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 27.8 34 59.2 49.5 75.7 41.7 23.4 80.8 23.6 23.6 66.9 41.6 21.5 24.4 39 68.8 34.9 23.2 36 75.3 56.7 22.6 51.5 25.5 22.9 43.5 74.4 73.5 45.7 23.7 26.9 55.1 28 21.9 23.7 23.2 57.6 34.3 24.4 40.5 23.3 Compa Midpoint 1.012 0.897 1.096 1.038 1.031 1.130 1.043 1.018 1.206 1.027 1.024 1.174 1.041 0.936 1.059 0.975 1.207 1.126 1.008 1.160 1.124 1.182 0.984 1.072 1.109 0.994 1.088 1.111 1.097 0.952 1.031 0.867 0.967 0.904 0.953 1.032 1.010 1.010 1.108 1.062 1.012 1.012 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 77.2 56.9 57.7 65.4 56.8 59.7 62.4 56.5 1.152 0.999 1.202 1.148 0.997 1.048 1.095 0.992 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 1.0504 Standard Deviation 0.0815 Range 0.3400 Mean 1.0651 Standard Deviation 0.0746 Range 0.2710 Mean 1.0358 Standard Deviation 0.0869 Range 0.3390 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 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 4 A How do you interpret the relationship between the data sets? What does this suggest about our equal pay fo Answer: We use the matrix to find the relationship between the variables. The salaries with remaining variable in the data set is high and are dependent to each othe There is a higher probability of female with compa-ratio above 1/3 of the group 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: The variance of compa-ratio between male and female are equal Ha: The variance of compa-ratio between male and female are not equal Step 2: Decision Rule: Reject Ho if p-value is less than 0.05. If not Fail to reject Ho Step 3: Statistical test: F-test Why? Two variances are being compared /ratio of 2 variances Step 4: Conduct the test - place cell B77 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)? 0.2295 No What is your decision: REJ or NOT reject the null? We do not reject the null hypothesis What does this result say about our question The compa-ratio variances of between male and female are e of variance equality? B Are male and female average compa-ratios equal? No they are not 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: The mean of compa-ratio between male and female are equal. Ha: The mean of compa-ratio between male and female are not equal. Step 2: Decision Rule: Reject Ho if p-value is less than 0.05. Otherwise, fail to reject Ho. Step 3: Statistical test: t-test for 2 means (equal variances) Why? We are testing for equality of 2 means. Step 4: Conduct the test - place cell B109 in the output location box. T-Test: Two-Sample Assuming Equal Variances female Mean male 1.065120 Variance 1.035760 0.00556236 0.00755369 Observations Pooled Variance Hypothesized Mean df 25 25 0.006558025 0 48 t Stat 1.281812563 P(T<=t) one-tail 0.10303274 t Critical one-tail 1.6772241961 P(T<=t) two-tail 0.2060654799 t Critical two-tail 2.0106 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)? 0.2061 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 Null What does your decision on rejecting the null We don't accept that the compa-ratios between males and fem hypothesis mean? So by rejecting Ho, It means that compa-ratios between male If the null hypothesis was rejected, calculate the effect size value:N/A Ho rejected If the effect size was calculated, what doe the result Ho rejected mean in terms of why the null hypothesis was rejected? Effect size is the difference between the true What does the result of this test tell us about our question on salary equality? That its not equal, compa-ratio between males and females a 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: K67:L92 Step 1: Ho: Female average compa-ratio is equal to or less than the midpoint value o Ha: Female average compa-ratio is greater than the midpoint value of 1.00 Step 2: Decision Rule: Reject Ho if p-value is less than 0.05. if not accept Ho. Step 3: Statistical test: one sample t-test Why? One sample mean to population mean and since population standard devi Step 4: Conduct the test - place cell B162 in the output location box. female Mean Variance Observations Hypothesized Mean df 1.06512 0.006 25 1 24 t Stat 4.3657096584 P(T<=t) one-tail 0.0001042072 t Critical one-tail 1.7108820799 P(T<=t) two-tail 0.0002084143 t Critical two-tail 2.0638985616 Step 5: Conclusion and Interpretation What is the p-value: 0.0001 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 If the statistic is postive or negatrive considered with a one tail test? Decision: Reject or do not reject Ho? Reject Ho What does your decision on rejecting the null Female average compa-ratio is greater than the midpoint val hypothesis mean? If the null hypothesis was rejected, calculate the effect size value: 0.87 If the effect size was calculated, what doe the result mean in terms of why the null hypothesis was rejected? Its larger What does the result of this test tell us about The Female average compa-ratio is greater than the midpoin our question on salary equality? 6 Considering both the salary information in the lectures and your compa-ratio information, what conclusions Female receive higher salary than male for equal work Variation of pay is equal witin gender Why - what statistical results support this conclusion? Compa ratio is greater then midpoint of 1.00 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) point we can do this grade levels. Column1Grade Column2Column3 Total Probability E or abov F 25 0.88 Male 21 4 25 0.48 Female 23 2 50 0.84 Same Total 44 6 Because population and samples are different. In the first case it's a radomly selected person in grade of E, in the othe re the values for each question below?: 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 17.0 8.0 8.0 1.095 1.108 1.095 0.55 0.57 0.68 0.2923 0.2827 0.2477 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 est about our equal pay for equal work question? are dependent to each other. 1/3 of the group tion be equal to each other? ecide which t-test to use. female are equal female are not equal l to reject Ho No based off our Compa findings they are not equal een male and female are equal male are equal. male are not equal. e, fail to reject Ho. ios between males and females are equal, on the average ompa-ratios between males and females are equal, on the average fference between the true value and the value specified in the null hypothesis ween males and females are different or below the grade midpoint (which is than the midpoint value of 1.00 midpoint value of 1.00 e population standard deviation N/A ater than the midpoint value of 1.00. greater than the midpoint value of 1.00 rmation, what conclusions can you reach about equal pay for equal work? ater then midpoint of 1.00, therefore we expect female salary to be higher on averange than that of males in grade of E, in the other two the population is a male in grade E 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