ID 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 Salary Compa- Midpoint ratio 57.7 27.3 35.5 60.9 47 72.8 41.8 21.8 76.3 22.5 22.8 64.5 41.4 23.1 23.5 47.9 67 35.2 24.3 33.6 77.5 53.6 22.9 61.2 24.5 22.3 38.4 75.3 73.2 49.5 23.9 27.2 61.8 28.1 24.5 23 23.6 59.7 34.4 23.9 40.6 23.3 1.013 0.880 1.146 1.068 0.979 1.086 1.046 0.947 1.139 0.978 0.991 1.132 1.035 1.003 1.021 1.198 1.175 1.134 1.058 1.085 1.156 1.116 0.996 1.276 1.066 0.970 0.961 1.124 1.092 1.031 1.040 0.877 1.084 0.905 1.066 0.998 1.026 1.047 1.111 1.040 1.016 1.011 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 77.3 62.3 58 61.5 61.2 64.6 62.5 63.9 1.154 1.093 1.209 1.079 1.074 1.133 1.096 1.121 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 Grade 1 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 Comparatio Overall Female Male Mean Standard Deviation Range Mean Standard Deviation Range Mean Standard Deviation Range 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 dat 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: 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? 3 Normal Curve based probability: For each group (overall, females, males), what are the values for each que A Probability 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 Women are paid less than men and have larger variation in their pay 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 average compa-ratio<=1.00 Ha: female average compa-ratio>1.00 Step 2: Decision Rule: Reject Ho if p-values < 0.05 Step 3: Statistical test: One sample t-testing using two swample t-test assuming u Why? assuming unequal variance as Ho value has no variance Step 4: Conduct the test - place cell B77 in the output location box. Mean Variance Observations Hypoth Mean diff df P(T-<=t)one tail 1.06512 1 0.00556236 0 25 25 0.000 4.365710 0.0001042072 Step 5: Conclusion and Interpretation What is the p-value: 0.000208143 Is the P-value < 0.05 (for a one tail test) or 0.025 (for a two tail test)? yes p value > alpha value What is your decision: REJ or NOT reject the null? reject the null What does this result say about our question of variance equality? B Are male and female average compa-ratios equal? no (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: Ha: Step 2: Decision Rule: Step 3: Statistical test: Why? Step 4: Conduct the test - place cell B109 in the output location box. Step 5: Conclusion and Interpretation What is the p-value: 0.0002084143 Is the P-value < 0.05 (for a one tail test) or 0.025 (for a two tail test)? Is the P-value < 0.05 (for a one tail test) or 0.025 (for a two tail test)? No p value > alpha value What is your decision: REJ or NOT reject the null? do not reject reject the null What does your decision on rejecting the null hypothesis mean? the full average compa-rati mean equals 45 If the null hypothesis was rejected, calculate the effect size value: 1.06328125 If the effect size was calculated, what doe the result mean in terms of why the null hypothesis wastheres rejected? is no strong enough data to m What does the result of this test tell us about our question on salary equality? no test complete on salary 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: Ha: Step 2: Decision Rule: Step 3: Statistical test: Why? Step 4: Conduct the test - place cell B162 in the output location box. Step 5: Conclusion and Interpretation What is the p-value: Is the P-value < 0.05 (for a one tail test) or 0.025 (for a two tail test)? What, besides the p-value, needs to be considered with a one tail test? Decision: Reject or do not reject Ho? reject What does your decision on rejecting the null 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 our question on salary equality? 6 Considering both the salary information in the lectures and your compa-ratio information, what conclusions Why - what statistical results support this conclusion? following the five steps in the hypothesis test y Data Set file is copied over to this Assignment file. ht clicking on the Data tab, selecting Move or Copy, and copying the entire sheet to this file e 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, mber 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. are 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. for key variables. Since the assignment problems will and range for our groups: Males, Females, and Overall. e Compa-ratio and Gender1 columns, and then sort on Gender1. e use, and - if desired - to test your approach to the compa-ratio answers e and =stdev functions. ns with Fx functions or from Descriptive Statistics. der data in column U. of a column to the right. how the location of the data (Example: =average(T2:T51) Note - remember the data is a sample from the larger company population point we can do this grade levels. Probability 0.36 0.56 0.16 the properbilities are calculated on different counts a=50 and b=25 re the values for each question below?: 50/3=17 ge(range, value). d be the value that starts the top 1/3 of the range, oups, it would be the 25/3 = 8th (rounded) value. Overall Female Male 1 1 60 42 54 0.78 0.22 0.68 0.32 0.32 0.32 est about our equal pay for equal work question? tion be equal to each other? ecide which t-test to use. assuming u no All of the functions below are in the fx statistical list. Use the "=ROUND" function (found in Math or All list) Use the "=LARGE" function Use Excel's STANDARDIZE function Use "=1-NORM.S.DIST" function or below the grade midpoint (which is rmation, what conclusions can you reach about equal pay for equal work? based on the resluts of the compa-ratio test I would co teps in the hypothesis testing were were able to create three different test. The compa-ratio results show a small difference in ma Salary Overall Mean Standard Deviation Range Female Mean Standard Deviation Range Male Mean Standard Deviation Range Compa-ratAge 45.0000 1.1 19.2014 0.0770 55.000 0.005 -38.0000 1.1 18.2940 0.1 55.000 0.2 52.0000 1.0 17.7760 0.1 53.000 1.9 35.7 8.2513 30 32.5 6.9 26.0 38.9 8.4 28.0 Perf Rate Service 85.9 11.4150 45 84.2 13.6 45.0 87.6 8.7 30.0 9.0 5.7177 21 7.9 4.9 18.0 10.0 6.4 21.0 mpa-ratio test I would conclude male and femalre are paid equally w a small difference in male and female 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 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 43 44 57.7 27.3 35.5 60.9 47 72.8 41.8 21.8 76.3 22.5 22.8 64.5 41.4 23.1 23.5 47.9 67 35.2 24.3 33.6 77.5 53.6 22.9 61.2 24.5 22.3 38.4 75.3 73.2 49.5 23.9 27.2 61.8 28.1 24.5 23 23.6 59.7 34.4 23.9 40.6 23.3 77.3 62.3 Compa Midpoint 1.013 0.880 1.146 1.068 0.979 1.086 1.046 0.947 1.139 0.978 0.991 1.132 1.035 1.003 1.021 1.198 1.175 1.134 1.058 1.085 1.156 1.116 0.996 1.276 1.066 0.970 0.961 1.124 1.092 1.031 1.040 0.877 1.084 0.905 1.066 0.998 1.026 1.047 1.111 1.040 1.016 1.011 1.154 1.093 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 Age Performance Rating Service Gender Raise 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 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 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 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 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 45 46 47 48 49 50 58 61.5 61.2 64.6 62.5 63.9 1.209 1.079 1.074 1.133 1.096 1.121 48 57 57 57 57 57 36 39 37 34 41 38 95 75 95 90 95 80 8 20 5 11 21 12 1 0 0 1 0 0 5.2 3.9 5.5 5.3 6.6 4.6 Degree Gender1 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 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 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 1 1 1 1 0 0 F M M F M M D E E E E E ID 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 Salary Compa- Midpoint ratio 59.3 26.5 34.1 56.3 46.8 79.5 41.2 23.6 76 22.7 23.8 62.9 41.4 22.3 23.1 46.6 67.6 33.8 24 35 75.2 51.5 22.1 55.4 24.9 24.3 42.9 76.6 75.4 48.9 22.9 28 61.3 26.8 23.6 24.6 22.7 60.1 33.4 23.9 39.5 23.6 1.040 0.856 1.099 0.987 0.975 1.187 1.031 1.026 1.134 0.985 1.036 1.104 1.035 0.968 1.006 1.166 1.186 1.091 1.043 1.129 1.122 1.073 0.960 1.155 1.084 1.055 1.073 1.144 1.125 1.019 0.997 0.904 1.075 0.864 1.026 1.070 0.985 1.055 1.079 1.038 0.987 1.028 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 76.9 63.3 55.7 62.9 63.9 67.7 58.8 55 1.148 1.110 1.161 1.103 1.121 1.187 1.032 0.965 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 Gender1 Grade 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 e 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 o this page. ocus on is: Are males and females paid the same for equal work (under the Equal Pay Act)? thin each grade comprise equal work. housands g - Appraisal rating (Employee evaluation score) 1 = female ry divided by midpoint 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: T2:Y51 Place C9 in output box. Compa-ratio Midpoint Compa-rati Age Performance Rating Service 1 Midpoint 0.517072 Age 0.246439 0.567111 1 1 Performanc-0.032925 0.191751 0.139238 Service Raise b c d 2 Multiple R 0.66445 R Square 0.441494 0.34841 Standard Er0.063387 ANOVA 0.174277 0.471147 0.565133 0.2257007594 1 -0.089419 -0.028913 -0.180427 0.673659763 0.1027869 1 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: T2:AA51 Note: be sure to include the appropriate hypothesis statements. Regression hypotheses Ho: All the coefficients of the independent variables are equal to 0 Ha: Atleast one independent variable has coefficient not equal to 0 Coefficient hyhpotheses (one to stand for all the separate variables) Ho: The coefficient for independent variable i=0 Ha: The coefficient for independent variable i is not equal to 0 Place B36 in output box. Regression Statistics Observatio 1 What are the statistically significant correlations related to Compa-ratio? Midpoint Are there any surprises - correlations you though would be significant and are not, or non sign It was expected that compa-ratio would have significant relationships with Performance ratin Why does or does not this information help answer our equal pay question? This information tells us that compa-ratio is independent of other variables except midpoint. T SUMMARY OUTPUT Adjusted R Raise 50 df Regression SS MS F Significance F 7 0.133396 0.019057 4.742951 0.0005410517 Residual 42 0.16875 0.004018 Total 49 0.302146 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Intercept 0.893299 0.092289 9.679354 2.94E-012 0.7070520481 1.07954601 0.70705205 Midpoint 0.003556 0.000733 4.849513 1.73E-005 0.002076165 0.00503571 0.00207616 Age 0.00121 0.001633 0.7409 0.462877 -0.002085661 0.00450547 -0.00208566 Performanc-0.001162 0.001158 -1.003997 0.321129 -0.003499132 0.00117416 -0.00349913 Service -0.001891 0.002064 -0.916024 0.364884 -0.006056841 0.00227496 -0.00605684 Raise 0.010413 0.015708 0.662863 0.51104 -0.021288314 0.04211336 -0.02128831 Degree 0.004443 0.018194 0.244224 0.808247 -0.032273713 0.04116057 -0.03227371 Gender 0.069458 0.020712 3.353427 0.0017 0.0276582223 0.11125693 0.02765822 What is the value of the F statistic: 4.742951358 What is the p-value associated with this value: 0.000541052 Is the p-value < 0.05? Yes What is your decision: REJ or NOT reject the null? Reject the null What does this decision mean? It means there is a significant linear relationship betw For each of the coefficients: Midpoint Age Perf. Rat. What is the coefficient's p-value for each of the variables: 1.73E-05 0.46287657 0.32112943 Is the p-value < 0.05? Yes No No Do you reject or not reject each null hypothesis: Reject nullDo not rejectDo null not reject null What are the coefficients for the significant variables? Using the intercept coefficient and only the significant variables, what is the equation? Is gender a significant factor in compa-ratio? 0.004 Compa-ratio = 0.8933+0.004*Midpoint+ Yes Regardless of statistical significance, who gets paid more with all other things being equal? The employees in higher grade jobs, employees who How do we know? We know this by looking at the sign of the coefficien 3 What does regression analysis show us about analyzing complex measures? It shows the variables that have a significant relationship with the dependent variab 4 Between the lecture results and your results, what else would you like to know 5 before answering our question on equal pay? Why? We would like to know if the assumption that there is equal work for employees of the same g This is because the analysis is valid only if this assumption holds 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? For equal work females get slightly higher pay than males. This is because there is a significa functions, show the input range when asked. vel variables, except for Salary. T = 4.185307 Significant r = 0.517072 t and are not, or non significant correlations you thought would be? s with Performance ratings and service, but they were not to be iables except midpoint. This tells us that pay is not influenced by these other variables which are unrelated to the am and the variables used in Q1 along with indings by answering the following questions. 4.849513 3.353427 Upper 95.0% 1.07954601 0.005035707 0.004505466 0.001174163 0.002274964 0.042113364 0.04116057 0.111256927 nt linear relationship between compa-ratios and atleast one independent variable Service Gender Degree 0.36488394 0.0017 0.808247 No Yes No Do not reject null Reject null Do not reject null 0.069 .8933+0.004*Midpoint+0.069*Gender ade jobs, employees who are female, employees with higher age, employees with lower performance rating, employees with l the sign of the coefficients of the independent variables in the regression equation. with the dependent variable. employees of the same grade is validated by evaluating the nature of work of employees in the same grade. he question cause there is a significant linear relationship of gender with compa-ratios(positive for females), and the standardised coeffic Compa- Midpoint ratio 1.040 57 0.856 31 1.099 31 0.987 57 0.975 48 1.187 67 1.031 40 1.026 23 unrelated to the am 1.134 0.985 1.036 1.104 1.035 0.968 1.006 1.166 1.186 1.091 1.043 1.129 1.122 1.073 0.960 1.155 1.084 1.055 1.073 1.144 1.125 1.019 0.997 0.904 1.075 0.864 1.026 1.070 0.985 1.055 1.079 1.038 0.987 1.028 1.148 1.110 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 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 42 45 Performa Service nce 85 8 Rating 80 7 75 5 100 16 90 16 70 12 100 8 90 9 100 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 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 Raise 5.7 3.9 3.6 5.5 5.7 4.5 5.7 5.8 Degree 0 0 1 1 1 1 1 1 Gender 0 0 1 0 0 0 1 1 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 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 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 1.161 1.103 1.121 1.187 1.032 0.965 48 57 57 57 57 57 36 39 37 34 41 38 95 75 95 90 95 80 8 20 5 11 21 12 5.2 3.9 5.5 5.3 6.6 4.6 1 1 1 1 0 0 1 0 0 1 0 0 ance rating, employees with lower service levels, employees with higher raise, employees with a MS degree get paid more ame grade. and the standardised coefficients for gender and midpoint are of the same order, meaning the magnitude of their effect on com gree get paid more e of their effect on compa-ratio is similar.Thus pay changes with both amount of work and gender 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 57.7 27.3 35.5 60.9 47 72.8 41.8 21.8 76.3 22.5 22.8 64.5 41.4 23.1 23.5 47.9 67 35.2 24.3 33.6 77.5 53.6 22.9 61.2 24.5 22.3 38.4 75.3 73.2 49.5 23.9 27.2 61.8 28.1 24.5 23 23.6 59.7 34.4 23.9 40.6 23.3 Compa Midpoint 1.013 0.880 1.146 1.068 0.979 1.086 1.046 0.947 1.139 0.978 0.991 1.132 1.035 1.003 1.021 1.198 1.175 1.134 1.058 1.085 1.156 1.116 0.996 1.276 1.066 0.970 0.961 1.124 1.092 1.031 1.040 0.877 1.084 0.905 1.066 0.998 1.026 1.047 1.111 1.040 1.016 1.011 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 77.3 62.3 58 61.5 61.2 64.6 62.5 63.9 1.154 1.093 1.209 1.079 1.074 1.133 1.096 1.121 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 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 eva Service - Years of service (roun 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 - salary divided by midpoint F M F M M F M M F E D E E E E E : Are males and females paid the same for equal work (under the Equal Pay Act)? grade comprise equal work. sal rating (employee evaluation score) 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 1.0616 Standard Deviation 0.0821 Range 0.3990 Mean 1.0716 Standard Deviation 0.0832 Range 0.3290 Mean 1.0516 Standard Deviation 0.0813 Range 0.3210 Age 35.7 8.2513 30 32.5 6.9 26.0 38.9 8.4 28.0 Perf. Rat. 85.9 11.4147 45 84.2 13.6 45.0 87.6 8.7 30.0 Service 9.0 5.7177 Note - remember the d 21 7.9 4.9 18.0 10.0 6.4 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: 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? 3 Normal Curve based probability: For each group (overall, females, males), what are the values for each que A Probability 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 many compa-ratios 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 Given the different values for z and probability of exceeding, the distributions of compa-ratios do not appea This suggests that males and females might not be paid in the same manner. 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: Answers will differ; in this sheet T2:U51 Step 1: Ho: Male compa-ratio variance = Female compa-ratio Ha: Male compa-ratio variance =/= Female compa-ratio Step 2: Decision Rule: Reject Ho if p-value exceeds alpha = 0.05. Step 3: Statistical test: F-test Why? This test looks at variance equality, but for 2 tail Step 4: Conduct the test - place cell B77 in the output location box. F-Test Two-Sample for Variances Males Mean Variance Females 1.052 1.072 0.0066171567 0.00691949 Observations 25 25 df 24 24 F 0.9563069918 P(F<=f) one-tail 0.5431195436 F Critical one-tail 1.9837595685 Step 5: Conclusion and Interpretation What is the p-value: 0.5431195436 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? Do Not Reject Ho What does this result say about our question of variance equality? Population variances equal 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: t2:t51 and y2:y51 Answers will vary Step 1: Ho: Male average compa-ratio = Female average compa-ratio Ha: Male average compa-ratio =/= Female average compa-ratio Step 2: Decision Rule: Reject Ho if p-value < 0.05 Step 3: Statistical test: Two-sample t-test assuming equal variance Why? Assuming equal variances, testing mean differences Step 4: Conduct the test - place cell B109 in the output location box. t-Test: Two-Sample Assuming Equal Variances Male Mean Female 1.052 Variance 1.072 0.0066171567 0.00691949 Observations Pooled Variance Hypothesized Mean df 25 25 0.0067683233 0 48 t Stat -0.8594971747 P(T<=t) one-tail 0.1971693178 t Critical one-tail 1.6772241961 P(T<=t) two-tail 0.3943386356 t Critical two-tail 2.0106347576 Step 5: Conclusion and Interpretation What is the p-value: 0.3943386356 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? Do Not Reject Ho What does your decision on rejecting the null Population means equal hypothesis mean? If the null hypothesis was rejected, calculate the effect size value: NA If the effect size was calculated, what doe the result mean in terms of why the null hypothesis was rejected? NA What does the result of this test tell us about our question on salary equality? The means could be equal 5 and effect size is not impor Is the Female average compa-ratio equal to or less than the compa-ratio equivalent of the midpoint, which i 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. Remember, this is a one sample t-test where we "trick" excel by using the unequal variance version (see lec What is the data input ranged used for this question: Step 1: Ho: Female average compa-ratio <= 1.00 Ha: Female average compa-ratio > 1.00 Step 2: Decision Rule: Reject Ho if p-value < 0.05 Step 3: Statistical test: One sample t-test using Two-sample t-test assuming unequal variance (E Why? Assuming unequal variances as Ho value has no variance Step 4: Conduct the test - place cell B162 in the output location box. t-Test: Two-Sample Assuming Unequal Variances Compa-Ratio Mean Variance Observations Hypothesized Mean df t Stat Q5 Ho 1.072 1 0.00691949 0 25 25 0 24 4.3061438979 P(T<=t) one-tail 0.0001212425 t Critical one-tail 1.7108820799 P(T<=t) two-tail 0.0002424851 t Critical two-tail 2.0638985616 Step 5: Conclusion and Interpretation What is the p-value: 0.000121 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 considered with a one tail test? If t-value is in tail shown by Ha arrow Decision: Reject or do not reject Ho? Reject Ho What does your decision on rejecting the null Females average compa-ratio is above 1.0 hypothesis mean? If the null hypothesis was rejected, calculate the effect size value: 0.873 If the effect size was calculated, what doe the result Average compa > 1.0 mean in terms of why the null hypothesis was rejected? and Effect size shows the v What does the result of this test tell us about Since only one gender tested, it does not help answer the que our question on salary equality? 6 Considering both the salary information in the lectures and your compa-ratio information, what conclusions Answers will vary but should not that salary averages and compa aveages show different outcomes. Might Why - what statistical results support this conclusion? Salary t-test in lecture, Compa t-test in Q4; at a minimum. Data Set file is copied over to this Assignment file. clicking on the Data tab, selecting Move or Copy, and copying the entire sheet to this file ight so that whatever you do will not disrupt the original data values and relationships. ple, Question 1 asks for several data values. If you obtain them using descriptive statistics, er showing the value in the descriptive statistics table. If you choose to generate each e data values should be shown. Having only a numerical value will not earn full credit. e not correct - we need to see how the results were obtained. eing if differences exist. Probing into reasons and mitigating factors is a follow-up activity. r key variables. Since the assignment problems will d range for our groups: Males, Females, and Overall. 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. with Fx functions or from Descriptive Statistics. er data in column U. f a column to the right. w the location of the data (Example: =average(T2:T51) Note - remember the data is a sample from the larger company population int we can do this Probability =18/50 0.36 =14/50 0.28 =14/25 0.56 Different sample groups and (for b) selected successes the values for each question below?: e(range, value). be the value that starts the top 1/3 of the range, ps, it would be the 25/3 = 8th (rounded) value. Overall Female Male All of the functions below are in the fx statistical list. ach group? 17 8 8 Use the "=ROUND" function (found in Math or All list) 1.093 1.124 1.092 Use the "=LARGE" function 0.382205 0.629452 0.496153 Use Excel's STANDARDIZE function 0.3511546 0.264527 0.309893 Use "=1-NORM.S.DIST" function t about our equal pay for equal work question? mpa-ratios do not appear to be similar. on be equal to each other? cide which t-test to use. n this sheet T2:U51 Answers will vary effect size is not important of the midpoint, which is a compa-ratio value of 1.00? below the grade midpoint (which is ariance version (see lecture). ng unequal variance (Excel Trick) Effect size shows the variables have a strong impact on the rejection of the null not help answer the question. mation, what conclusions can you reach about equal pay for equal work? erent outcomes. Might include comments on distribution from Q3. CompaGender Grade Ratio 0.947 F A 0.978 F A 0.991 F A 1.003 F A 1.021 F A 0.996 F A 0.970 F A 1.040 F A 1.066 F A 0.998 F A 1.026 F A 1.011 F A 1.146 F B 1.134 F B 1.085 F B 1.111 F B 1.046 F C 1.035 F C 1.116 F D 1.276 F D 1.209 F D 1.175 F E 1.133 F E 1.124 F F 1.154 F F 1.058 M A 1.066 M A 1.040 M A 0.880 M B 0.877 0.905 1.198 0.961 1.016 0.979 1.031 1.013 1.068 1.132 1.084 M M M M M M M M M M M B B C C C D D E E E E Q5 Ho 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 1.047 1.093 1.079 1.074 1.096 1.121 1.086 1.139 1.156 1.092 M M M M M M M M M M E E E E E E F F F F 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: Depending on number in each group, N5:S23 Step 1: Ho: Average compa-ratios are equal across the salary ranges Ha: At least one mean differs Step 2: Decision Rule: Reject Ho if p-value < alpha = .05 Note: Instructors can cre Step 3: Statistical test: Single Factor ANOVA using results at right and Why? Testing multiple means with only 1 factor Step 4: Conduct the test - place cell b16 in the output location box. Anova: Single Factor SUMMARY Groups 22-29 30-39 40-49 50-59 60-69 70-79 Count 18 5 6 4 11 6 ANOVA Source of Variation SS Between Gro 0.157 Within Group 0.173 Total 0.32988 Sum 17.873 5.437 6.305 4.385 12.331 6.751 df Average 0.993 1.087 1.051 1.096 1.121 1.125 Variance 0.0034397 0.0055363 0.0057398 0.0074863 0.0036766 0.0009218 MS F P-value F crit 5 0.031345 7.9652142 2.05878E-005 2.4270401198 44 0.003935 49 Step 5: Conclusions and Interpretation What is the p-value? 2.05878E-005 Is P-value < 0.05? Yes What is your decision: REJ or NOT reject the null? reject the null hypothesis If the null hypothesis was rejected, what is the effect size value (eta squared)? 0.475 If calculated, what does the effect size value tell us about why the null hypothesis was rejected? Variable interaction has an impact on th What does that decision mean in terms of our equal pay question? It suggests a relationship between salary a 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 -0.09446 -0.05789 -0.10331 -0.12806 -0.13222 T 2.015 2.015 2.015 2.015 2.015 +/- Term 0.063912 0.059599 0.069886 0.048385 0.059599 Low -0.158 -0.117 -0.173 -0.176 -0.192 G2 G3 G2 G4 G2 G5 G2 G6 0.036567 -0.00885 -0.0336 -0.03777 2.015 2.015 2.015 2.015 0.076556 0.08481 0.06819 0.076556 -0.040 -0.094 -0.102 -0.114 0.113 0.076 0.035 0.039 G3 G4 G3 G5 G3 G6 -0.04542 -0.07017 -0.07433 2.015 2.015 2.015 0.081609 0.064165 0.072993 -0.127 -0.134 -0.147 0.036 -0.006 -0.001 G4 G5 G4 G6 -0.02475 -0.02892 2.015 2.015 0.073818 0.081609 -0.099 -0.111 0.049 0.053 G5 G6 -0.00417 2.015 0.064165 -0.068 0.060 to 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? Not really, results are not factored for gender. High -0.031 0.002 -0.033 -0.080 -0.073 unctions, show the input range when asked. Group name: es of 10K each. different pay levels, data values at right.) Salary Intervals: G1 G2 G3 G4 G5 G6 20-29 30-39 40-49 50-59 60-69 70+ Compa-ratio values: h group, N5:S23 Note: Instructors can create table using results at right and removing x's l hypothesis raction has an impact on the rejection of the null hypothesis elationship between salary and compa that is not clear yet. Why? Difference Significant? YES NO YES YES YES Why? Does not contain 0 Contains 0 Does not contain 0 Does not contain 0 Does not contain 0 NO NO NO NO Contains 0 Contains 0 Contains 0 Contains 0 NO YES YES Contains 0 Does not contain 0 Does not contain 0 NO NO Contains 0 Contains 0 NO Contains 0 Salary Compa-ratios SS total G1 G2 30-39 57.7 1.013 0.002366 27.3 0.88 0.032993 20-29 x 35.5 1.146 0.007117 0.880 60.9 1.068 4.0E-005 x 1.146 47 0.979 0.006829 x x 0.000593 x x 0.000245 x x 0.013142 x 0.005985 0.947 72.8 41.8 21.8 76.3 1.086 1.046 0.947 1.139 x 0.013 x x 0.002 x 22.5 0.978 0.006996 x 22.8 0.991 0.00499 0.978 0.000 x 64.5 1.132 0.004951 0.991 0.000 x 41.4 1.035 0.00071 x 23.1 23.5 47.9 67 35.2 24.3 33.6 77.5 53.6 22.9 61.2 24.5 22.3 38.4 75.3 73.2 49.5 23.9 27.2 1.003 1.021 1.198 1.175 1.134 1.058 1.085 1.156 1.116 0.996 1.276 1.066 0.97 0.961 1.124 1.092 1.031 1.04 0.877 0.003439 0.001652 0.018594 0.01285 0.005236 1.3E-005 0.000546 0.008904 0.002955 0.004309 0.04595 1.9E-005 0.008398 0.010128 0.003889 0.000922 0.000939 0.000468 0.034092 61.8 1.084 0.0005 x 1.003 1.021 x x x 1.058 x x x 0.996 x 1.066 0.970 x x x x 1.040 0.877 28.1 0.905 0.024536 x 24.5 1.066 1.9E-005 0.905 0.008 x 23 0.998 0.00405 1.066 0.005 x 0.00127 0.998 0.000 x 0.000214 1.026 0.001 x x 23.6 59.7 1.026 1.047 34.4 1.111 0.002436 23.9 40.6 1.04 1.016 0.000468 0.002083 23.3 77.3 1.011 1.154 0.002564 0.00853 62.3 1.093 0.000983 x x 0.000 0.001 0.004 0.000 0.005 0.001 0.002 0.013 x 0.002 1.111 x 0.000 x x x 1.011 x x x x 1.040 x x x x x 1.134 x 1.085 x x x x x x 0.961 x x x x x 58 61.5 1.209 1.079 0.021715 0.000301 61.2 1.074 64.6 1.133 62.5 1.096 0.001181 63.9 1.121 0.003524 1.06164 x x 0.000153 x x x 0.005092 x x x x 0.32988 SSt x x x x x Mean 0.993 Sum 17.873 5.437 18 5 0.00344 0.005536 Count Var Sse = 0.058 0.173 1.087 0.003 G3 G4 G5 G6 40-49 50-59 60-69 70+ x 1.013 x x x x x x x x x x x 1.068 x x x x x 1.086 x x x x x x x x x x 1.139 x x x x x x x x x x 1.132 x x x x x x x x x 1.116 x x x x x x x x x x x x x 1.175 x x x x x x 1.276 x x x x x x x x 0.979 0.005 x 1.046 0.002 0.000 0.016 0.001 1.035 x x 1.198 x x x x x x x x x x x x x 1.031 x 0.000 0.000 0.022 0.000 0.007 0.000 0.003 0.000 0.003 0.024 x x x x x x x x x 1.156 x x x x x x 1.124 1.092 x x x x x x 1.084 x x x x x x x x x x x x x x x x x x 0.001 x x x x x x x x x x x x x x x x 1.154 x 0.000 0.001 x 1.047 0.001 0.001 x x 1.016 x 0.000 x x 0.002 0.002 0.001 x x x 1.209 1.093 x 0.001 x x x x 1.079 0.002 x x x 1.074 0.002 x x x 1.133 x x 1.096 0.001 x 1.121 0.000 x 1.121 0.037 1.125 x 0.022 1.051 0.013 x 0.029 1.096 0.022 0.000 x 6.305 4.385 12.331 6.751 6 4 11 6 0.00574 0.007486 0.003677 0.000922 0.005 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 57.7 27.3 35.5 60.9 47 72.8 41.8 21.8 76.3 22.5 22.8 64.5 41.4 23.1 23.5 47.9 67 35.2 24.3 33.6 77.5 53.6 22.9 61.2 24.5 22.3 38.4 75.3 73.2 49.5 23.9 27.2 61.8 28.1 24.5 23 23.6 59.7 34.4 23.9 40.6 23.3 Compa Midpoint 1.013 0.880 1.146 1.068 0.979 1.086 1.046 0.947 1.139 0.978 0.991 1.132 1.035 1.003 1.021 1.198 1.175 1.134 1.058 1.085 1.156 1.116 0.996 1.276 1.066 0.970 0.961 1.124 1.092 1.031 1.040 0.877 1.084 0.905 1.066 0.998 1.026 1.047 1.111 1.040 1.016 1.011 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 77.3 62.3 58 61.5 61.2 64.6 62.5 63.9 1.154 1.093 1.209 1.079 1.074 1.133 1.096 1.121 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 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 eva Service - Years of service (roun 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 - salary divided by midpoint F M F M M F M M F E D E E E E E : Are males and females paid the same for equal work (under the Equal Pay Act)? grade comprise equal work. sal rating (employee evaluation score) 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 1.0616 Standard Deviation 0.0821 Range 0.3990 Mean 1.0716 Standard Deviation 0.0832 Range 0.3290 Mean 1.0516 Standard Deviation 0.0813 Range 0.3210 Age 35.7 8.2513 30 32.5 6.9 26.0 38.9 8.4 28.0 Perf. Rat. 85.9 11.4147 45 84.2 13.6 45.0 87.6 8.7 30.0 Service 9.0 5.7177 Note - remember the d 21 7.9 4.9 18.0 10.0 6.4 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: 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? 3 Normal Curve based probability: For each group (overall, females, males), what are the values for each que A Probability 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 many compa-ratios 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 Given the different values for z and probability of exceeding, the distributions of compa-ratios do not appea This suggests that males and females might not be paid in the same manner. 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: Answers will differ; in this sheet T2:U51 Step 1: Ho: Male compa-ratio variance = Female compa-ratio Ha: Male compa-ratio variance =/= Female compa-ratio Step 2: Decision Rule: Reject Ho if p-value exceeds alpha = 0.05. Step 3: Statistical test: F-test Why? This test looks at variance equality, but for 2 tail Step 4: Conduct the test - place cell B77 in the output location box. F-Test Two-Sample for Variances Males Mean Variance Females 1.052 1.072 0.0066171567 0.00691949 Observations 25 25 df 24 24 F 0.9563069918 P(F<=f) one-tail 0.5431195436 F Critical one-tail 1.9837595685 Step 5: Conclusion and Interpretation What is the p-value: 0.5431195436 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? Do Not Reject Ho What does this result say about our question of variance equality? Population variances equal 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: t2:t51 and y2:y51 Answers will vary Step 1: Ho: Male average compa-ratio = Female average compa-ratio Ha: Male average compa-ratio =/= Female average compa-ratio Step 2: Decision Rule: Reject Ho if p-value < 0.05 Step 3: Statistical test: Two-sample t-test assuming equal variance Why? Assuming equal variances, testing mean differences Step 4: Conduct the test - place cell B109 in the output location box. t-Test: Two-Sample Assuming Equal Variances Male Mean Female 1.052 Variance 1.072 0.0066171567 0.00691949 Observations Pooled Variance Hypothesized Mean df 25 25 0.0067683233 0 48 t Stat -0.8594971747 P(T<=t) one-tail 0.1971693178 t Critical one-tail 1.6772241961 P(T<=t) two-tail 0.3943386356 t Critical two-tail 2.0106347576 Step 5: Conclusion and Interpretation What is the p-value: 0.3943386356 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? Do Not Reject Ho What does your decision on rejecting the null Population means equal hypothesis mean? If the null hypothesis was rejected, calculate the effect size value: NA If the effect size was calculated, what doe the result mean in terms of why the null hypothesis was rejected? NA What does the result of this test tell us about our question on salary equality? The means could be equal 5 and effect size is not impor Is the Female average compa-ratio equal to or less than the compa-ratio equivalent of the midpoint, which i 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. Remember, this is a one sample t-test where we "trick" excel by using the unequal variance version (see lec What is the data input ranged used for this question: Step 1: Ho: Female average compa-ratio <= 1.00 Ha: Female average compa-ratio > 1.00 Step 2: Decision Rule: Reject Ho if p-value < 0.05 Step 3: Statistical test: One sample t-test using Two-sample t-test assuming unequal variance (E Why? Assuming unequal variances as Ho value has no variance Step 4: Conduct the test - place cell B162 in the output location box. t-Test: Two-Sample Assuming Unequal Variances Compa-Ratio Mean Variance Observations Hypothesized Mean df t Stat Q5 Ho 1.072 1 0.00691949 0 25 25 0 24 4.3061438979 P(T<=t) one-tail 0.0001212425 t Critical one-tail 1.7108820799 P(T<=t) two-tail 0.0002424851 t Critical two-tail 2.0638985616 Step 5: Conclusion and Interpretation What is the p-value: 0.000121 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 considered with a one tail test? If t-value is in tail shown by Ha arrow Decision: Reject or do not reject Ho? Reject Ho What does your decision on rejecting the null Females average compa-ratio is above 1.0 hypothesis mean? If the null hypothesis was rejected, calculate the effect size value: 0.873 If the effect size was calculated, what doe the result Average compa > 1.0 mean in terms of why the null hypothesis was rejected? and Effect size shows the v What does the result of this test tell us about Since only one gender tested, it does not help answer the que our question on salary equality? 6 Considering both the salary information in the lectures and your compa-ratio information, what conclusions Answers will vary but should not that salary averages and compa aveages show different outcomes. Might Why - what statistical results support this conclusion? Salary t-test in lecture, Compa t-test in Q4; at a minimum. Data Set file is copied over to this Assignment file. clicking on the Data tab, selecting Move or Copy, and copying the entire sheet to this file ight so that whatever you do will not disrupt the original data values and relationships. ple, Question 1 asks for several data values. If you obtain them using descriptive statistics, er showing the value in the descriptive statistics table. If you choose to generate each e data values should be shown. Having only a numerical value will not earn full credit. e not correct - we need to see how the results were obtained. eing if differences exist. Probing into reasons and mitigating factors is a follow-up activity. r key variables. Since the assignment problems will d range for our groups: Males, Females, and Overall. 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. with Fx functions or from Descriptive Statistics. er data in column U. f a column to the right. w the location of the data (Example: =average(T2:T51) Note - remember the data is a sample from the larger company population int we can do this Probability =18/50 0.36 =14/50 0.28 =14/25 0.56 Different sample groups and (for b) selected successes the values for each question below?: e(range, value). be the value that starts the top 1/3 of the range, ps, it would be the 25/3 = 8th (rounded) value. Overall Female Male All of the functions below are in the fx statistical list. ach group? 17 8 8 Use the "=ROUND" function (found in Math or All list) 1.093 1.124 1.092 Use the "=LARGE" function 0.382205 0.629452 0.496153 Use Excel's STANDARDIZE function 0.3511546 0.264527 0.309893 Use "=1-NORM.S.DIST" function t about our equal pay for equal work question? mpa-ratios do not appear to be similar. on be equal to each other? cide which t-test to use. n this sheet T2:U51 Answers will vary effect size is not important of the midpoint, which is a compa-ratio value of 1.00? below the grade midpoint (which is ariance version (see lecture). ng unequal variance (Excel Trick) Effect size shows the variables have a strong impact on the rejection of the null not help answer the question. mation, what conclusions can you reach about equal pay for equal work? erent outcomes. Might include comments on distribution from Q3. CompaGender Grade Ratio 0.947 F A 0.978 F A 0.991 F A 1.003 F A 1.021 F A 0.996 F A 0.970 F A 1.040 F A 1.066 F A 0.998 F A 1.026 F A 1.011 F A 1.146 F B 1.134 F B 1.085 F B 1.111 F B 1.046 F C 1.035 F C 1.116 F D 1.276 F D 1.209 F D 1.175 F E 1.133 F E 1.124 F F 1.154 F F 1.058 M A 1.066 M A 1.040 M A 0.880 M B 0.877 0.905 1.198 0.961 1.016 0.979 1.031 1.013 1.068 1.132 1.084 M M M M M M M M M M M B B C C C D D E E E E Q5 Ho 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 1.047 1.093 1.079 1.074 1.096 1.121 1.086 1.139 1.156 1.092 M M M M M M M M M M E E E E E E F F F F 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: Depending on number in each group, N5:S23 Step 1: Ho: Average compa-ratios are equal across the salary ranges Ha: