90 80 95 80 90 80 80 90 90 85 100 95 90 95 90 75 95 95 80 70 100 95 95 SR 9 7 19 12 8 6 2 4 4 3 2 8 5 11 16 6 8 2 6 9 8 3 11 9 20 1 4 2 7 4 2 4 7 5 16 18 8 16 22 9 11 16 20 5 21 12 12 10 13 5 G 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Raise 5.8 4.7 4.8 6 4.9 3.3 6.2 3.9 5.3 4.3 6.2 5.7 3.6 5.6 4.8 5.5 5.7 4.7 3.8 3.8 5.2 3 5.3 4.4 5.5 4.6 4 6.3 3.9 5.6 4.9 5.7 3.9 4.3 5.7 4.3 5.7 5.5 4.5 5.5 4.5 5.2 3.9 5.5 6.6 4.6 4.5 4 6.3 5.4 Deg 1 1 1 1 1 0 0 1 0 0 0 1 1 0 0 0 1 0 1 0 1 1 1 0 0 1 0 0 0 0 1 0 1 0 1 0 0 1 0 1 0 1 1 1 0 0 1 1 1 0 SUMMARY OUTPUT SUMMARY OUTPUT Regression Statistics Regression Statistics Multiple R 0.7050179484 Multiple R 0.9931286935 R Square 0.4970503076 R Square 0.9863046018 Adjusted R Square 0.4132253589 Adjusted R Square 0.9840220355 Standard Error 0.0561252686 Standard Error 2.4352822665 Observations 50 Observations ANOVA 50 ANOVA df SS Regression 7 Residual 42 Total 49 Coefficients MS F Significance F df SS 0.1307500775 0.0186785825 5.9296225662 7.829064E-005 Regression 0.1323019225 0.0031500458 Residual 42 249.085188137 Total 49 0.263052 Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% 7 17938.4246119 Coefficients 18187.5098 Standard Error Intercept 0.9486238772 0.0817167716 11.608680312 1.08821E-014 0.7837127557 1.1135349987 0.7837127557 1.1135349987 Intercept -4.8714544587 3.54570071 Mid 0.0034995027 0.0006492568 5.3900133356 2.97671E-006 0.0021892495 0.0048097559 0.0021892495 0.0048097559 Mid 1.2284155048 0.0281713308 Age 0.0005527738 0.0014459446 0.3822925256 0.7041721007 -0.0023652605 0.0034708081 -0.0023652605 0.0034708081 Age 0.0368279425 0.0627397124 EES -0.0018462553 0.0010252155 -1.8008461371 0.0789105539 -0.0039152239 0.0002227133 -0.0039152239 0.0002227133 EES -0.0821579785 0.0444842245 SR -0.0004182288 0.0018278101 -0.2288141345 0.820123898 -0.004106899 0.0032704414 -0.004106899 0.0032704414 SR -0.0778484529 0.079308905 G 0.0646649961 0.0183396697 3.5259629624 0.001034866 0.0276540443 0.101675948 0.0276540443 0.101675948 G 2.9145083112 0.7957605113 Raise 0.0146549564 0.0139088976 1.0536389608 0.2980722322 -0.0134143354 0.0427242483 -0.0134143354 0.0427242483 Raise 0.6763294824 0.6035087689 Deg 0.0014675988 0.0161098249 0.0910996125 0.9278465471 -0.0310433441 0.0339785418 -0.0310433441 0.0339785418 Deg 0.0345044482 0.6990072742 t-Test: Two-Sample Assuming Equal Variances Variable 1 Mean Variance Observations Pooled Variance Hypothesized Mean Difference df t Stat Variable 2 1.06684 1.04836 0.00430164 0.00648099 25 25 0.005391315 0 48 0.8898352784 P(T<=t) one-tail 0.188996287 t Critical one-tail 1.6772241961 P(T<=t) two-tail 0.3779925741 t Critical two-tail 2.0106347576 MS F Significance F 2562.6320874 432.10336382 5.299063E-037 5.9305997175 t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% -1.3739045839 0.1767599037 -12.0269681853 2.2840592678 -12.026968185 2.2840592678 43.605164163 1.32019E-036 1.1715634576 1.2852675521 1.1715634576 1.2852675521 0.5869957178 0.5603489282 -0.0897859231 0.1634418081 -0.0897859231 0.1634418081 -1.8469014451 0.0718147225 -0.171930778 0.007614821 -0.171930778 0.007614821 -0.9815852701 0.3319249969 -0.2379003029 0.0822033971 -0.2379003029 0.0822033971 3.6625445343 0.000693549 1.3085985836 4.5204180389 1.3085985836 4.5204180389 1.1206622295 0.2687988764 -0.5416005215 1.8942594864 -0.5416005215 1.8942594864 0.0493620731 0.9608647532 -1.3761493419 1.4451582383 -1.3761493419 1.4451582383 Week 2 1 Testing means - T-tests In questions 2, 3, and 4 be sure to include the null and alternate hypotheses you will be testing. In the first 4 questions use alpha = 0.05 in making your decisions on rejecting or not rejecting the null hypothesis. Below are 2 one-sample t-tests comparing male and female average salaries to the overall sample mean. (Note: a one-sample t-test in Excel can be performed by selecting the 2-sample unequal variance t-test and making the second variable = Ho value - a Note: These values are not the same as the data the assignment uses. The purpose is to analyze the results of t-tests rather than directly answer our eq Based on these results, how do you interpret the results and what do these results suggest about the population means for male and female average sal Males Ho: Mean salary = Ha: Mean salary =/= Females Ho: Mean salary = Ha: Mean salary =/= 45.00 45.00 45.00 45.00 Note: While the results both below are actually from Excel's t-Test: Two-Sample Assuming Unequal Variances, having no variance in the Ho variable makes the calculations default to the one-sample t-test outcome - we are tricking Excel into doing a one sample Male Ho Female Ho Mean 52 45 Mean 38 45 Variance 316 0 Variance 334.66667 0 Observations 25 25 Observations 25 25 Hypothesized Mean Difference df t Stat P(T<=t) one-tail t Critical one-tail P(T<=t) two-tail Hypothesized Mean Difference df t Stat P(T<=t) one-tail t Critical one-tail P(T<=t) two-tail 0 24 1.9689038266 0.0303078503 1.7108820799 0.0606157006 t Critical two-tail 2.0638985616 Conclusion: Do not reject Ho; mean equals 45 t Critical two-tail 2.0638986 Conclusion: Do not reject Ho; mean equals 45 Note: the Female results are done for you, please complete the male results. Is this a 1 or 2 tail test? 2 Tail test - why? Ha contains =/= P-value is: 0.06061 Is P-value < 0.05 (one tail test) or 0.25 (two tail test)? Is this a 1 or 2 tail test? 2 tail - why? Ho contains = P-value is: 0.0677242 Is P-value < 0.05 (one tail test) or 0.25 (two tail test)? No Why do we not reject the null Because hypothesis? 0 24 -1.913206 0.0338621 1.7108821 0.0677242 No the P-value is > rejection alpha. Why do we not reject the null hypothesis? P-value greater than (>) rejection alpha Interpretation of test outcomes: Since we do not reject Ho, the results recommend the male and female means could be equal to each other. 2 Based on our sample data set, perform a 2-sample t-test to see if the population male and female average salaries could be equal to each other. (Since we have not yet covered testing for variance equality, assume the data sets have statistically equal variances.) Ho: Ha: Test to use: Male salary mean = Female salary mean Male salary mean =/= Female salary mean t-Test: Two-Sample Assuming Equal Variances T-Test: Two-Sample (Equal Variances) Mean Variance Observations Pooled Variance Hypothesized Mean Difference df t Stat P(T<=t) one-tail t Critical one-tail P(T<=t) two-tail t Critical two-tail P-value is: Is P-value < 0.05 (one tail test) or 0.25 (two tail test)? Reject or do not reject Ho: 0.0085 No Reject Ho Male Female 52 38 316 334.6667 25 25 325.3333333 0 48 2.744218961 0.004253009 1.677224196 0.008506018 2.010634758 If the null hypothesis was rejected, calculate the effect size value: If calculated, what is the meaning of effect size measure: Interpretation: 0.7291666667 Gender has a large impact on salary difference. Results show that males and females cannot have equal, average salaries. b. Is the one or two sample t-test the proper/correct apporach to comparing salary equality? Why? The two sample t-test is the propper/correct approach to comparing salary equlity. This is because the two sample is more efficient and produces resul 3 Based on our sample data set, can the male and female compas in the population be equal to each other? (Another 2-sample t-test.) Again, please assume equal variances for these groups. Ho: Male mean compa = Female mean compa Ha: Male mean compa =/= Female mean compa Statistical test to use: T-Test: Two-Sample Assuming Equal Variances t-Test: Two-Sample Assuming Equal Variances Mean Variance Observations Pooled Variance Hypothesized Mean Difference df t Stat P(T<=t) one-tail t Critical one-tail P(T<=t) two-tail t Critical two-tail What is the p-value: Is P-value < 0.05 (one tail test) or 0.25 (two tail test)? Reject or do not reject Ho: If the null hypothesis was rejected, calculate the effect size value: If calculated, what is the meaning of effect size measure: Male Female 1.05624 1.06872 0.007020607 0.004948 25 25 0.005984492 0 48 -0.57036906 0.285543918 1.677224196 0.571087836 2.010634758 0.571 Yes Do not reject Ho n/a n/a Interpretation: There is not enough evidence to support different average compa rates between the two genders. 4 Since performance is often a factor in pay levels, is the average Performance Rating the same for both genders? NOTE: do NOT assume variances are equal in this situation. Ho: Average Performance Rating is equal for both genders Ha: Average Performacne Rating is unequal Test to ust-Test: Two-Sample Assuming Unequal Variances What is the p-value: Is P-value < 0.05 (one tail test) or 0.25 (two tail test)? Do we REJ or Not reject the null? If the null hypothesis was rejected, calculate the effect size value: If calculated, what is the meaning of effect size measure: Interpretation: 5 If the salary and compa mean tests in questions 2 and 3 provide different results about male and female salary equality, which would be more appropriate to use in answering the question about salary equity? Why? I think that the compa would be the better option to choose. The rerason is because it removes any kind of variation to the measure. What are your conclusions about equal pay at this point? My conclusion so far is that the average salaries are different. The compas do not seem as different as the salaries. lue - a constant.) our equal pay question. age salaries? ample test for us. s results within preffered ranges