ID Salary Compa- Midpoint ratio Age Performance Service Gender Rating Raise Degree Gender Grade 1 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 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 Age Perf. Rat. Service Overall Mean 35.7 85.9 9.0 Standard Deviation 8.2513 11.4147 5.7177 Note - remember the dat Range 30 45 21 Female Mean 32.5 84.2 7.9 Standard Deviation 6.9 13.6 4.9 Range 26.0 45.0 18.0 Male Mean 38.9 87.6 10.0 Standard Deviation 8.4 8.7 6.4 Range 28.0 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 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: Ha: Step 2: Decision Rule: Step 3: Statistical test: Why? 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)? What is your decision: REJ or NOT reject the null? What does this result say about our question 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: 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: Is the P-value < 0.05 (for a one tail test) or 0.025 (for a two tail test)? What is your decision: REJ or NOT reject the null? 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? 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? 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? 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 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 est about our equal pay for equal work question? tion be equal to each other? ecide which t-test to use. 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? 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 This assignment covers the material presented in weeks 1 and 2. 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 som focus mostly on the compa-ratios, we need to find Sorting the compa-ratios into male and females w The values for age, performance rating, and servi (see if you can replicate the values). You can use either the Data Analysis Descriptive The range can be found using the difference betw Suggestion: Copy and paste the compa-ratio data If you use Descriptive statistic If you did not use Descriptive S Overall Female Male Mean Standard Deviation Range Mean Standard Deviation Range Mean Standard Deviation Range 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. Randomly selected person being in grade E b. Randomly selected person being a male in g c. Randomly selected male being in grade E or d. Why are the results different? 3 Normal Curve based probability: For each group A Make sure your answer cells show the Excel func The probability of being in the top 1/3 of the com Note, we can find the cutoff value for the top 1/3 Value is the number that identifies the x-largest va For the overall group, this would be the 50/3 or 1 i. How nany salaries are in the top 1/3 (rounded to n ii What Compa-ratio value starts the top 1/3 of the r iii What is the z-score for this value? iv. What is the normal curve probability of exceeding B How do you interpret the relationship between the Males at the higher end of the payscale earn highe 4 A Based on our sample data set, can the male and fe First, we need to determine if these two groups ha What is the data input ranged used for Step 1: Ho: Ha: Step 2: Decision Rule: Step 3: Statistical test: Why? Step 4: Conduct the test - place cell B7 F-Test Two-Sample for Variances Mean Variance Observations df F P(F<=f) one-tail F Critical one-tail 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 is your decision: REJ or NOT reject the null? What does this result say about our question of variance equality? B Are male and female average compa-ratios equal? (Regardless of the outcome of the above F-test, as What is the data input ranged used for Step 1: Ho: Ha: Step 2: Decision Rule: Step 3: Statistical test: Why? Step 4: Conduct the test - place cell B1 t-Test: Two-Sample Assuming Equ Mean Variance Observations Pooled Variance Hypothesized Mea df t Stat P(T<=t) one-tail t Critical one-tail P(T<=t) two-tail t Critical two-tail 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 is your decision: REJ or NOT reject the null? 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? 5 Is the Female average compa-ratio equal to or les This question is the same as: Does the company, p considered the market rate)? Suggestion: Use the data column T to the right fo What is the data input ranged used for this questio Step 1: Ho: Ha: Step 2: Decision Rule: Step 3: Statistical test: Why? Step 4: Conduct the test - place cell B1 t-Test: Paired Two Sample for Me Mean Variance Observations Pearson Correlati Hypothesized Mea df t Stat P(T<=t) one-tail t Critical one-tail P(T<=t) two-tail t Critical two-tail 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? 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 lec The average salaries for male and female employe Why - what statistical results support this conclus The results from the test comparing male and fem Six Questions ry 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. ample, 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 the 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. ng data sets is to find some summary descriptive statistics for key variables. Since the assignment problems will mpa-ratios, we need to find the mean, standard deviations, and range for our groups: Males, Females, and Overall. s into male and females will require you copy and paste the Compa-ratio and Gender1 columns, and then sort on Gender1. formance rating, and service are provided for you for future use, and - if desired - to test your approach to the compa-ratio answe e the values). Data Analysis Descriptive Statistics tool or the Fx =average and =stdev functions. d using the difference between the =max and =min functions with Fx functions or from Descriptive Statistics. paste the compa-ratio data to the right (Column T) and gender data in column U. u use Descriptive statistics, Place the output table in row 1 of a column to the right. u did not use Descriptive Statistics, make sure your cells show the location of the data (Example: =average(T2:T51) Comparatio 1.0566 0.0785 0.331 1.0664 0.0692 0.227 1.0468 0.0872 0.331 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 data is a sample from the larger company popul 45 21 84.2 7.9 13.6 4.9 45.0 18.0 87.6 10.0 0 8.7 6.4 30.0 21.0 point we can do this grade levels. What is the probability for a: ed person being in grade E or above? d person being a male in grade E or above? d male being in grade E or above? s different? Probability 0.36 0.28 0.56 It is because being in grade E or above and gender are not obability: For each group (overall, females, males), what are the values for each question below?: cells show the Excel function and cell location of the data used. g in the top 1/3 of the compa-ratio distribution. utoff value for the top 1/3 using the fx Large function: =large(range, value). t identifies the x-largest value. For the top 1/3 value would be the value that starts the top 1/3 of the range, his would be the 50/3 or 17th (rounded), for the gender groups, it would be the 25/3 = 8th (rounded) value. Overall Female Male n the top 1/3 (rounded to nearest whole number) for each group? 17 8 8 e starts the top 1/3 of the range for each group? 1.099 1.091 1.103 this value? 0.5402069 0.355562 0.645042 ve probability of exceeding this score? 0.2945272 0.361084 0.25945 he relationship between the data sets? What does this suggest about our equal pay for equal work question? of the payscale earn higher than their female counterparts. This is partially because of the proportion of males in higher grade jo ata set, can the male and female compa-ratios in the population be equal to each other? mine if these two groups have equal variances, in order to decide which t-test to use. data input ranged used for this question: S4:S28 and S29:S53 Variance of male and female compa-ratios are equal Variance of male and female compa-ratios are unequal Do not reject Ho if p-value is less than 0.025, otherwise reject H0 F-test two sample for variances The sampling distribution of the division of the two sample variances follows a F-distribution uct the test - place cell B77 in the output location box. t Two-Sample for Variances Variable 1 Variable 2 1.04676 1.0664 0.00760177 0.00478675 25 25 24 24 Note: Variable 1 is Male Compa-ratio and Variable 2 is Female Compa-ratio 1.58808656 0.13213842 1.98375957 lusion and Interpretation What is the p-value: 0.132138416 5 (for a one tail test) or No(for a one tail test) 25 (for a two tail test)? or NOT reject the null? Do not reject the null say about our question We do not have significant evidence to prove that the two variances are not equal of variance equality? verage compa-ratios equal? ome of the above F-test, assume equal variances for this test.) data input ranged used for this question: S4:S28 and S29:S53 Male and female average compa-ratios are equal Male and female average compa-ratios are not equal Do not reject Ho if p-value is lesser than 0.025 , otherwise reject Ho T-test two sample assuming equal variances The difference in sample means from two normally distributed populations follows a t-distribution uct the test - place cell B109 in the output location box. : Two-Sample Assuming Equal Variances Variable 1 Variable 2 1.04676 1.0664 0.00760177 0.00478675 25 25 0.00619426 0 48 -0.88227041 0.19101384 1.6772242 0.38202768 2.01063476 lusion and Interpretation What is the p-value: 0.3820276841 Note: Variable 1 is Male Compa-ratio and Variable 2 is Female Compa-ratio 5 (for a one tail test) or No(for a two tailed test) 25 (for a two tail test)? or NOT reject the null? Do not reject the null null hypothesis mean? If the null hypothesis were rejected it would mean that the mean male ompa-ratios and mean female com Null hypothesis was not was rejected, calculate rejected the effect size value: ypothesis was rejected? Not applicable of this test tell us about The average salaries of male and female employees , taking into account the employee grade by means of tion on salary equality? This result suggests that there is equal pay for equal work across genders ompa-ratio equal to or less than the midpoint value of 1.00? me as: Does the company, pay its females - on average - at or below the grade midpoint (which is ate)? a column T to the right for your null hypothesis value. anged used for this question: S29:S53 and X4:X28 Female average compa-ratio is equal to 1 Female average compa-ratio is lesser than 1 Do not reject Ho if p-value less than 0.05, otherwise reject Ho Hypothesis test about a population mean with unknown population standard deviation We assume that the sample mean of the female compa-ratio follows a t-distribution uct the test - place cell B162 in the output location box. : Paired Two Sample for Means Variable 1 Variable 2 1.0664 0 0.00478675 0 Note that variable 1 is female compa-ratios and variable 2 is an array 25 25 #DIV/0! 1 24 4.79863493 3.465E-005 1.71088208 6.930E-005 2.06389856 lusion and Interpretation What is the p-value: 0.9999653517 5 (for a one tail test) or Yes(for a one tail test) 25 (for a two tail test)? he p-value, needs to be Whether the test is left tailed or righ tailed should be considered red with a one tail test? ect or do not reject Ho? Do not Reject Ho null hypothesis mean? Null hypothesis is not rejected was rejected, calculate Not applicable the effect size value: ypothesis was rejected? Not applicable of this test tell us about It tells us that on average across all grades of work average salaries paid to females is not lesser than the tion on salary equality? lary information in the lectures and your compa-ratio information, what conclusions can you reach about equal pay for equal wo r male and female employees are equal for equal work on average across all grades of work esults support this conclusion? t comparing male and female average compa-ratios and the results from the test comparing average female compa-ratios to the m oblems will and Overall. hen sort on Gender1. h to the compa-ratio answers rage(T2:T51) m the larger company population ID Salary Compa Midpoint 1 2 4 5 6 9 12 16 19 21 25 27 29 30 32 33 34 38 40 41 44 46 47 49 50 3 7 59.3 26.5 56.3 46.8 79.5 76 62.9 46.6 24 75.2 24.9 42.9 75.4 48.9 28 61.3 26.8 60.1 23.9 39.5 63.3 62.9 63.9 58.8 55 34.1 41.2 1.040 8 10 11 13 14 15 17 18 20 22 23.6 22.7 23.8 41.4 22.3 23.1 67.6 33.8 35 51.5 1.026 0.856 0.987 0.975 1.187 1.134 1.104 1.166 1.043 1.122 1.084 1.073 1.125 1.019 0.904 1.075 0.864 1.055 1.038 0.987 1.110 1.103 1.121 1.032 0.965 1.099 1.031 0.985 1.036 1.035 0.968 1.006 1.186 1.091 1.129 1.073 Age Performa nce Rating 57 31 57 48 67 67 57 40 23 67 23 40 67 48 31 57 31 57 23 40 57 57 57 57 57 31 40 34 52 42 36 36 49 52 44 32 43 41 35 52 45 25 35 26 45 24 25 45 39 37 41 38 30 32 85 80 100 90 70 100 95 90 85 95 70 80 95 90 95 90 80 95 90 80 90 75 95 95 80 75 100 23 23 23 40 23 23 57 31 31 48 32 30 41 30 32 32 27 31 44 48 90 80 100 100 90 80 55 80 70 65 r above and gender are not independent. The proport 23 24 26 28 31 35 36 37 39 42 43 45 48 22.1 55.4 24.3 76.6 22.9 23.6 24.6 22.7 33.4 23.6 76.9 55.7 67.7 0.960 1.155 1.055 1.144 0.997 1.026 1.070 0.985 1.079 1.028 1.148 1.161 1.187 23 48 23 67 23 23 23 23 31 23 67 48 57 36 30 22 44 29 23 27 22 27 32 42 36 34 65 75 95 95 60 90 75 95 90 100 95 95 90 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 of males in higher grade jobs being higher. It is also possible that females are being paid less for equal work but the results obtai 2 is Female Compa-ratio 2 is Female Compa-ratio tios and mean female compa-ratios are not equal mployee grade by means of the compa-ratio, are equal s and variable 2 is an array of 0s males is not lesser than the midpoint salaries out equal pay for equal work? male compa-ratios to the midpoint, both of which had their null hypothesis accepted, support this conclusion Service Gender Raise Degree Gender1 Gr 8 7 16 16 12 10 22 4 1 13 4 7 5 18 4 9 2 11 2 5 16 20 5 21 12 5 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 5.7 3.9 5.5 5.7 4.5 4 4.5 5.7 4.6 6.3 4 3.9 5.4 4.3 5.6 5.5 4.9 4.5 6.3 4.3 5.2 3.9 5.5 6.6 4.6 3.6 5.7 0 0 1 1 1 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 1 1 1 0 0 1 1 M M M M M M M M M M M M M M M M M M M M M M M M M F F E B E D F F E C A F A C F D B E B E A C E E E E E B C 9 7 19 2 12 8 3 11 16 6 1 1 1 1 1 1 1 1 1 1 5.8 4.7 4.8 4.7 6 4.9 3 5.6 4.8 3.8 1 1 1 0 1 1 1 0 0 1 F F F F F F F F F F A A A C A A E B B D 6 9 2 9 4 4 3 2 6 8 20 8 11 1 1 1 1 1 1 1 1 1 1 1 1 1 3.3 3.8 6.2 4.4 3.9 5.3 4.3 6.2 5.5 5.7 5.5 5.2 5.3 0 0 0 0 1 0 0 0 0 1 0 1 1 F F F F F F F F F F F F F A D A F A A A A B A F D E ual work but the results obtained cannot be used to test if it is true or not. 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: N6:S23 Step 1: Ho: The mean compa-ratios are equal for different compa-ratios Ha: Mean compa-ratio is different from the mean compa-ratios of the other salar Step 2: Decision Rule: Fail to reject Ho if p-value is greater than the level of significance, Step 3: Statistical test: Single factor Anova Why? We are testing for the equality of three or more population means u Step 4: Conduct the test - place cell b16 in the output location box. Anova: Single Factor SUMMARY Groups Count Sum Average Variance Column 1 18 17.931 0.9961667 0.0042946 Column 2 5 5.385 Column 3 6 6.299 1.0498333 0.0042314 Column 4 7 7.413 Column 5 8 8.941 1.117625 0.0022423 Column 6 6 6.86 1.1433333 0.0005615 1.077 1.059 0.002872 0.005821 ANOVA Source of Variation SS df MS F P-value F crit Between Groups Within Groups 0.1430636 0.1590825 5 0.0286127 7.9138792 2.19E-005 2.4270401198 44 0.0036155 Total 0.3021462 49 Step 5: Conclusions and Interpretation What is the p-value? 2.19227E-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)? 0.473491468 If calculated, what does the effect size value tell us about why the null hypothesis was rejected? The effect size tells us that 47.349 What does that decision mean in terms of our equal pay question? This decision means people at differe 2 If the null hypothesis in question 1 was rejected, which pairs of means differ? Here Fisher's LSD Procedure using confidence intervals has been used Groups Compared G1 G2 G1 G3 G1 G4 G1 G5 G1 G6 Diff -0.081 -0.054 -0.063 -0.121 -0.147 T -2.659 -1.893 -2.346 -4.754 -5.192 +/- Term 0.061117 0.056992 0.053852 0.051372 0.056992 Low -0.142 -0.111 -0.117 -0.173 -0.204 G2 G3 G2 G4 G2 G5 G2 G6 0.027 0.746 0.018 0.511 -0.041 -1.185 -0.066 -1.822 0.073207 0.07079 0.068922 0.073207 -0.046 -0.053 -0.110 -0.140 G3 G4 G3 G5 G3 G6 -0.009 -0.274 -0.068 -2.088 -0.094 -2.693 0.067261 0.065292 0.0698 -0.076 -0.133 -0.163 G4 G5 G4 G6 -0.059 -1.884 -0.084 -2.521 0.062571 0.067261 -0.121 -0.152 G5 G6 -0.026 -0.792 0.065292 -0.091 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? Theresults suggest that mean compa-ratios are higher for employees in higher salary ranges. It means that ing functions, show the input range when asked. ranges of 10K each. nt for different pay levels, (Put data values at right.) Group name: G2 G3 G4 22-29 30-39 40-49 50-59 0.960 Compa-ratio values: 0.968 0.985 0.985 0.997 compa-ratios compa-ratios of the other salary ranges for one or more salary rang 1.006 1.026 r than the level of significance, otherwise reject Ho 1.026 ee or more population means using data obtained from an observat 1.028 1.036 1.038 1.043 1.055 1.070 1.084 0.856 0.864 0.904 1.079 1.091 1.099 1.129 0.987 1.031 1.035 1.073 1.166 0.975 1.019 1.073 0.965 1.155 1.161 0.987 1.032 1.040 ect the null Salary Intervals: G1 Mean 0.996 1.077 1.050 1.059 Count 18 5 6 7 e effect size tells us that 47.349% of total variance is accounted for by treatment effect. Since this is quite a large value, the null h s decision means people at different salary levels are not paid equally with respect to the grade midpoint The pairs Why? has been used Difference High Significant? -0.020 Yes 0.003 No -0.009 Yes -0.070 Yes -0.090 Yes 0.100 0.089 0.028 0.007 No No No No 0.058 -0.002 -0.024 No Yes Yes 0.004 -0.017 No Yes 0.040 No The confidence interval for difference of means does not contain 0 Why? confidence interval does not contain 0 confidence interval contains 0 confidence interval does not contain 0 confidence interval does not contain 0 confidence interval does not contain 0 confidence interval contains 0 confidence interval contains 0 confidence interval contains 0 confidence interval contains 0 confidence interval contains 0 confidence interval contains 0 confidence interval contains 0 confidence interval does not contain 0 confidence interval does not contain 0 confidence interval contains 0 confidence interval contains 0 confidence interval does not contain 0 confidence interval contains 0 confidence interval contains 0 er salary ranges. It means that the variation in pay for employees in the same grade is higher for higher grades.Otherwise, these Sorted data G5 G6 60-69 70-79 1.055 1.075 1.104 1.103 1.110 1.121 1.186 1.187 1.122 1.125 1.134 1.144 1.148 1.187 1.118 1.143 8 6 ID Salary 23 14 10 37 31 15 8 35 42 11 40 19 26 36 25 2 34 32 39 18 3 20 41 7 13 27 16 5 30 22 50 24 45 4 49 1 38 22.1 22.3 22.7 22.7 22.9 23.1 23.6 23.6 23.6 23.8 23.9 24 24.3 24.6 24.9 26.5 26.8 28 33.4 33.8 34.1 35 39.5 41.2 41.4 42.9 46.6 46.8 48.9 51.5 55 55.4 55.7 56.3 58.8 59.3 60.1 Compa- Midpoint ratio 0.960 0.968 0.985 0.985 0.997 1.006 1.026 1.026 1.028 1.036 1.038 1.043 1.055 1.070 1.084 0.856 0.864 0.904 1.079 1.091 1.099 1.129 0.987 1.031 1.035 1.073 1.166 0.975 1.019 1.073 0.965 1.155 1.161 0.987 1.032 1.040 1.055 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 31 31 31 31 31 31 31 40 40 40 40 40 48 48 48 57 48 48 57 57 57 57 Age 36 32 30 22 29 32 32 23 32 41 24 32 22 27 41 52 26 25 27 31 30 44 25 32 30 35 44 36 45 48 38 30 36 42 41 34 45 Performa Service nce Rating 65 90 80 95 60 80 90 90 100 100 90 85 95 75 70 80 80 95 90 80 75 70 80 100 100 80 90 90 90 65 80 75 95 100 95 85 95 6 12 7 2 4 8 9 4 8 19 2 1 2 3 4 7 2 4 6 11 5 16 5 8 2 7 4 16 18 6 12 9 8 16 21 8 11 33 61.3 1.075 57 35 90 9 12 46 62.9 62.9 1.104 1.103 57 57 52 39 95 75 22 20 44 47 17 48 21 29 9 63.3 63.9 67.6 67.7 75.2 75.4 76 1.110 1.121 1.186 1.187 1.122 1.125 1.134 57 57 57 57 67 67 67 45 37 27 34 43 52 49 90 95 55 90 95 95 100 16 5 3 11 13 5 10 28 43 6 76.6 76.9 79.5 1.144 1.148 1.187 67 67 67 44 42 36 95 95 70 9 20 12 s quite a large value, the null hypothesis w gher grades.Otherwise, these results do not affect our conclusion on equal pay for equal work. Gender Raise Degree Gender1 Grade 1 1 1 1 1 1 1 1 1 1 0 0 1 1 0 0 0 0 1 1 1 1 0 1 1 0 0 0 0 1 0 1 1 0 0 0 0 3.3 6 4.7 6.2 3.9 4.9 5.8 5.3 5.7 4.8 6.3 4.6 6.2 4.3 4 3.9 4.9 5.6 5.5 5.6 3.6 4.8 4.3 5.7 4.7 3.9 5.7 5.7 4.3 3.8 4.6 3.8 5.2 5.5 6.6 5.7 4.5 0 1 1 0 1 1 1 0 1 1 0 1 0 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 1 0 0 1 1 0 0 0 F F F F F F F F F F M M F F M M M M F F F F M F F M M M M F M F F M M M M A A A A A A A A A A A A A A A B B B B B B B C C C C C D D D E D D E E E E 0 5.5 1 M E 0 0 4.5 3.9 0 1 M M E E 0 0 1 1 0 0 0 5.2 5.5 3 5.3 6.3 5.4 4 1 1 1 1 1 0 1 M M F F M M M E E E E F F F 1 1 0 4.4 5.5 4.5 0 0 1 F F M F F F 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