Set Week Three During this week, we will look at ways of testing multiple (more than two) data samples at the same time. We will continue to use the data and assignment file that we opened in Week 2, we just move on to the Week 3 tab. The first question asks us to determine if the average compa-ratio is equal across 10K salary groups (20 - 29K. 30 - 39K, etc.). The second question asks us to identify which of the salary groups have different averages. The final question asks us to interpret the new information presented in the lecture and assignment; how does the new information we analyzed help us answer our equal pay for equal work question. The data and assignment file can be found in the Course Materials link, at the bottom in the Multi-Media section. If you save the files from last week, you do not need to open them again. 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 63.9 27.7 34.3 57.6 47.4 75.2 41.9 23.4 74 24.2 23.7 58.3 41.4 23.7 23 41.5 63.6 34.3 24.7 35.5 78.1 49 23.1 56.8 24.2 23.1 45.3 76.4 74.6 48.2 23.1 27.8 61.7 27.5 23.7 25.1 23.4 60.1 1.121 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 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 0.892 1.105 1.010 0.987 1.122 1.048 1.018 1.105 1.054 1.032 1.022 1.034 1.030 1.001 1.037 1.115 1.107 1.073 1.144 1.166 1.020 1.005 1.183 1.053 1.003 1.132 1.141 1.113 1.005 1.006 0.898 1.083 0.886 1.032 1.093 1.016 1.054 Performance Service Gender Raise 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 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 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 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 39 40 41 42 43 44 45 46 47 48 49 50 36.7 25.1 38.8 23 75 64.4 47.4 68.7 59.6 65.9 69.1 65.2 1.184 1.090 0.971 1.001 1.120 1.129 0.988 1.205 1.045 1.156 1.213 1.143 31 23 40 23 67 57 48 57 57 57 57 57 27 24 25 32 42 45 36 39 37 34 41 38 90 90 80 100 95 90 95 75 95 90 95 80 6 2 5 8 20 16 8 20 5 11 21 12 1 0 0 1 1 0 1 0 0 1 0 0 5.5 6.3 4.3 5.7 5.5 5.2 5.2 3.9 5.5 5.3 6.6 4.6 Degree Gender 1 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 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 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 The ongoing question that the weekly assignments will focus on is: Are males and fema Note: to simplfy the analysis, we will assume that jobs within each grade comprise equa The column labels in the table mean: ID - Employee sample number Salary - Salary in thousands Age - Age in years Performance Rating - Appraisal rating (emp 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 0 0 0 1 0 1 1 1 1 1 0 0 F M M F F M F M M F M M B A C A F E D E E E E E on is: Are males and females paid the same for equal work (under the Equal Pay Act)? each grade comprise equal work. thousands g - Appraisal rating (employee evaluation score) , 1 = female vided by midpoint 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 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 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 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 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 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 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 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 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 63.8 1.12 79 1.179 77 1.149 74.8 1.116 76 1.135 0 0 0 0 0 57 67 67 67 67 38 36 49 43 52 80 70 100 95 95 12 12 10 13 5 0 0 0 0 0 4.6 4.5 4 6.3 5.4 0 1 1 1 0 SUMMARY OUTPUT Regression Statistics Multiple R 0.705018 R Square 0.49705 Adjusted R 0.413225 Standard E 0.056125 Observatio 50 ANOVA df Regression SS 7 MS Significance F 0.13075 0.018679 5.929623 7.83E-005 Residual 42 0.132302 Total 49 0.263052 0.00315 Coefficients Standard Error t Stat Intercept F P-value Lower 95%Upper 95% Lower 95.0% Upper 95.0% 0.948624 0.081717 11.60868 1.09E-014 0.783713 1.113535 0.783713 1.113535 Mid 0.0035 0.000649 5.390013 2.98E-006 0.002189 0.00481 0.002189 0.00481 Age 0.000553 0.001446 0.382293 0.704172 -0.002365 0.003471 -0.002365 0.003471 EES -0.001846 0.001025 -1.800846 0.078911 -0.003915 0.000223 -0.003915 0.000223 SR -0.000418 0.001828 -0.228814 0.820124 -0.004107 0.00327 -0.004107 0.00327 G 0.064665 0.01834 3.525963 0.001035 0.027654 0.101676 0.027654 0.101676 Raise 0.014655 0.013909 1.053639 0.298072 -0.013414 0.042724 -0.013414 0.042724 Deg 0.001468 0.01611 0.0911 0.927847 -0.031043 0.033979 -0.031043 0.033979 t-Test: Two-Sample Assuming Equal Variances Variable 1 Variable 2 Mean Variance Observatio 1.06684 0.004302 0.006481 25 Pooled Var 0.005391 Hypothesiz df t Stat 1.04836 0 48 0.889835 P(T<=t) one0.188996 t Critical on 1.677224 P(T<=t) two0.377993 t Critical tw 2.010635 25 SUMMARY OUTPUT Regression Statistics Multiple R 0.993129 R Square 0.986305 Adjusted R 0.984022 Standard E 2.435282 Observatio 50 ANOVA df Regression SS 42 249.0852 Total 49 18187.51 Significance F 5.9306 Coefficients Standard Error t Stat Intercept F 7 17938.42 2562.632 432.1034 5.30E-037 Residual Upper 95.0% MS -4.871454 3.545701 -1.373905 P-value Lower 95%Upper 95% Lower 95.0% Upper 95.0% 0.17676 -12.02697 2.284059 -12.02697 2.284059 Mid 1.228416 0.028171 43.60516 1.32E-036 1.171563 1.285268 1.171563 1.285268 Age 0.036828 0.06274 0.586996 0.560349 -0.089786 0.163442 -0.089786 0.163442 EES -0.082158 0.044484 -1.846901 0.071815 -0.171931 0.007615 -0.171931 0.007615 SR -0.077848 0.079309 -0.981585 0.331925 -0.2379 0.082203 -0.2379 0.082203 G 2.914508 0.795761 3.662545 0.000694 1.308599 4.520418 1.308599 4.520418 Raise 0.676329 0.603509 1.120662 0.268799 -0.541601 1.894259 -0.541601 1.894259 Deg 0.034504 0.699007 0.049362 0.960865 -1.376149 1.445158 -1.376149 1.445158 Upper 95.0% Sum - Gender1 Gender1 F M Total Result Gr A B C D E F Total Result ID Salary 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 63.9 27.7 34.3 57.6 47.4 75.2 41.9 23.4 74 24.2 23.7 58.3 41.4 23.7 23 41.5 63.6 34.3 24.7 35.5 78.1 49 23.1 56.8 24.2 23.1 45.3 76.4 74.6 48.2 23.1 27.8 61.7 27.5 23.7 25.1 23.4 60.1 36.7 25.1 38.8 23 Compa Midpoint 1.121 0.892 1.105 1.010 0.987 1.122 1.048 1.018 1.105 1.054 1.032 1.022 1.034 1.030 1.001 1.037 1.115 1.107 1.073 1.144 1.166 1.020 1.005 1.183 1.053 1.003 1.132 1.141 1.113 1.005 1.006 0.898 1.083 0.886 1.032 1.093 1.016 1.054 1.184 1.090 0.971 1.001 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 Age 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 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 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 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 Raise Degree 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 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 43 44 45 46 47 48 49 50 75 64.4 47.4 68.7 59.6 65.9 69.1 65.2 1.120 1.129 0.988 1.205 1.045 1.156 1.213 1.143 67 57 48 57 57 57 57 57 42 45 36 39 37 34 41 38 95 90 95 75 95 90 95 80 20 16 8 20 5 11 21 12 1 0 1 0 0 1 0 0 5.5 5.2 5.2 3.9 5.5 5.3 6.6 4.6 0 1 1 1 1 1 0 0 Gender 1 Gr 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 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 Copy Employee Data set to this page. The ongoing question that the weekly assignments will focus on is: Are males and females p Note: to simplfy the analysis, we will assume that jobs within each grade comprise equal wor The column labels in the table mean: ID - Employee sample number Salary - Salary in thousands Age - Age in years Performance Rating - Appraisal rating (Employee ev SERvice - Years of service Gender: 0 = male, 1 = female Midpoint - salary grade midpointRaise - percent of last raise Grade - job/pay grade Degree (0= BS\\BA 1 = MS) Gender1 (Male or Female) Compa-ratio - salary divided by midpoint F M F M M F M M F E D E E E E E age. : Are males and females paid the same for equal work (under the Equal Pay Act)? grade comprise equal work. aisal rating (Employee evaluation score) by midpoint This assignment covers the material presented in weeks 1 and 2. Six Questions Before starting this assignment, make sure the the assignment data from the Employee Salary Data Set file is copied o You can do this either by a copy and paste of all the columns or by opening the data file, right clicking on the Data tab (Weekly Assignment Sheet or whatever you are calling your master assignment file). It is highly recommended that you copy the data columns (with labels) and paste them to the right so that whatever yo To Ensure full credit for each question, you need to show how you got your results. For example, Question 1 asks for then the cells should have an "=XX" formula in them, where XX is the column and row number showing the value in value using fxfunctions, then each function should be located in the cell and the location of the data values should be So, Cell D31 - as an example - shoud contain something like "=T6" or "=average(T2:T26)". Having only a numerica The reason for this is to allow instructors to provide feedback on Excel tools if the answers are not correct - we need t In starting the analysis on a research question, we focus on overall descriptive statistics and seeing if differences exist 1 The first step in analyzing data sets is to find some summary descriptive statistics for key variables. Since t focus mostly on the compa-ratios, we need to find the mean, standard deviations, and range for our groups: Sorting the compa-ratios into male and females will require you copy and paste the Compa-ratio and Gende The values for age, performance rating, and service are provided for you for future use, and - if desired - to (see if you can replicate the values). You can use either the Data Analysis Descriptive Statistics tool or the Fx =average and =stdev functions. The range can be found using the difference between the =max and =min functions with Fx functions or fr Suggestion: Copy and paste the compa-ratio data to the right (Column T) and gender data in column U. If you use Descriptive statistics, Place the output table in row 1 of a column to the right. If you did not use Descriptive Statistics, make sure your cells show the location of the da Overall Female Male Comparatio Mean 1.0638 Standard Deviation 0.0765 Range 0.327 Mean 1.0654 Standard Deviation 0.0628 Range 0.196 Mean 1.0622 Standard Deviation 0.0895 Range 0.327 Age 35.7 8.2513 30 32.5 6.9 26.0 38.9 8.4 28.0 Perf. Rat. Service 85.9 9.0 11.4147 5.7177 Note - remember the da 45 21 84.2 7.9 13.6 4.9 45.0 18.0 87.6 10.0 8.7 6.4 30.0 21.0 A key issue in comparing data sets is to see if they are distributed/shaped the same. At this point we can do this by looking at the probabilities that males and females are distributed in the same way for a grade levels. 2 Empirical Probability: What is the probability for a: Probability a. Randomly selected person being in grade E or above? b. Randomly selected person being a male in grade E or above? c. Randomly selected male being in grade E or above? d. Why are the results different? (a) is marginal probability, (b) is joint proba 3 Normal Curve based probability: For each group (overall, females, males), what are the values for each que A Make sure your answer cells show the Excel function and cell location of the data used. The probability of being in the top 1/3 of the compa-ratio distribution. Note, we can find the cutoff value for the top 1/3 using the fx Large function: =large(range, value). Value is the number that identifies the x-largest value. For the top 1/3 value would be the value that starts t For the overall group, this would be the 50/3 or 17th (rounded), for the gender groups, it would be the 25/3 i. How nany salaries are in the top 1/3 (rounded to nearest whole number) for each group? ii What Compa-ratio value starts the top 1/3 of the range for each group? iii What is the z-score for this value? iv. What is the normal curve probability of exceeding this score? B How do you interpret the relationship between the data sets? What does this suggest about our equal pay fo The Z scores for males and females are pretty close to each other. Moreover the normal curve probability of Thus no evidence of unequal pay is observed based on the result. 4 A Based on our sample data set, can the male and female compa-ratios in the population be equal to each othe First, we need to determine if these two groups have equal variances, in order to decide which t-test to use. What is the data input ranged used for this question: Step 1: Ho: (female)^2 = (male)^2 Ha: (female)^2 (male)^2 Step 2: Decision Rule: Reject Ho if p-value < 0.05 Step 3: Statistical test: F test for equal variance Why? We want to compare the variance between two groups Step 4: Conduct the test - place cell B77 in the output location box. F-Test Two-Sample for Variances Variable 1 Mean Variance Variable 2 1.06544 1.0622 0.0039377567 0.00800758 Observations 25 25 df 24 24 F 0.491753442 P(F<=f) one-tail 0.0442649014 F Critical one-tail 0.5040933467 Step 5: Conclusion and Interpretation What is the p-value: 0.0442649014 Is the P-value < 0.05 (for a one tail test) or 0.025 (for a two tail test)? No What is your decision: REJ or NOT reject the null? Not reject the null What does this result say about our question Variances are equal of variance equality? B Are male and female average compa-ratios equal? (Regardless of the outcome of the above F-test, assume equal variances for this test.) What is the data input ranged used for this question: Step 1: Ho: (female) = (male) Ha: (female) (male) Step 2: Decision Rule: Reject Ho if p-value < 0.05 Step 3: Statistical test: independent sample t-test assuming equal variance Why? The variances are not significantly different and we are comparing the m Step 4: Conduct the test - place cell B109 in the output location box. t-Test: Two-Sample Assuming Equal Variances Variable 1 Mean Variable 2 1.06544 Variance 1.0622 0.0039377567 0.00800758 Observations Pooled Variance Hypothesized Mean df 25 25 0.00597267 0 48 t Stat 0.1482230538 P(T<=t) one-tail 0.4413938347 t Critical one-tail 1.6772241961 P(T<=t) two-tail 0.8827876693 t Critical two-tail 2.0106347576 Step 5: Conclusion and Interpretation What is the p-value: 0.8827876693 Is the P-value < 0.05 (for a one tail test) or 0.025 (for a two tail test)? No What is your decision: REJ or NOT reject the null? Not reject the null What does your decision on rejecting the null Compa means are not significantly different between gender hypothesis mean? If the null hypothesis was rejected, calculate the effect size value: If the effect size was calculated, what doe the result mean in terms of why the null hypothesis was rejected? What does the result of this test tell us about There is no evidence to indicate that the salaries are differen our question on salary equality? 5 Is the Female average compa-ratio equal to or less than the midpoint value of 1.00? This question is the same as: Does the company, pay its females - on average - at or below the grade midpo considered the market rate)? Suggestion: Use the data column T to the right for your null hypothesis value. What is the data input ranged used for this question: Step 1: Ho: (female) = 1 Ha: (female) < 1 Step 2: Decision Rule: Reject Ho if p-value < 0.05 Step 3: Statistical test: one sample, left tailed t-test Why? We are comparing single sample mean with a hypothesized mean Step 4: Conduct the test - place cell B162 in the output location box. t-Test: Two-Sample Assuming Unequal Variances Variable 1 Mean Variance Observations Hypothesized Mean df t Stat Variable 2 1.06544 1 0.0039377567 0 25 25 0 24 5.214214071 P(T<=t) one-tail 1.2090742E-005 t Critical one-tail 1.7108820799 P(T<=t) two-tail 2.4181483E-005 t Critical two-tail 2.0638985616 Step 5: Conclusion and Interpretation What is the p-value: 1.209074E-005 Is the P-value < 0.05 (for a one tail test) or 0.025 (for a two tail test)? Yes What, besides the p-value, needs to be Sign of the test statistic considered with a one tail test? Decision: Reject or do not reject Ho? Do not reject Ho What does your decision on rejecting the null There is not enough evidence to conclude that the Female av hypothesis mean? If the null hypothesis was rejected, calculate the effect size value: If the effect size was calculated, what doe the result mean in terms of why the null hypothesis was rejected? What does the result of this test tell us about It does not help so much to answer our question because we our question on salary equality? 6 Considering both the salary information in the lectures and your compa-ratio information, what conclusions The results are supporting equal pay. There is no evidence against equal pay. Why - what statistical results support this conclusion? The results from question 3 and 4 above is indicating no significant difference between males and females i y Data Set file is copied over to this Assignment file. t clicking on the Data tab, selecting Move or Copy, and copying the entire sheet to this file right so that whatever you do will not disrupt the original data values and relationships. mple, Question 1 asks for several data values. If you obtain them using descriptive statistics, ber showing the value in the descriptive statistics table. If you choose to generate each he data values should be shown. Having only a numerical value will not earn full credit. re not correct - we need to see how the results were obtained. seeing if differences exist. Probing into reasons and mitigating factors is a follow-up activity. or key variables. Since the assignment problems will nd range for our groups: Males, Females, and Overall. e Compa-ratio and Gender1 columns, and then sort on Gender1. use, and - if desired - to test your approach to the compa-ratio answers and =stdev functions. s with Fx functions or from Descriptive Statistics. der data in column U. of a column to the right. ow the location of the data (Example: =average(T2:T51) Note - remember the data is a sample from the larger company population oint we can do this rade levels. Sum - GenGr Gender1 A F M Total Result B C D E F Total Result Probability 0.36 0.28 0.56 bability, (b) is joint probability and (c ) is conditional probability. So the answers are different. e the values for each question below?: ge(range, value). d be the value that starts the top 1/3 of the range, ups, it would be the 25/3 = 8th (rounded) value. Overall Female Male All of the functions below are in the fx statistical list. 17 8 8 Use the "=ROUND" function (found in Math or All list) 1.107 1.107 1.121 Use the "=LARGE" function 0.5643863 0.662294 0.657093 Use Excel's STANDARDIZE function 0.2862456 0.253891 0.255561 Use "=1-NORM.S.DIST" function est about our equal pay for equal work question? rmal curve probability of exceeding this score is also almost same for males and females. ion be equal to each other? ecide which t-test to use. we are comparing the mean between two independent samples different between genders t the salaries are different r below the grade midpoint (which is ypothesized mean nclude that the Female average compa-ratio is less than the midpoint value of 1.00. Thus females are not getting paid below the g our question because we are not considering the male population in this case. mation, what conclusions can you reach about equal pay for equal work? ween males and females in terms of compa ratio. Thus the above conclusion can be made. 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 Compa Gender 1 1.105 1.048 1.018 1.054 1.032 1.034 1.030 1.001 1.115 1.107 1.144 1.020 1.005 1.183 1.003 1.141 1.006 1.032 1.093 1.016 1.184 1.001 1.120 0.988 1.156 1.121 0.892 1.010 0.987 F F F F F F F F F F F F F F F F F F F F F F F F F M M M M 1.122 1.105 1.022 1.037 1.073 1.166 1.053 1.132 1.113 1.005 0.898 M M M M M M M M M M M Total Result 1.083 0.886 1.054 1.090 0.971 1.129 1.205 1.045 1.213 1.143 M M M M M M M M M M t getting paid below the grade midpoint Week 3 ANOVA Three Questions Remember to show how you got your results in the appropriate cells. For questions using functions, show the input r 1 One interesting question is are the average compa-ratios equal across salary ranges of 10K each. While compa-ratios remove the impact of grade on salaries, are they different for different pay levels, that is are people at different levels paid differently relative to the midpoint? (Put data values at right.) What is the data input ranged used for this question: Step 1: Ho: Ha: Step 2: Decision Rule: Step 3: Statistical test: Why? Step 4: Conduct the test - place cell b16 in the output location box. Step 5: Conclusions and Interpretation What is the p-value? Is P-value < 0.05? What is your decision: REJ or NOT reject the null? If the null hypothesis was rejected, what is the effect size value (eta squared)? If calculated, what does the effect size value tell us about why the null hypothesis was rejected? What does that decision mean in terms of our equal pay question? 2 If the null hypothesis in question 1 was rejected, which pairs of means differ? Groups Compared G1 G2 G1 G3 G1 G4 G1 G5 G1 G6 Diff T +/- Term Low to G2 G3 G2 G4 G2 G5 G2 G6 G3 G4 G3 G5 G3 G6 G4 G5 G4 G6 G5 G6 3 Since compa is already a measure of pay for equal work, do these results impact your conclusion on equal pay for equal work? Why or why not? High ng functions, show the input range when asked. anges of 10K each. t for different pay levels, (Put data values at right.) Group name: Salary Intervals: Compa-ratio values: G1 G2 G3 G4 G5 G6 22-29 30-39 40-49 50-59 60-69 70-79 Why? Difference Significant? Why? Regression and Corellation Five Questions Remember to show how you got your results in the appropriate cells. For questions using functions, show the inp 1 Create a correlation table using Compa-ratio and the other interval level variables, except for Suggestion, place data in columns T - Y. What range was placed in the Correlation input range box: Place C9 in output box. b What are the statistically significant correlations related to Compa-ratio? c Are there any surprises - correlations you though would be significant and are not, or non sign d Why does or does not this information help answer our equal pay question? 2 Perform a regression analysis using compa as the dependent variable and the variables used in including the dummy variables. Show the result, and interpret your findings by answering the Suggestion: Place the dummy variables values to the right of column Y. What range was placed in the Regression input range box: Note: be sure to include the appropriate hypothesis statements. Regression hypotheses Ho: Ha: Coefficient hyhpotheses (one to stand for all the separate variables) Ho: Ha: Place B36 in output box. Interpretation: For the Regression as a whole: What is the value of the F statistic: What is the p-value associated with this value: Is the p-value < 0.05? What is your decision: REJ or NOT reject the null? What does this decision mean? For each of the coefficients: What is the coefficient's p-value for each of the variables: Is the p-value < 0.05? Do you reject or not reject each null hypothesis: Midpoint Age Perf. Rat. What are the coefficients for the significant variables? Using the intercept coefficient and only the significant variables, what is the equation? Compa-ratio = Is gender a significant factor in compa-ratio? Regardless of statistical significance, who gets paid more with all other things being equal? How do we know? 3 What does regression analysis show us about analyzing complex measures? 4 Between the lecture results and your results, what else would you like to know before answering our question on equal pay? Why? 5 Between the lecture results and your results, what is your answer to the question of equal pay for equal work for males and females? Why? g functions, show the input range when asked. evel variables, except for Salary. T= Significant r = nt and are not, or non significant correlations you thought would be? e and the variables used in Q1 along with findings by answering the following questions. Service Gender Degree the question Compa- Midpoint ratio Age Performa Service nce Rating Raise Degree Gender Sum - Gender1 Gender1 F M Total Result Gr A B C D E F Total Result ID Salary 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 63.9 27.7 34.3 57.6 47.4 75.2 41.9 23.4 74 24.2 23.7 58.3 41.4 23.7 23 41.5 63.6 34.3 24.7 35.5 78.1 49 23.1 56.8 24.2 23.1 45.3 76.4 74.6 48.2 23.1 27.8 61.7 27.5 23.7 25.1 23.4 60.1 36.7 25.1 38.8 23 Compa Midpoint 1.121 0.892 1.105 1.010 0.987 1.122 1.048 1.018 1.105 1.054 1.032 1.022 1.034 1.030 1.001 1.037 1.115 1.107 1.073 1.144 1.166 1.020 1.005 1.183 1.053 1.003 1.132 1.141 1.113 1.005 1.006 0.898 1.083 0.886 1.032 1.093 1.016 1.054 1.184 1.090 0.971 1.001 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 Age 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 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 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 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 Raise Degree 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 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 43 44 45 46 47 48 49 50 75 64.4 47.4 68.7 59.6 65.9 69.1 65.2 1.120 1.129 0.988 1.205 1.045 1.156 1.213 1.143 67 57 48 57 57 57 57 57 42 45 36 39 37 34 41 38 95 90 95 75 95 90 95 80 20 16 8 20 5 11 21 12 1 0 1 0 0 1 0 0 5.5 5.2 5.2 3.9 5.5 5.3 6.6 4.6 0 1 1 1 1 1 0 0 Gender 1 Gr 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 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 Copy Employee Data set to this page. The ongoing question that the weekly assignments will focus on is: Are males and females p Note: to simplfy the analysis, we will assume that jobs within each grade comprise equal wor The column labels in the table mean: ID - Employee sample number Salary - Salary in thousands Age - Age in years Performance Rating - Appraisal rating (Employee ev SERvice - Years of service Gender: 0 = male, 1 = female Midpoint - salary grade midpointRaise - percent of last raise Grade - job/pay grade Degree (0= BS\\BA 1 = MS) Gender1 (Male or Female) Compa-ratio - salary divided by midpoint F M F M M F M M F E D E E E E E age. : Are males and females paid the same for equal work (under the Equal Pay Act)? grade comprise equal work. aisal rating (Employee evaluation score) by midpoint This assignment covers the material presented in weeks 1 and 2. Six Questions Before starting this assignment, make sure the the assignment data from the Employee Salary Data Set file is copied o You can do this either by a copy and paste of all the columns or by opening the data file, right clicking on the Data tab (Weekly Assignment Sheet or whatever you are calling your master assignment file). It is highly recommended that you copy the data columns (with labels) and paste them to the right so that whatever yo To Ensure full credit for each question, you need to show how you got your results. For example, Question 1 asks for then the cells should have an "=XX" formula in them, where XX is the column and row number showing the value in value using fxfunctions, then each function should be located in the cell and the location of the data values should be So, Cell D31 - as an example - shoud contain something like "=T6" or "=average(T2:T26)". Having only a numerica The reason for this is to allow instructors to provide feedback on Excel tools if the answers are not correct - we need t In starting the analysis on a research question, we focus on overall descriptive statistics and seeing if differences exist 1 The first step in analyzing data sets is to find some summary descriptive statistics for key variables. Since t focus mostly on the compa-ratios, we need to find the mean, standard deviations, and range for our groups: Sorting the compa-ratios into male and females will require you copy and paste the Compa-ratio and Gende The values for age, performance rating, and service are provided for you for future use, and - if desired - to (see if you can replicate the values). You can use either the Data Analysis Descriptive Statistics tool or the Fx =average and =stdev functions. The range can be found using the difference between the =max and =min functions with Fx functions or fr Suggestion: Copy and paste the compa-ratio data to the right (Column T) and gender data in column U. If you use Descriptive statistics, Place the output table in row 1 of a column to the right. If you did not use Descriptive Statistics, make sure your cells show the location of the da Overall Female Male Comparatio Mean 1.0638 Standard Deviation 0.0765 Range 0.327 Mean 1.0654 Standard Deviation 0.0628 Range 0.196 Mean 1.0622 Standard Deviation 0.0895 Range 0.327 Age 35.7 8.2513 30 32.5 6.9 26.0 38.9 8.4 28.0 Perf. Rat. Service 85.9 9.0 11.4147 5.7177 Note - remember the da 45 21 84.2 7.9 13.6 4.9 45.0 18.0 87.6 10.0 8.7 6.4 30.0 21.0 A key issue in comparing data sets is to see if they are distributed/shaped the same. At this point we can do this by looking at the probabilities that males and females are distributed in the same way for a grade levels. 2 Empirical Probability: What is the probability for a: Probability a. Randomly selected person being in grade E or above? b. Randomly selected person being a male in grade E or above? c. Randomly selected male being in grade E or above? d. Why are the results different? (a) is marginal probability, (b) is joint proba 3 Normal Curve based probability: For each group (overall, females, males), what are the values for each que A Make sure your answer cells show the Excel function and cell location of the data used. The probability of being in the top 1/3 of the compa-ratio distribution. Note, we can find the cutoff value for the top 1/3 using the fx Large function: =large(range, value). Value is the number that identifies the x-largest value. For the top 1/3 value would be the value that starts t For the overall group, this would be the 50/3 or 17th (rounded), for the gender groups, it would be the 25/3 i. How nany salaries are in the top 1/3 (rounded to nearest whole number) for each group? ii What Compa-ratio value starts the top 1/3 of the range for each group? iii What is the z-score for this value? iv. What is the normal curve probability of exceeding this score? B How do you interpret the relationship between the data sets? What does this suggest about our equal pay fo The Z scores for males and females are pretty close to each other. Moreover the normal curve probability of Thus no evidence of unequal pay is observed based on the result. 4 A Based on our sample data set, can the male and female compa-ratios in the population be equal to each othe First, we need to determine if these two groups have equal variances, in order to decide which t-test to use. What is the data input ranged used for this question: Step 1: Ho: (female)^2 = (male)^2 Ha: (female)^2 (male)^2 Step 2: Decision Rule: Reject Ho if p-value < 0.05 Step 3: Statistical test: F test for equal variance Why? We want to compare the variance between two groups Step 4: Conduct the test - place cell B77 in the output location box. F-Test Two-Sample for Variances Variable 1 Mean Variance Variable 2 1.06544 1.0622 0.0039377567 0.00800758 Observations 25 25 df 24 24 F 0.491753442 P(F<=f) one-tail 0.0442649014 F Critical one-tail 0.5040933467 Step 5: Conclusion and Interpretation What is the p-value: 0.0442649014 Is the P-value < 0.05 (for a one tail test) or 0.025 (for a two tail test)? No What is your decision: REJ or NOT reject the null? Not reject the null What does this result say about our question Variances are equal of variance equality? B Are male and female average compa-ratios equal? (Regardless of the outcome of the above F-test, assume equal variances for this test.) What is the data input ranged used for this question: Step 1: Ho: (female) = (male) Ha: (female) (male) Step 2: Decision Rule: Reject Ho if p-value < 0.05 Step 3: Statistical test: independent sample t-test assuming equal variance Why? The variances are not significantly different and we are comparing the m Step 4: Conduct the test - place cell B109 in the output location box. t-Test: Two-Sample Assuming Equal Variances Variable 1 Mean Variable 2 1.06544 Variance 1.0622 0.0039377567 0.00800758 Observations Pooled Variance Hypothesized Mean df 25 25 0.00597267 0 48 t Stat 0.1482230538 P(T<=t) one-tail 0.4413938347 t Critical one-tail 1.6772241961 P(T<=t) two-tail 0.8827876693 t Critical two-tail 2.0106347576 Step 5: Conclusion and Interpretation What is the p-value: 0.8827876693 Is the P-value < 0.05 (for a one tail test) or 0.025 (for a two tail test)? No What is your decision: REJ or NOT reject the null? Not reject the null What does your decision on rejecting the null Compa means are not significantly different between gender hypothesis mean? If the null hypothesis was rejected, calculate the effect size value: If the effect size was calculated, what doe the result mean in terms of why the null hypothesis was rejected? What does the result of this test tell us about There is no evidence to indicate that the salaries are differen our question on salary equality? 5 Is the Female average compa-ratio equal to or less than the midpoint value of 1.00? This question is the same as: Does the company, pay its females - on average - at or below the grade midpo considered the market rate)? Suggestion: Use the data column T to the right for your null hypothesis value. What is the data input ranged used for this question: Step 1: Ho: (female) = 1 Ha: (female) < 1 Step 2: Decision Rule: Reject Ho if p-value < 0.05 Step 3: Statistical test: one sample, left tailed t-test Why? We are comparing single sample mean with a hypothesized mean Step 4: Conduct the test - place cell B162 in the output location box. t-Test: Two-Sample Assuming Unequal Variances Variable 1 Mean Variance Observations Hypothesized Mean df t Stat Variable 2 1.06544 1 0.0039377567 0 25 25 0 24 5.214214071 P(T<=t) one-tail 1.2090742E-005 t Critical one-tail 1.7108820799 P(T<=t) two-tail 2.4181483E-005 t Critical two-tail 2.0638985616 Step 5: Conclusion and Interpretation What is the p-value: 1.209074E-005 Is the P-value < 0.05 (for a one tail test) or 0.025 (for a two tail test)? Yes What, besides the p-value, needs to be Sign of the test statistic considered with a one tail test? Decision: Reject or do not reject Ho? Do not reject Ho What does your decision on rejecting the null There is not enough evidence to conclude that the Female av hypothesis mean? If the null hypothesis was rejected, calculate the effect size value: If the effect size was calculated, what doe the result mean in terms of why the null hypothesis was rejected? What does the result of this test tell us about It does not help so much to answer our question because we our question on salary equality? 6 Considering both the salary information in the lectures and your compa-ratio information, what conclusions The results are supporting equal pay. There is no evidence against equal pay. Why - what statistical results support this conclusion? The results from question 3 and 4 above is indicating no significant difference between males and females i y Data Set file is copied over to this Assignment file. t clicking on the Data tab, selecting Move or Copy, and copying the entire sheet to this file right so that whatever you do will not disrupt the original data values and relationships. mple, Question 1 asks for several data values. If you obtain them using descriptive statistics, ber showing the value in the descriptive statistics table. If you choose to generate each he data values should be shown. Having only a numerical value will not earn full credit. re not correct - we need to see how the results were obtained. seeing if differences exist. Probing into reasons and mitigating factors is a follow-up activity. or key variables. Since the assignment problems will nd range for our groups: Males, Females, and Overall. e Compa-ratio and Gender1 columns, and then sort on Gender1. use, and - if desired - to test your approach to the compa-ratio answers and =stdev functions. s with Fx functions or from Descriptive Statistics. der data in column U. of a column to the right. ow the location of the data (Example: =average(T2:T51) Note - remember the data is a sample from the larger company population oint we can do this rade levels. Sum - GenGr Gender1 A F M Total Result B C D E F Total Result Probability 0.36 0.28 0.56 bability, (b) is joint probability and (c ) is conditional probability. So the answers are different. e the values for each question below?: ge(range, value). d be the value that starts the top 1/3 of the range, ups, it would be the 25/3 = 8th (rounded) value. Overall Female Male All of the functions below are in the fx statistical list. 17 8 8 Use the "=ROUND" function (found in Math or All list) 1.107 1.107 1.121 Use the "=LARGE" function 0.5643863 0.662294 0.657093 Use Excel's STANDARDIZE function 0.2862456 0.253891 0.255561 Use "=1-NORM.S.DIST" function est about our equal pay for equal work question? rmal curve probability of exceeding this score is also almost same for males and females. ion be equal to each other? ecide which t-test to use. we are comparing the mean between two independent samples different between genders t the salaries are different r below the grade midpoint (which is ypothesized mean nclude that the Female average compa-ratio is less than the midpoint value of 1.00. Thus females are not getting paid below the g our question because we are not considering the male population in this case. mation, what conclusions can you reach about equal pay for equal work? ween males and females in terms of compa ratio. Thus the above conclusion can be made. 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 Compa Gender 1 1.105 1.048 1.018 1.054 1.032 1.034 1.030 1.001 1.115 1.107 1.144 1.020 1.005 1.183 1.003 1.141 1.006 1.032 1.093 1.016 1.184 1.001 1.120 0.988 1.156 1.121 0.892 1.010 0.987 F F F F F F F F F F F F F F F F F F F F F F F F F M M M M 1.122 1.105 1.022 1.037 1.073 1.166 1.053 1.132 1.113 1.005 0.898 M M M M M M M M M M M Total Result 1.083 0.886 1.054 1.090 0.971 1.129 1.205 1.045 1.213 1.143 M M M M M M M M M M t getting paid below the grade midpoint Week 3 ANOVA Three Questions Remember to show how you got your results in the appropriate cells. For questions using functions, show the input r 1 One interesting question is are the average compa-ratios equal across salary ranges of 10K each. While compa-ratios remove the impact of grade on salaries, are they different for different pay levels, that is are people at different levels paid differently relative to the midpoint? (Put data values at right.) What is the data input ranged used for this question: N5:S23 Step 1: Ho: All group means are equal Ha: At least one group mean is different Step 2: Decision Rule: Reject Ho if p-value < 0.05 Step 3: Statistical test: One Way ANOVA Why? We are comparing the mean of 6 groups Step 4: Conduct the test - place cell b16 in the output location box. Anova: Single Factor SUMMARY Groups Count Sum Average Variance 22-29 18 18.183 1.010167 0.0038004 30-39 5 5.511 40-49 8 8.251 1.031375 0.0021594 50-59 4 60-69 9 70-79 6 4.26 1.1022 0.0064207 1.065 0.0063993 10.219 1.135444 0.002673 6.767 1.127833 0.0004934 ANOVA Source of Variation SS df MS F P-value F crit Between Gro 0.138365 Within Group 0.148454 5 0.027673 8.2019442 1.54E-005 2.4270401198 44 0.003374 Total 49 0.286819 Step 5: Conclusions and Interpretation What is the p-value? 1.54421E-005 Is P-value < 0.05? Yes What is your decision: REJ or NOT reject the null? Reject the null If the null hypothesis was rejected, what is the effect size value (eta squared)? 0.482412135 If calculated, what does the effect size value tell us about why the null hypothesis was rejected? There is a moderate effect What does that decision mean in terms of our equal pay question? The null is rejected so there is a difference in th 2 If the null hypothesis in question 1 was rejected, which pairs of means differ? Groups Compared G1 G2 G1 G3 G1 G4 G1 G5 G1 G6 Diff -0.09203 -0.02121 -0.05483 -0.12528 -0.11767 T 2.015 2.015 2.015 2.015 2.015 +/- Term 0.059179 0.049743 0.06471 0.047791 0.055185 Low -0.15121 -0.07095 -0.11954 -0.17307 -0.17285 G2 G3 G2 G4 G2 G5 G2 G6 0.070825 0.0372 -0.03324 -0.02563 2.015 2.015 2.015 2.015 0.066737 0.078529 0.065295 0.070886 0.004088 -0.04133 -0.09854 -0.09652 0.137562 0.115729 0.032051 0.045253 G3 G4 G3 G5 G3 G6 -0.03363 2.015 -0.10407 2.015 -0.09646 2.015 0.071687 0.056883 0.063222 -0.10531 -0.16095 -0.15968 0.038062 -0.04719 -0.03324 G4 G5 G4 G6 -0.07044 2.015 -0.06283 2.015 0.070347 0.075565 -0.14079 -0.1384 -1E-004 0.012731 G5 G6 0.007611 2.015 0.061698 -0.05409 0.069309 to High -0.03285 0.028534 0.009876 -0.07749 -0.06248 3 Since compa is already a measure of pay for equal work, do these results impact your conclusion on equal pay for equal work? Why or why not? The result indicates that the midpoint is different among the salary ranges so based on the salary range som Therefore though it indicates a significant difference in salary ranges but does not indicate anything related We an only conclude that that there is unequal pay for equal work but no conclusion on gender biased pay. ng functions, show the input range when asked. anges of 10K each. for different pay levels, (Put data values at right.) Group name: G1 G2 G3 G4 G5 G6 Salary Intervals: 22-29 30-39 40-49 50-59 60-69 70-79 Compa-ratio values: 1.001 1.001 1.005 1.003 1.006 1.018 1.016 1.032 1.030 1.032 1.054 1.053 1.073 1.093 1.090 0.886 0.892 0.898 1.105 1.107 1.144 1.184 0.971 1.034 1.037 1.048 1.132 0.987 0.988 1.005 1.020 1.183 1.010 1.022 1.045 1.054 1.083 1.115 1.121 1.129 1.143 1.156 1.205 1.213 1.105 1.113 1.120 1.122 1.141 1.166 derate effect cted so there is a difference in the midpoint among different salary ranges. Why? Difference Significant? Yes No No Yes Yes Why? 0 is not within the confidence interval 0 is within the confidence interval 0 is within the confidence interval 0 is not within the confidence interval 0 is not within the confidence interval Yes No No No 0 is not within the confidence interval 0 is within the confidence interval 0 is within the confidence interval 0 is within the confidence interval No Yes Yes 0 is within the confidence interval 0 is not within the confidence interval 0 is not within the confidence interval Yes No 0 is not within the confidence interval 0 is within the confidence interval No 0 is within the confidence interval based on the salary range some are getting higher pay and some are getting lower pay, it is not depending on gender s not indicate anything related to gender biasedness. clusion on gender biased pay. Regression and Corellation Five Questions Remember to show how you got your results in the appropriate cells. For questions using functions, show the inp 1 Create a correlation table using Compa-ratio and the other interval level variables, except for Suggestion, place data in columns T - Y. What range was placed in the Correlation input range box: Place C9 in output box. b What are the statistically significant correlations related to Compa-ratio? c Are there any surprises - correlations you though would be significant and are not, or non sign d Why does or does not this information help answer our equal pay question? 2 Perform a regression analysis using compa as the dependent variable and the variables used in including the dummy variables. Show the result, and interpret your findings by answering the Suggestion: Place the dummy variables values to the right of column Y. What range was placed in the Regression input range box: Note: be sure to include the appropriate hypothesis statements. Regression hypotheses Ho: Ha: Coefficient hyhpotheses (one to stand for all the separate variables) Ho: Ha: Place B36 in output box. Interpretation: For the Regression as a whole: What is the value of the F statistic: What is the p-value associated with this value: Is the p-value < 0.05? What is your decision: REJ or NOT reject the null? What does this decision mean? For each of the coefficients: What is the coefficient's p-value for each of the variables: Is the p-value < 0.05? Do you reject or not reject each null hypothesis: Midpoint Age Perf. Rat. What are the coefficients for the significant variables? Using the intercept coefficient and only the significant variables, what is the equation? Compa-ratio = Is gender a significant factor in compa-ratio? Regardless of statistical significance, who gets paid more with all other things being equal? How do we know? 3 What does regression analysis show us about analyzing complex measures? 4 Between the lecture results and your results, what else would you like to know before answering our question on equal pay? Why? 5 Between the lecture results and your results, what is your answer to the question of equal pay for equal work for males and females? Why? g functions, show the input range when asked. evel variables, except for Salary. T= Significant r = nt and are not, or non significant correlations you thought would be? e and the variables used in Q1 along with findings by answering the following questions. Service Gender Degree the question Compa- Midpoint ratio Age Performa Service nce Rating Raise Degree Gender