09 May The ongoing question that the weekly assignments w
The ongoing question that the weekly assignments will focus on is: Are males and females paid the same for equal work (under the Equal Pay Act)?Note: to simplfy the analysis, we will assume that jobs within each grade comprise equal work.The column labels in the table mean:ID Employee sample number Sal Salary in thousandsAge Age in yearsEES Appraisal rating (Employee evaluation score)SER Years of serviceG Gender (0 = male, 1 = female)Mid salary grade midpoint Raise percent of last raiseGrade job/pay gradeDeg (0= BSBA 1 = MS)Gen1 (Male or Female)Compa salary divided by midpoint, a measure of salary that removes the impact of gradeThis data should be treated as a sample of employees taken from a company that has about 1,000employees using a random sampling approach.Mac Users: The homework in this course assumes students have Windows Excel, andcan load the Analysis ToolPak into their version of Excel.The analysis tool pak has been removed from Excel for Windows, but a free third-partytool that can be used (found on an answers Microsoft site) is:http://www.analystsoft.com/en/products/statplusmacleLike the Microsoft site, I make cannot guarantee the program, but do know thatStatplus is a respected statistical package. You may use other approaches or toolsas desired to complete the assignments.Week 1. Describing the data.1 Using the Excel Analysis ToolPak function descriptive statistics, generate and show the descriptive statistics for each appropriate variable in the sample data set.a. For which variables in the data set does this function not work correctly for? Why?2Sort the data by Gen or Gen 1 (into males and females) and find the mean and standard deviation for each gender for the following variables:sal, compa, age, sr and raise. Use either the descriptive stats function or the Fx functions (average and stdev).3What is the probability for a:a.Randomly selected person being a male in grade E?b. Randomly selected male being in grade E?c. Why are the results different?45Find:a. The z score for each male salary, based on only the male salaries.b. The z score for each female salary, based on only the female salaries.c. The z score for each female compa, based on only the female compa values.d. The z score for each male compa, based on only the male compa values.e. What do the distributions and spread suggest about male and female salaries?Why might we want to use compa to measure salaries between males and females?Based on this sample, what conclusions can you make about the issue of male and female pay equality?Are all of the results consistent with your conclusion? If not, why not?W eek 2Testing means with the t-testFor questions 2 and 3 below, be sure to list the null and alternate hypothesis statements. Use .05 for your significance level in making your decisions.For full credit, you need to also show the statistical outcomes either the Excel test result or the calculations you performed.1Below are 2 one-sample t-tests comparing male and female average salaries to the overall sample mean.Based on our sample, how do you interpret the results and what do these results suggest about the population means for male and female salaries?MalesFemalesHo: Mean salary = 45Ho: Mean salary = 45Ha: Mean salary =/= 45Ha: Mean salary =/= 45Note when performing a one sample test with ANOVA, the second variable (Ho) is listed as the same value for every corresponding value in the data set.t-Test: Two-Sample Assuming Unequal Variancest-Test: Two-Sample Assuming Unequal VariancesSince the Ho variable has Var = 0, variances are unequal; this test defaults to 1 sample t in this situationMaleHoFemaleHoMean5245Mean3845Variance3160Variance334.66670Observations2525Observations2525Hypothesized Mean Difference 0Hypothesized Mean Difference0df24df24t Stat1.968903827t Stat-1.91321P(T<=t) one-tail0.03030785P(T<=t) one-tail0.033862t Critical one-tail1.71088208t Critical one-tail 1.710882P(T<=t) two-tail0.060615701P(T<=t) two-tail0.067724t Critical two-tail2.063898562t Critical two-tail 2.063899Conclusion: Do notConclusion: Do notreject Ho; meanreject Ho; meanequals 45equals 45MalesThe way that I interpret the results are that since the p-value =.061 is greater than the alpha = .05 it tells me that there is insufficient evidence to make the claim that the average salary of males is significantly different than the average for all employees.FemalesThe way that I interpret the results are that since the p-value =.068 is greater than the alpha = .05 it tells me that there is insufficient evidence to make the claim that the average salary of males is significantly different than the average for all employees.2Based on our sample results, perform a 2-sample t-test to see if the population male and female salaries could be equal to each other.t-Test : Two-sample Assuming equal variancesMale-salayFemale-salarymean5238Variance316 334.6667Observations2525Pooled Variance325.3333Hypothesized mean Difference 0degree of freedom48t-Stat2.7442190.004253P(T ? t) one-tailt Critical one-tail1.677224P(T ? t) Two-tail0.008506t Critical two-tailt-Test : Two-sample Assuming Unequal variancesMale-salay emale-salaryFmean5238Variance316 334.6667Observations2525Hypothesized mean Difference0degree of freedom48t-stat2.744219P(T ? t) one-tail0.004253t Critical one-tail1.67724P(T ? t) Two-tail0.008506t Critical two-tail2.0106352.010635Based on the results of the 2-sample t-test the p-value =.008 and being less than alpha which is .05 that tells me that there is sufficient evidence that indicates the average salaries of males and females significantly different.3Based on our sample results, can the male and female compas in the population be equal to each other? (Another 2-sample t-test.)t-Test: Two-Sample Assuming Equal Variancest-Test: Two-Sample Assuming UnEqual VariancesMale-compa Female-compaMean1.056241.06872Variance0.0070210.004948Observations2525Pooled Variance0.005984Hypothesized mean Difference0degree of freedom48t-Stat-0.57037P(T ? t) one-tail0.285544t Critical one-tail1.677224P(T ? t) Two-tail0.571088t Critical two-tail2.010635Male-compaemale-compaFMean1.05624 1.06872Variance 0.007021 0.004948Observations2525Hypothesized mean 0Differencedegree of freedom 48t-Stat-0.57037P(T ? t) one-tail0.285572t Critical one-tail1.677927P(T ? t) Two-tail0.571144t Critical two-tail2.011741Based on the sample results the p-value =.571 is greater than the alpha = .05 tells me that there is insufficientevidence to indicate the average compa's of males and females are significantly different, which also tells methat the male and female compass are equal.4What other information would you like to know to answer the question about salary equity between the genders? Why?The other information that would be needed to answer the question is about salary equity between thegenders are, years of service, degree, performance rating, and experience. All of these attributes are importantw hen salaries are negotiated and agreed upon5If the salary and compa mean tests in questions 3 and 4 provide different results about male and female salary equality,w hich would be more appropriate to use in answering the question about salary equity? Why?What are your conclusions about equal pay at this point?The mean test in questions 3 & 4 do give different conclusions.The reason why, is that by using the compa it removes the impact of grade.In my conclusions the better of the two t-test is the one which compares the comp's.Week 3Testing multiple means with ANOVAFor questions 3 and 4 below, be sure to list the null and alternate hypothesis statements. Use .05 for your significance level in making your decisions.For full credit, you need to also show the statistical outcomes either the Excel test result or the calculations you performed.1.Based on the sample data, can the average(mean) salary in the population be the same for each of the grade levels? (Assume equal variance, and use the analysis toolpak function ANOVA.)Set up the input table/range to use as follows: Put all of the salary values for each grade under the appropriate grade label.Be sure to incllude the null and alternate hypothesis along with the statistical test and result.Note: Assume equal variances for all grades.ABCDEF2.The table and analysis below demonstrate a 2-way ANOVA with replication. Please interpret the results.GradeGenderABCDEFThe salary values were randomly picked for each cell.M242740475676252847496677F223441506575243642576977Ho: Average salaries are equal for all gradesHa: Average salaries are not equal for all gradesHo: Average salaries by gender are equalHa: Average salaries by gender are not equalHo: Interaction is not significantHa: Interaction is significantPerform analysis:Anova: Two-Factor With ReplicationSUMMARYAMCountSumAverageVarianceBCDEFTotal24924.50.525527.50.528743.524.52964822122615021215356276.5 46.833330.5 364.515224623227035228341.50.5210753.524.5213467821215259276 49.333332 367.3333FCountSumAverageVarianceTotalCount444444Sum95125170203256305Average23.7531.2542.550.756476.25Variance1.58333 19.5833 9.66667 18.9167 31.3333 0.916667ANOVASource of VariationSSSample37.5Columns7841.83Interaction91.5Within117Total8087.83dfMSFP-value F crit137.5 3.84615 0.07348 4.7472255 1568.37 160.858 1E-010 3.105875518.3 1.87692 0.17231 3.105875129.75Note: a number with an E after it (E9 or E-6, for example)means we move the decimal point that number of places.For example, 1.2E4 becomes 12000; while 4.56E-5 becomes 0.000045623Do we reject or not reject each of the null hypotheses? What do your conclusions mean about the population values being tested?Interpretation:3.Using our sample results, can we say that the compa values in the population are equal by grade and/or gender, and are independent of each factor?Be sure to include the null and alternate hypothesis along with the statistical test and result.GradeGenderABCDEFfor the intersection of M and A might be 1.043.>Msalary values used in question 2 for a more direct comparison of the twoFoutcomes.>Conduct and show the results of a 2-way ANOVA with replication using the completed table above. The results should look something like those in question 2.Interpret the results. Are the average compas for each gender (listed as sample) equal? For each grade? Do grade and gender interaction impact compa values?4.Pick any other variable you are interested in and do a simple 2-way ANOVA without replication. Why did you pick this variable and what do the results show?Variable name:Be sure to include the null and alternate hypothesis along with the statistical test and result.GenderABCDEFHint: use mean values in the boxes.MF5.Using the results for this week, What are your conclusions about gender equal pay for equal work at this point?Week 4Confidence Intervals and Chi Square (Chs 11 12)Let’s look at some other factors that might influence pay.For question 3 below, be sure to list the null and alternate hypothesis statements. Use .05 for your significance level in making your decisions.For full credit, you need to also show the statistical outcomes either the Excel test result or the calculations you performed.One question we might have is if the distribution of graduate and undergraduate degrees independent of the grade the employee?(Note: this is the same as asking if the degrees are distributed the same way.)Based on the analysis of our sample data (shown below), what is your answer?Ho: The populaton correlation between grade and degree is 0.Ha: The population correlation between grade and degree is > 0Perform analysis:ABCDEFTotalOBSERVED75325325COUNT M or 082237325COUNT F or 11575512650totalEXPECTED7.53.52.52.563257.53.52.52.56325is found: row total times column total divided by1575512650grand total.>1By using either the Excel Chi Square functions or calculating the results directly as the text shows, do wereject or not reject the null hypothesis? What does your conclusion mean?Interpretation:Using our sample data, we can construct a 95% confidence interval for the population’s mean salary for each gender.Interpret the results. How do they compare with the findings in the week 2 one sample t-test outcomes (Question 1)?MalesMean St errorLowtoHigh523.6587844.448359.5517Results are mean +/-2.064*standard errorFemales383.6227530.522645.47742.064 is t value for 95% interval2Interpretation:3Based on our sample data, can we conclude that males and females are distributed across grades in a similar pattern within the population?4Using our sample data, construct a 95% confidence interval for the population’s mean service difference for each gender.Do they intersect or overlap? How do these results compare to the findings in week 2, question 2?5How do you interpret these results in light of our question about equal pay for equal work?Week 5 Correlation and RegressionFor each question involving a statistical test below, list the null and alternate hypothesis statements. Use .05 for your significance level in making your decisions.For full credit, you need to also show the statistical outcomes either the Excel test result or the calculations you performed.1Create a correlation table for the variables in our data set. (Use analysis ToolPak function Correlation.)a. Interpret the results. What variables seem to be important in seeing if we pay males and females equally for equal work?2Below is a regression analysis for salary being predicted/explained by the other variables in our sample (Mid,age, ees, sr, raise, and deg variables.) (Note: since salary and compa are different ways ofexpressing an employee’s salary, we do not want to have both used in the same regression.)Ho: The regression equation is not significant.Ha: The regression equation is significant.Ho: The regression coefficient for each variable is not significantHa: The regression coefficient for each variable is significantSalSUMMARY OUTPUTThe analysis used Sal as the y (dependent variable) andmid, age, ees, sr, g, raise, and deg as the dependentvariables (entered as a range).Regression StatisticsMultiple R 0.992154976R Square 0.984371497Adjusted R Square 0.981766746Standard Error 2.592776307Observations50ANOVAdfRegressionResidualTotalSSMSFSignificance F7 17783.66 2540.522 377.9139 8.440427E-03642 282.3445 6.7224894918066CoefficientsIntercept-4.009Mid1.220Age0.029EES-0.096SR-0.074G2.552Raise0.834Deg1.002StandardError3.7750.0300.0670.0470.0840.8470.6430.744t Stat-1.06240.6740.439-2.020-0.8763.0121.2991.347P-value0.2940.0000.6630.0500.3860.0040.2010.185Lower 95%-11.6271.159-0.105-0.191-0.2440.842-0.462-0.500Upper 95% Lower 95.0% Upper 95.0%3.609-11.6273.6091.2801.1591.2800.164-0.1050.1640.000-0.1910.0000.096-0.2440.0964.2610.8424.2612.131-0.4622.1312.504-0.5002.504Interpretation: Do you reject or not reject the regression null hypothesis?Do you reject or not reject the null hypothesis for each variable?What is the regression equation, using only significant variables if any exist?What does result tell us about equal pay for equal work for males and females?3Perform a regression analysis using compa as the dependent variable and the same independentvariables as used in question 2. Show the result, and interpret your findings by answering the same questions.Note: be sure to include the appropriate hypothesis statements.4Based on all of your results to date, is gender a factor in the pay practices of this company? Why or why not?Which is the best variable to use in analyzing pay practices salary or compa? Why?5Why did the single factor tests and analysis (such as t and single factor ANOVA tests on salary equality) not provide a complete answer to our salary equality question?What outcomes in your life or work might benefit from a multiple regression examination rather than a simpler one variable test?
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