Managerial Statistics

the questions are on one tab and the data sheet is on the other.

Data

IDSalaryCompaMidpointAgePerformance RatingServiceGenderRaiseDegreeGender1Gr
164.41.130573485805.70METhe 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)?
227.40.884315280703.90MBNote: to simplfy the analysis, we will assume that jobs within each grade comprise equal work.
335.61.148313075513.61FB
462.31.09357421001605.51METhe column labels in the table mean:
548.71.0144836901605.71MDID – Employee sample numberSalary – Salary in thousands
6751.1206736701204.51MFAge – Age in yearsPerformance Rating – Appraisal rating (employee evaluation score)
741.81.0464032100815.71FCService – Years of service (rounded)Gender – 0 = male, 1 = female
823.71.029233290915.81FAMidpoint – salary grade midpointRaise – percent of last raise
976.81.147674910010041MFGrade – job/pay gradeDegree (0= BS\BA 1 = MS)
10241.044233080714.71FAGender1 (Male or Female)Compa – salary divided by midpoint
1123.91.04123411001914.81FA
1262.51.0965752952204.50ME
1342.71.0674030100214.70FC
1423.41.01623329012161FA
1523.31.012233280814.91FA
1648.71.217404490405.70MC
1765.11.1425727553131FE
1834.61.1163131801115.60FB
1924.51.065233285104.61MA
2034.91.1253144701614.80FB
2176.51.1426743951306.31MF
2257.81.204484865613.81FD
2322.70.987233665613.30FA
2456.51.177483075913.80FD
2524.51.0642341704040MA
2623.21.010232295216.20FA
2746.81.171403580703.91MC
2876.61.144674495914.40FF
2975.91.133675295505.40MF
3047.40.9874845901804.30MD
3125.31.101232960413.91FA
3227.20.878312595405.60MB
33661.158573590905.51ME
3428.10.907312680204.91MB
3522.50.980232390415.30FA
3622.70.985232775314.30FA
3723.41.017232295216.20FA
3858.51.0265745951104.50ME
3935.51.144312790615.50FB
4024.81.078232490206.30MA
4145.81.144402580504.30MC
4222.20.9652332100815.71FA
4377.41.1556742952015.50FF
4458.81.0325745901605.21ME
4551.21.066483695815.21FD
4661.31.0765739752003.91ME
4764.31.128573795505.51ME
4867.61.1865734901115.31FE
4961.31.0755741952106.60ME
5066.11.1595738801204.60ME

Sheet1

SalCompaGMidAgeEESSRGRaiseDegSUMMARY OUTPUTSUMMARY OUTPUT
241.0451233290915.81
24.21.0531233080714.71Regression StatisticsRegression Statistics
23.41.018123411001914.81Multiple R0.7050179484Multiple R0.9931286935
23.41.017123329012161R Square0.4970503076R Square0.9863046018
22.60.9831233280814.91Adjusted R Square0.4132253589Adjusted R Square0.9840220355
22.90.9951233665613.30Standard Error0.0561252686Standard Error2.4352822665
23.11.0031232295216.20Observations50Observations50
23.31.0111232960413.91
22.70.9851232390415.30ANOVAANOVA
23.51.0231232775314.30dfSSMSFSignificance FdfSSMSFSignificance F
231.0021232295216.20Regression70.13075007750.01867858255.92962256620.0000782906Regression717938.4246118632562.632087409432.10336381775.29906273684337E-37
241.04212332100815.71Residual420.13230192250.0031500458Residual42249.0851881375.9305997175
35.51.1451313075513.61Total490.263052Total4918187.5098
34.71.11913131801115.60
35.51.14613144701614.80CoefficientsStandard Errort StatP-valueLower 95%Upper 95%Lower 95.0%Upper 95.0%CoefficientsStandard Errort StatP-valueLower 95%Upper 95%Lower 95.0%Upper 95.0%
35.21.1361312790615.50Intercept0.94862387720.081716771611.608680311900.78371275571.11353499870.78371275571.1135349987Intercept-4.87145445873.54570071-1.37390458390.1767599037-12.02696818532.2840592678-12.02696818532.2840592678
40.41.0114032100815.71Mid0.00349950270.00064925685.39001333560.00000297670.00218924950.00480975590.00218924950.0048097559Mid1.22841550480.028171330843.60516416291.32019333894083E-361.17156345761.28526755211.17156345761.2852675521
42.71.06814030100214.70Age0.00055277380.00144594460.38229252560.7041721007-0.00236526050.0034708081-0.00236526050.0034708081Age0.03682794250.06273971240.58699571780.5603489282-0.08978592310.1634418081-0.08978592310.1634418081
53.41.1121484865613.81EES-0.00184625530.0010252155-1.80084613710.0789105539-0.00391522390.0002227133-0.00391522390.0002227133EES-0.08215797850.0444842245-1.84690144510.0718147225-0.1719307780.007614821-0.1719307780.007614821
51.51.0721483075913.80SR-0.00041822880.0018278101-0.22881413450.820123898-0.0041068990.0032704414-0.0041068990.0032704414SR-0.07784845290.079308905-0.98158527010.3319249969-0.23790030290.0822033971-0.23790030290.0822033971
49.81.0371483695815.21G0.06466499610.01833966973.52596296240.0010348660.02765404430.1016759480.02765404430.101675948G2.91450831120.79576051133.66254453430.0006935491.30859858364.52041803891.30859858364.5204180389
68.31.19815727553131Raise0.01465495640.01390889761.05363896080.2980722322-0.01341433540.0427242483-0.01341433540.0427242483Raise0.67632948240.60350876891.12066222950.2687988764-0.54160052151.8942594864-0.54160052151.8942594864
65.41.14815734901115.31Deg0.00146759880.01610982490.09109961250.9278465471-0.03104334410.0339785418-0.03104334410.0339785418Deg0.03450444820.69900727420.04936207310.9608647532-1.37614934191.4451582383-1.37614934191.4451582383
78.41.171674495914.40
75.91.13316742952015.50
241.0440233285104.61
23.31.01202341704040
24.11.0490232490206.30
27.50.8870315280703.90t-Test: Two-Sample Assuming Equal Variances
27.10.8750312595405.60
27.70.8950312680204.91Variable 1Variable 2
40.81.0190404490405.70Mean1.066841.04836
43.91.0970403580703.91Variance0.004301640.00648099
411.0250402580504.30Observations2525
48.71.01404836901605.71Pooled Variance0.005391315
49.41.02904845901804.30Hypothesized Mean Difference0
64.41.130573485805.70df48
64.51.132057421001605.51t Stat0.8898352784
58.91.03305752952204.50P(T<=t) one-tail0.188996287
57.91.0160573590905.51t Critical one-tail1.6772241961
591.03505745951104.50P(T<=t) two-tail0.3779925741
63.31.11105745901605.21t Critical two-tail2.0106347576
56.80.99605739752003.91
581.0170573795505.51
62.41.09405741952106.60
63.81.1205738801204.60
791.17906736701204.51
771.1490674910010041
74.81.11606743951306.31
761.1350675295505.40

questions to answer

Score:Week 3ANOVA and Paired T-test
At 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.
<1 point>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.)You can use these columns to place grade Perf Ratings if desired.
ABCDEF
Null 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:
<1 point>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.)
Use the input table to the right to list salaries under each grade level.
Null Hypothesis:If desired, place salaries per grade in these columns
Alt. Hypothesis:ABCDEF
Place 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:
<1 point>3The table and analysis below demonstrate a 2-way ANOVA with replication. Please interpret the results.
BAMAHo: Average compas by gender are equal
Male1.0171.157Ha: Average compas by gender are not equal
0.8700.979Ho: Average compas are equal for each degree
1.0521.134Ha: Average compas are not equal for each degree
1.1751.149Ho: Interaction is not significant
1.0431.043Ha: Interaction is significant
1.0741.134
1.0201.000Perform analysis:
0.9031.122
0.9820.903Anova: Two-Factor With Replication
1.0861.052
1.0751.140SUMMARYBAMATotal
1.0521.087Male
Female1.0961.050Count121224
1.0251.161Sum12.34912.925.249
1.0001.096Average1.02908333331.0751.0520416667
0.9561.000Variance0.0066864470.00651981820.0068660417
1.0001.041
1.0431.043Female
1.0431.119Count121224
1.2101.043Sum12.79112.78725.578
1.1871.000Average1.06591666671.06558333331.06575
1.0430.956Variance0.0061024470.00421281060.004933413
1.0431.129
1.1451.149Total
Count2424
Sum25.1425.687
Average1.04751.0702916667
Variance0.00647034780.0051561286
ANOVA
Source of VariationSSdfMSFP-valueF crit
Sample0.002255020810.00225502080.38348211710.53893895074.0617064601(This is the row variable or gender.)
Columns0.006233520810.00623352081.06005396090.30882956334.0617064601(This is the column variable or Degree.)
Interaction0.006417187510.00641718751.09128776640.30189150624.0617064601
Within0.25873675440.0058803807
Total0.273642479247
Interpretation:
For Ho: Average compas by gender are equalHa: Average compas by gender are not equal
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:
For Ho: Average compas are equal for all degreesHa: Average compas are not equal for all grades
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:
For: Ho: Interaction is not significantHa: Interaction is significant
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:
What do these decisions mean in terms of our equal pay question:
Place data values in these columns
<1 point>4Many companies consider the grade midpoint to be the “market rate” – what is needed to hire a new employee.SalaryMidpoint
Does 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 test.
What is the p-value:
Is P-value < 0.05?
What else needs to be checked on a 1-tail in order to reject the null?
Do we REJ or Not reject the null?
If the null hypothesis was rejected, what is the effect size value:NA
Meaning of effect size measure:NA
Interpretation:
<2 points>5.  Using the results up thru this week, what are your conclusions about gender equal pay for equal work at this point?