Raw Preview of Attachment:(refer to the detailed question and attachment below)
Looking at the above correlations - both significant or not - are there any surprises -by that I mean any relationships you expected to be meaningful and are not and vice-versa?Plase interpret the findings. How do we know?If so, which gender gets paid more? See comments at the right of the data set.Put C94 in output range boxb. Place table here (C8 in Output range box):Coefficient hypotheses (one to stand for all the separate variables)Place B106 in Outcome range box.Place B55 in Outcome range box.Place B17 in Outcome range box.BAMA (This is the column variable or Degree.)Ho: Average compas by gender are equalHa: Average compas by gender are not equalHo: Average compas are equal for each degreeHo: Average compas are not equal for each degreeFor Ho: Average compas by gender are equalMeasurement issues. Data, even numerically coded variables, can be one of 4 levels - nominal, ordinal, interval, or ratio. It is important to identify which level a variable is, asFor salary, compa, age, performance rating, and service; find the mean, standard deviation, and range for 3 groups: overall sample, Females, and Males.You can use either the Data Analysis Descriptive Statistics tool or the Fx =average and =stdev functions. (the range must be found using the difference between the =max and =min functions with Fx) functions.Using our sample data, construct a 95% confidence interval for the population's mean salary for each gender. How does this compare to the findings in week 2, question 2?We found last week that the degrees compa values within the population. do not impact compa rates. This does not mean that degrees are distributed evenly across the grades and genders.5. How do you interpret these results in light of our question about equal pay for equal work?Using r = approximately .28 as the signicant r value (at p = 0.05) for a correlation between 50 values, what variables areMany companies consider the grade midpoint to be the "market rate" - what is needed to hire a new employee.Does the company, on average, pay its existing employees at or above the market rate?Place the cursor in B160 for correl.Since the effect size was not discussed in this chapter, we do not have a formula for it - it differs from the non-paired t.Is P-value < 0.05?MidpointPerformance RatingServiceDegreeGender1Salary – Salary in thousands Performance Rating – Appraisal rating (Employee evaluation score)Service – Years of service (rounded)Midpoint – salary grade midpoint Gender1 (Male or Female)Degree (0= BS\BA 1 = MS)Gender: 0 = male, 1 = female Perf. Rat.Let's look at some other factors that might influence pay - education(degree) and performance ratings.d. Average performance ratings per gender are equal.Now we need to see if they differ among the grades. Is the average performace rating the same for all grades?Last week, we found that average performance ratings do not differ between males and females in the population.(Assume variances are equal across the grades for this ANOVA.)Use the input table to the right to list salaries under each grade level.Meaning of effect size measure:Do males and females have athe same distribution of degrees by grade?Is the p-value <0.05?What does this correlation mean?1. Create a correlation table for the variables in our data set. (Use analysis ToolPak or StatPlus:mac LE function Correlation.)Below is a regression analysis for salary being predicted/explained by the other variables in our sample (Midpoint, age, performance rating, service, gender, and degree variables. (Note: since salary and compa are different ways ofPerformace RatingNote: since Gender and Degree are expressed as 0 and 1, they are considered dummy variables and can be used in a multiple regression equation.Is the p-value < 0.05?What is most interesting or surprising about the results we got doing the analysis during the last 5 weeks?Why do we not reject Ho?Is this a 1 or 2 tail test?- why?Place B43 in Outcome range box.Place B75 in Outcome range box.How do you interpret the relationship between the data sets? What do they mean about our equal pay for equal work question?The value that cuts off the top 1/3 salary in each group.The value that cuts off the top 1/3 compa in each group.While it appears that average salaries per each grade differ, we need to test this assumption. Interpretation: The table and analysis below demonstrate a 2-way ANOVA with replication. Please interpret the results.GradeGenderHa: Average salaries are not equal for all gradesHo: Interaction is not significantHa: Interaction is significantPerform analysis:Anova: Two-Factor With ReplicationSampleColumnsInteractionWithin (This is the row variable or gender.)For Ho: Average salaries are equal for all grades For: Ho: Interaction is not significantWhat do these decisions mean in terms of our equal pay question:For this exercise - ignore the requirement for a correctionfor expected values less than 5.If you rejected the null, what is the Phi correlation:If you rejected the null, what is the Cramer's V correlation:Reviewing the data levels from week 1, what variables can be used in a Pearson's Correlation table (which is what Excel produces)?Ha: What is the empirical probability of being at or exceeding this compa value?Based on our sample, how do you interpret the results and what do these results suggest about the population means for male and female average salaries?Based on our sample data set, perform a 2-sample t-test to see if the population male and female average salaries could be equal to each other.If the salary and compa mean tests in questions 2 and 3 provide different results about male and female salary equality, Since performance is often a factor in pay levels, is the average Performance Rating the same for both genders?Test to use:Using our sample data, construct a 95% confidence interval for the mean salary difference between the genders in the population. Why is using a two sample tool (t-test, confidence interval) a better choice than using 2 one-sample techniques when comparing two samples?M GradFem GradMale UndFemale UndDo manual calculations per cell here (if desired)What is the value of the chi square statistic: What is the p-value associated with this value: Do you reject or not reject the null hypothesis: What does this decision mean for our equal pay question: Sum = What is the value of the F statistic: Do you reject or not reject each null hypothesis: What are the coefficients for the significant variables?Using only the significant variables, what is the equation?Salary =Is gender a significant factor in salary:If so, who gets paid more with all other things being equal?Regression hypotheses Note: technically we have one for each input variable. Listing it this way to save space.Is gender a significant factor in compa:Compa = Based on all of your results to date, do we have an answer to the question of are males and females paid equally for equal work?For the Regression as a whole:For each of the coefficients: What is the coefficient's p-value for each of the variables: For each of the coefficients:How do we know? Is the average salary the same for each of the grade levels? (Assume equal variance, and use the analysis toolpak function ANOVA.) What is the empirical probability of being at or exceeding this salary value?a. significantly related to Salary?To compa?Does this help us answer our equal pay for equal work question?Please list under each label, the variables in our data set that belong in each group.Data input tables - graduate degrees by gender and grade level(Note: while technically the sample size might not be large enough to perform this test, ignore this limitation for this exercise.)What are the hypothesis statements:Based on our sample data, can we conclude that males and females are distributed across grades in a similar patternwithin the population?Note: You can either use the Excel Chi-related functions or do the calculations manually.b. Randomly selected male being in grade E? Note part b is the same as given a male, what is probabilty of being in grade E?For each group (overall, females, and males) find:Since the one and two tail t-test results provided different outcomes, which is the proper/correct apporach to comparing salary equality? Why?Ho:Statistical test to use:P-value is:Is P-value > 0.05?Reject or do not reject Ho:(Note: a one-sample t-test in Excel can be performed by selecting the 2-sample unequal variance t-test and making the second variable = Ho value -- see column S)having no variance in the Ho variable makes the calculations default to the one-sample t-test outcome - we are tricking Excel into doing a one sample test for us.Note: While the results both below are actually from Excel's t-Test: Two-Sample Assuming Unequal Variances, At this point we know the following about male and female salaries.Male and female overall average salaries are not equal in the population.RangeThe male and female salary range are almost the same, as is their age and service.Male and female overall average compas are equal in the population, but males are a bit more spread out.Do we REJ or Not reject the null?If the null hypothesis was rejected, what is the effect size value: Using the results up thru this week, what are your conclusions about gender equal pay for equal work at this point?(Since we have not yet covered testing for variance equality, assume the data sets have statistically equal variances.) Measurement and Description - chapters 1 and 2this impact the kind of analysis we can do with the data. For example, descriptive statistics such as means can only be done on interval or ratio level data.NominalOrdinalIntervalRatioSalaryFor each variable that you did not call ratio, why did you make that decision?The first step in analyzing data sets is to find some summary descriptive statistics for key variables.OverallNote: Place data to the right, if you use Descriptive statistics, place that to the right as well.ProbabilityThe z score for each value:The normal curve probability of exceeding this score:e.f.g.Conclusions from looking at salary results:Conclusions from looking at compa results:Do both salary measures show the same results?Can we make any conclusions about equal pay for equal work yet?5. What conclusions can you make about the issue of male and female pay equality? Are all of the results consistent? What is the difference between the sal and compa measures of pay?Null Hypothesis:Alt. Hypothesis:What is the p-value:Do you reject or not reject the null hypothesis:What does that decision mean in terms of our equal pay question:If the null hypothesis was rejected, what is the effect size value (eta squared):NAh.i.t valueDifferenceSt Err.T valueCan the means be equal?Yes/NoWhy?How does this compare to the week 2, question 2 result (2 sampe t-test)?For 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.Ho: Ha:Below are 2 one-sample t-tests comparing male and female average salaries to the overall sample mean. Interpretation:What are your conclusions about equal pay at this point?5. Confidence Intervals and Chi Square (Chs 11 - 12)For full credit, you need to also show the statistical outcomes - either the Excel test result or the calculations you performed.OBSERVEDInterpret the results. How do they compare with the findings in the week 2 one sample t-test outcomes (Question 1)?St error <Reminder: standard error is the sample standard deviation divided by the square root of the sample size.>Ho: The regression equation is not significant.Ho: The regression coefficient for each variable is not significantHa: The regression coefficient for each variable is significantWhich is the best variable to use in analyzing pay practices - salary or compa? Why?Why 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?variables 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.Ha: The regression equation is significant.What outcomes in your life or work might benefit from a multiple regression examination rather than a simpler one variable test?Perform a regression analysis using compa as the dependent variable and the same independentIn questions 2 and 3, be sure to include the null and alternate hypotheses you will be testing. In the first 3 questions use alpha = 0.05 in making your decisions on rejecting or not rejecting the null hypothesis.Based on our sample data set, can the male and female compas in the population be equal to each other? (Another 2-sample t-test.)IDSalCompaAgeRaiseMEBFDCAAge – Age in yearsRaise – percent of last raiseGrade – job/pay gradeThe column labels in the table mean:Week 1.Week 2Week 4Week 3Week 5 Correlation and RegressionCompa - salary divided by midpointID – Employee sample number 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.Testing meansMeanStandard ErrorStandard DeviationSumCountQ3a.b.MaleFemaleMalesHoVarianceObservationsHypothesized Mean Differencedft StatP(T<=t) one-tailt Critical one-tailP(T<=t) two-tailt Critical two-tailFemalesHo: Mean salary = 45Ha: Mean salary =/= 45Conclusion: Do not reject Ho; mean equals 45which would be more appropriate to use in answering the question about salary equity? Why?ANOVASUMMARYAverageSource of VariationSSMSP-valueF critTotalA EXPECTEDSum =Low to HighOBS COUNT - mOBS COUNT - f expressing an employee’s salary, we do not want to have both used in the same regression.)SUMMARY OUTPUTRegression StatisticsMultiple RR SquareAdjusted R SquareRegressionResidualInterceptSignificance FCoefficientsLower 95%Upper 95%Lower 95.0%Upper 95.0%What is the probability for a:c. Why are the results different?a. Randomly selected person being a male in grade E?c.d.
Solution: BUS 308 WEEK 5 ASSIGNMENT