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MARKETING MANAGEMENT PHILOSOPHIESCHAPTER 1 - ASSIGNMENTQuest.docx
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### Chi-square tests are great to show if distributions differ or i.docx

1. Chi-square tests are great to show if distributions differ or if two variables interact in producing outcomes. What are some examples of variables that you might want to check using the chi-square tests? What would these results tell you? DataSee comments at the right of the data set.IDSalaryCompaMidpointAgePerformance RatingServiceGenderRaiseDegreeGender1Grade8231.000233290 915.80FAThe 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)? 10220.956233080714.70FANote: to simplfy the analysis, we will assume that jobs within each grade comprise equal work.11231.00023411001914.80FA14241.04323329012160FAT he column labels in the table mean:15241.043233280814.90FAID – Employee sample number Salary – Salary in thousands 23231.000233665613.31FAAge – Age in yearsPerformance Rating – Appraisal rating (Employee evaluation score)26241.043232295216.21FAService – Years of service (rounded)Gender: 0 = male, 1 = female 31241.043232960413.90FAMidpoint – salary grade midpoint Raise – percent of last raise35241.043232390415.31FAGrade – job/pay gradeDegree (0= BSBA 1 = MS)36231.000232775314.31FAGender1 (Male or Female)Compa - salary divided by midpoint37220.956232295216.21FA42241.0432332100815.70F A3341.096313075513.60FB18361.1613131801115.61FB20341.0 963144701614.81FB39351.129312790615.51FB7411.025403210 0815.70FC13421.0504030100214.71FC22571.187484865613.80 FD24501.041483075913.81FD45551.145483695815.20FD17691 .2105727553130FE48651.1405734901115.31FE28751.11967449 5914.41FF43771.1496742952015.51FF19241.043233285104.61
2. MA25241.0432341704040MA40251.086232490206.30MA2270. 870315280703.90MB32280.903312595405.60MB34280.903312 680204.91MB16471.175404490405.70MC27401.000403580703. 91MC41431.075402580504.30MC5470.9794836901605.71MD3 0491.0204845901804.30MD1581.017573485805.70ME4661.157 57421001605.51ME12601.0525752952204.50ME33641.1225735 90905.51ME38560.9825745951104.50ME44601.0525745901605 .21ME46651.1405739752003.91ME47621.087573795505.51ME 49601.0525741952106.60ME50661.1575738801204.60ME6761. 1346736701204.51MF9771.149674910010041MF21761.134674 3951306.31MF29721.074675295505.40MF Week 1Week 1.Measurement and Description - chapters 1 and 21Measurement 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, asthis 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.Please list under each label, the variables in our data set that belong in each group.NominalOrdinalIntervalRatiob.For each variable that you did not call ratio, why did you make that decision?2The first step in analyzing data sets is to find some summary descriptive statistics for key variables.For 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.Note: Place data to the right, if you use Descriptive statistics, place that to the right as well.SalaryCompaAgePerf. Rat.ServiceOverallMeanStandard DeviationRangeFemaleMeanStandard DeviationRangeMaleMeanStandard DeviationRange3What is the probability for a:Probabilitya. Randomly selected person being a male in grade E?b. Randomly selected male being in grade E? Note part b is the same as given a male, what is
3. probabilty of being in grade E?c. Why are the results different?4For each group (overall, females, and males) find:OverallFemaleMalea.The value that cuts off the top 1/3 salary in each group.b.The z score for each value:c.The normal curve probability of exceeding this score:d.What is the empirical probability of being at or exceeding this salary value?e.The value that cuts off the top 1/3 compa in each group.f.The z score for each value:g.The normal curve probability of exceeding this score:h.What is the empirical probability of being at or exceeding this compa value?i.How do you interpret the relationship between the data sets? What do they mean about our equal pay for equal work question?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?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? Week 2 Week 2Testing meansQ3In questions 2 and 3, be sure to include the null and alternate hypotheses you will be testing. HoFemaleMaleFemaleIn the first 3 questions use alpha = 0.05 in making your decisions on rejecting or not rejecting the null hypothesis.45341.0171.09645410.8701.0251Below are 2 one- sample t-tests comparing male and female average salaries to the overall sample mean. 45231.1571.000(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)45220.9790.956Based 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?45231.1341.000MalesFemales45421.1491.050Ho: Mean salary = 45Ho: Mean salary = 4545241.0521.043Ha: Mean salary =/= 45Ha: Mean salary =/= 4545241.1751.04345691.0431.210Note: While the results both below are actually from Excel's t-Test: Two-Sample Assuming
4. Unequal Variances, 45361.1341.161having 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.45341.0431.096MaleHoFemaleHo45571.0001.187Mean5245 Mean384545231.0741.000Variance3160Variance334.666666666 7045501.0201.041Observations2525Observations252545240.90 31.043Hypothesized Mean Difference0Hypothesized Mean Difference045751.1221.119df24df2445240.9031.043t Stat1.9689038266t Stat-1.913206357345240.9821.043P(T<=t) one-tail0.0303078503P(T<=t) one- tail0.033862118445231.0861.000t Critical one- tail1.7108820799t Critical one- tail1.710882079945221.0750.956P(T<=t) two- tail0.0606157006P(T<=t) two- tail0.067724236945351.0521.129t Critical two- tail2.0638985616t Critical two- tail2.063898561645241.1401.043Conclusion: Do not reject Ho; mean equals 45Conclusion: Do not reject Ho; mean equals 4545771.0871.149Is this a 1 or 2 tail test?Is this a 1 or 2 tail test?- why?- why?P-value is:P-value is:45551.0521.145Is P- value > 0.05?Is P-value > 0.05?45651.1571.140Why do we not reject Ho?Why do we not reject Ho?Interpretation:2Based 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.(Since we have not yet covered testing for variance equality, assume the data sets have statistically equal variances.)Ho: Ha: Test to use:Place B43 in Outcome range box.P-value is:Is P-value < 0.05?Reject or do not reject Ho:If the null hypothesis was rejected, what is the effect size value:Meaning of effect size measure:Interpretation:b.Since the one and two tail t-test results provided different outcomes, which is the proper/correct apporach to comparing salary equality? Why?3Based on our sample data set, can the male and female compas in the population be equal to each other? (Another 2-sample t-test.)Ho:Ha:Statistical test to use:Place
5. B75 in Outcome range box.What is the p-value:Is P-value < 0.05?Reject or do not reject Ho:If the null hypothesis was rejected, what is the effect size value:Meaning of effect size measure: Interpretation: 4Since performance is often a factor in pay levels, is the average Performance Rating the same for both genders?Ho:Ha:Test to use:Place B106 in Outcome range box.What is the p-value:Is P-value < 0.05?Do we REJ or Not reject the null?If the null hypothesis was rejected, what is the effect size value:Meaning of effect size measure:Interpretation:5If the salary and compa mean tests in questions 2 and 3 provide different results about male and female salary equality, which would be more appropriate to use in answering the question about salary equity? Why?What are your conclusions about equal pay at this point? Week 3Week 3At this point we know the following about male and female salaries.a.Male and female overall average salaries are not equal in the population.b.Male and female overall average compas are equal in the population, but males are a bit more spread out.c.The male and female salary range are almost the same, as is their age and service.d. Average performance ratings per gender are equal.Let's look at some other factors that might influence pay - education(degree) and performance ratings.1Last week, we found that average performance ratings do not differ between males and females in the population.Now we need to see if they differ among the grades. Is the average performace rating the same for all grades?(Assume variances are equal across the grades for this ANOVA.)ABCDEFNull Hypothesis:Alt. Hypothesis:Place B17 in Outcome range box.Interpretation:What is the p-value:Is P-value < 0.05?Do we REJ or Not reject the null?If the null hypothesis was rejected, what is the effect size value (eta squared):Meaning of effect size measure:What does that decision mean in terms of our equal pay question:2While it appears that average salaries per each grade differ, we need to test this assumption. Is the average salary the same for each of the grade levels? (Assume equal variance, and use the analysis toolpak function ANOVA.)
6. Use the input table to the right to list salaries under each grade level.Null Hypothesis:Alt. Hypothesis:ABCDEFPlace B55 in Outcome range box.What is the p-value:Is P-value < 0.05?Do you reject or not reject the null hypothesis:If the null hypothesis was rejected, what is the effect size value (eta squared):Meaning of effect size measure:Interpretation:3The table and analysis below demonstrate a 2-way ANOVA with replication. Please interpret the results.BAMAHo: Average compas by gender are equalMale1.0171.157Ha: Average compas by gender are not equal0.8700.979Ho: Average compas are equal for each degree1.0521.134Ho: Average compas are not equal for each degree1.1751.149Ho: Interaction is not significant1.0431.043Ha: Interaction is significant1.0741.1341.0201.000Perform analysis:0.9031.1220.9820.903Anova: Two-Factor With Replication1.0861.0521.0751.140SUMMARYBAMATotal1.052 1.087MaleFemale1.0961.050Count1212241.0251.161Sum12.349 12.925.2491.0001.096Average1.02908333331.0751.0520416667 0.9561.000Variance0.0066864470.00651981820.00686604171.0 001.0411.0431.043Female1.0431.119Count1212241.2101.043Su m12.79112.78725.5781.1871.000Average1.06591666671.06558 333331.065751.0430.956Variance0.0061024470.00421281060.0 049334131.0431.1291.1451.149TotalCount2424Sum25.1425.68 7Average1.04751.0702916667Variance0.00647034780.0051561 286ANOVASource of VariationSSdfMSFP-valueF critSample0.002255020810.00225502080.38348211710.5389389 5074.0617064601 (This is the row variable or gender.)Columns0.006233520810.00623352081.06005396090.3 0882956334.0617064601 (This is the column variable or Degree.)Interaction0.006417187510.00641718751.09128776640 .30189150624.0617064601Within0.25873675440.0058803807To tal0.273642479247Interpretation:For Ho: Average compas by gender are equalHa: Average compas by gender are not equalWhat is the p-value:Is P-value < 0.05?Do you reject or not reject the null hypothesis:If the null hypothesis was rejected, what is the effect size value (eta squared):Meaning of effect
7. size measure:For Ho: Average salaries are equal for all grades Ha: Average salaries are not equal for all gradesWhat is the p- value:Is P-value < 0.05?Do you reject or not reject the null hypothesis:If the null hypothesis was rejected, what is the effect size value (eta squared):Meaning of effect size measure:For: Ho: Interaction is not significantHa: Interaction is significantWhat is the p-value:Do you reject or not reject the null hypothesis:If the null hypothesis was rejected, what is the effect size value (eta squared):Meaning of effect size measure:What do these decisions mean in terms of our equal pay question:4Many companies consider the grade midpoint to be the "market rate" - what is needed to hire a new employee.MidpointSalaryDoes the company, on average, pay its existing employees at or above the market rate?Null Hypothesis:Alt. Hypothesis:Statistical test to use:Place the cursor in B160 for correl.What is the p-value:Is P-value < 0.05?Do we REJ or Not reject the null?If the null hypothesis was rejected, what is the effect size value: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.Meaning of effect size measure:NAInterpretation:5. Using the results up thru this week, what are your conclusions about gender equal pay for equal work at this point? Week 4Week 4Confidence Intervals and Chi Square (Chs 11 - 12)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.For full credit, you need to also show the statistical outcomes - either the Excel test result or the calculations you performed.1Using our sample data, 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)?MeanSt error t valueLow to HighMalesFemales<Reminder: standard error is the sample standard deviation divided by the square root of the sample size.>Interpretation:2Using our sample data, construct a 95% confidence interval for the mean
8. salary difference between the genders in the population. How does this compare to the findings in week 2, question 2?DifferenceSt Err.T valueLow to HighYes/NoCan the means be equal?Why?How does this compare to the week 2, question 2 result (2 sampe t-test)?a.Why is using a two sample tool (t-test, confidence interval) a better choice than using 2 one-sample techniques when comparing two samples?3We 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.Do males and females have athe same distribution of degrees by grade?(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:Ho: Ha:Note: You can either use the Excel Chi-related functions or do the calculations manually.Data input tables - graduate degrees by gender and grade levelOBSERVEDA BCDEFTotalDo manual calculations per cell here (if desired)M GradA BCDEFFem GradM GradMale UndFem GradFemale UndMale UndFemale UndSum =EXPECTEDM GradFor this exercise - ignore the requirement for a correctionFem Gradfor expected values less than 5.Male UndFemale UndInterpretation:What is the value of the chi square statistic: What is the p-value associated with this value: Is the p-value <0.05?Do you reject or not reject the null hypothesis: If you rejected the null, what is the Cramer's V correlation:What does this correlation mean?What does this decision mean for our equal pay question: 4Based on our sample data, can we conclude that males and females are distributed across grades in a similar patternwithin the population?What are the hypothesis statements:Ho: Ha:Do manual calculations per cell here (if desired)A BCDEFA BCDEFOBS COUNT - mMOBS COUNT - fFSum = EXPECTEDWhat is the value of the chi square statistic: What is the p-value associated with this value: Is the p-value <0.05?Do you reject or not reject the null hypothesis: If you rejected the null, what is the Phi correlation:What does this correlation mean?What does this
9. decision mean for our equal pay question: 5. How do you interpret these results in light of our question about equal pay for equal work? Week 5Week 5 Correlation and Regression1. Create a correlation table for the variables in our data set. (Use analysis ToolPak or StatPlus:mac LE function Correlation.)a. Reviewing the data levels from week 1, what variables can be used in a Pearson's Correlation table (which is what Excel produces)?b. Place table here (C8 in Output range box):c.Using r = approximately .28 as the signicant r value (at p = 0.05) for a correlation between 50 values, what variables aresignificantly related to Salary?To compa?d.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?e.Does this help us answer our equal pay for equal work question?2Below 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 of expressing an employee’s salary, we do not want to have both used in the same regression.)Plase interpret the findings.Ho: The regression equation is not significant.Ha: The regression equation is significant.Ho: The regression coefficient for each variable is not significant Note: technically we have one for each input variable.Ha: The regression coefficient for each variable is significant Listing it this way to save space.SalSUMMARY OUTPUTRegression StatisticsMultiple R0.9915590747R Square0.9831893985Adjusted R Square0.9808437332Standard Error2.6575925726Observations50ANOVAdfSSMSFSignificanc e FRegression617762.29967387432960.383278979419.151611129 41.8121523852609E- 36Residual43303.70032612577.062798282Total4918066Coeffic ientsStandard Errort StatP-valueLower 95%Upper 95%Lower 95.0%Upper 95.0%Intercept-1.74962121233.6183676583-
10. 0.48353881570.6311664899-9.04675504275.547512618- 9.04675504275.547512618Midpoint1.21670105050.0319023509 38.13828811638.66416336978111E- 351.15236382831.28103827271.15236382831.2810382727Age- 0.00462801020.065197212-0.07098478760.9437389875- 0.13611071910.1268546987- 0.13611071910.1268546987Performace Rating- 0.05659644050.0344950678-1.64071109710.1081531819- 0.12616237470.0129694936- 0.12616237470.0129694936Service- 0.04250035730.0843369821-0.50393500330.6168793519- 0.21258209120.1275813765- 0.21258209120.1275813765Gender2.4203372120.86084431762. 81158528040.00739661880.6842791924.1563952320.68427919 24.156395232Degree0.27553341430.79980230480.34450190090 .732148119-1.33742165471.8884884833- 1.33742165471.8884884833Note: since Gender and Degree are expressed as 0 and 1, they are considered dummy variables and can be used in a multiple regression equation.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?Do you reject or not reject the null hypothesis: What does this decision mean for our equal pay question: For each of the coefficients:InterceptMidpointAgePerf. Rat.ServiceGenderDegreeWhat 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: 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?How do we know? 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.Regression hypothesesHo:Ha:Coefficient hypotheses
11. (one to stand for all the separate variables)Ho:Ha:Put C94 in output range boxInterpretation: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?Do you reject or not reject the null hypothesis: What does this decision mean for our equal pay question: For each of the coefficients: InterceptMidpointAgePerf. Rat.ServiceGenderDegreeWhat 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: What are the coefficients for the significant variables?Using only the significant variables, what is the equation?Compa = Is gender a significant factor in compa:If so, who gets paid more with all other things being equal?How do we know? 4Based 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?If so, which gender gets paid more? How do we know?Which is the best variable to use in analyzing pay practices - salary or compa? Why?What is most interesting or surprising about the results we got doing the analysis during the last 5 weeks?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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