# BUS308 Statistics – week 3

BUS308 Statistics – week 3
Paper details:
Complete the problems included in the resources below and submit your work in an Excel document. Be sure to show all of your work and clearly label all calculations. All statistical calculations will use the Employee Salary Data Set and the Week 3 assignment sheet.
Score:    Week 3    ANOVA 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>    1    Last 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.
A    B    C    D    E    F
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>    2    While 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:                            A    B    C    D    E    F
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>    3    The table and analysis below demonstrate a 2-way ANOVA with replication.  Please interpret the results.
BA    MA        Ho: Average compas by gender are equal
Male    1.017    1.157        Ha: Average compas by gender are not equal
0.870    0.979        Ho: Average compas are equal for each degree
1.052    1.134        Ha: Average compas are not equal for each degree
1.175    1.149        Ho: Interaction is not significant
1.043    1.043        Ha: Interaction is significant
1.074    1.134
1.020    1.000        Perform analysis:
0.903    1.122
0.982    0.903        Anova: Two-Factor With Replication
1.086    1.052
1.075    1.140        SUMMARY    BA    MA    Total
1.052    1.087        Male
Female    1.096    1.050        Count    12    12    24
1.025    1.161        Sum    12.349    12.9    25.249
1.000    1.096        Average    1.029083333    1.075    1.052041667
0.956    1.000        Variance    0.006686447    0.006519818    0.006866042
1.000    1.041
1.043    1.043        Female
1.043    1.119        Count    12    12    24
1.210    1.043        Sum    12.791    12.787    25.578
1.187    1.000        Average    1.065916667    1.065583333    1.06575
1.043    0.956        Variance    0.006102447    0.004212811    0.004933413
1.043    1.129
1.145    1.149        Total
Count    24    24
Sum    25.14    25.687
Average    1.0475    1.070291667
Variance    0.006470348    0.005156129
ANOVA
Source of Variation    SS    df    MS    F    P-value    F crit
Sample    0.002255021    1    0.002255021    0.383482117    0.538938951    4.06170646      (This is the row variable or gender.)
Columns    0.006233521    1    0.006233521    1.060053961    0.308829563    4.06170646      (This is the column variable or Degree.)
Interaction    0.006417188    1    0.006417188    1.091287766    0.301891506    4.06170646
Within    0.25873675    44    0.005880381
Total    0.273642479    47
Interpretation:
For Ho: Average compas by gender are equal                    Ha: 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 degrees                      Ha: 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 significant            Ha: 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>    4    Many companies consider the grade midpoint to be the “market rate” – what is needed to hire a new employee.                                            Salary    Midpoint
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?
See comments at the right of the data set.
ID    Salary    Compa    Midpoint    Age    Performance Rating    Service    Gender    Raise    Degree    Gender1    Grade
8    23    1.000    23    32    90    9    1    5.8    0    F    A        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)?
10    22    0.956    23    30    80    7    1    4.7    0    F    A        Note: to simplfy the analysis, we will assume that jobs within each grade comprise equal work.
11    23    1.000    23    41    100    19    1    4.8    0    F    A
14    24    1.043    23    32    90    12    1    6    0    F    A        The column labels in the  table mean:
15    24    1.043    23    32    80    8    1    4.9    0    F    A        ID – Employee sample number
23    23    1.000    23    36    65    6    1    3.3    1    F    A        Age – Age in years
26    24    1.043    23    22    95    2    1    6.2    1    F    A        Service – Years of service (rounded)
31    24    1.043    23    29    60    4    1    3.9    0    F    A        Midpoint – salary grade midpoint
35    24    1.043    23    23    90    4    1    5.3    1    F    A        Grade – job/pay grade
36    23    1.000    23    27    75    3    1    4.3    1    F    A        Gender1 (Male or Female)
37    22    0.956    23    22    95    2    1    6.2    1    F    A
42    24    1.043    23    32    100    8    1    5.7    0    F    A
3    34    1.096    31    30    75    5    1    3.6    0    F    B
18    36    1.161    31    31    80    11    1    5.6    1    F    B
20    34    1.096    31    44    70    16    1    4.8    1    F    B
39    35    1.129    31    27    90    6    1    5.5    1    F    B
7    41    1.025    40    32    100    8    1    5.7    0    F    C
13    42    1.050    40    30    100    2    1    4.7    1    F    C
22    57    1.187    48    48    65    6    1    3.8    0    F    D
24    50    1.041    48    30    75    9    1    3.8    1    F    D
45    55    1.145    48    36    95    8    1    5.2    0    F    D
17    69    1.210    57    27    55    3    1    3    0    F    E
48    65    1.140    57    34    90    11    1    5.3    1    F    E
28    75    1.119    67    44    95    9    1    4.4    1    F    F
43    77    1.149    67    42    95    20    1    5.5    1    F    F
19    24    1.043    23    32    85    1    0    4.6    1    M    A
25    24    1.043    23    41    70    4    0    4    0    M    A
40    25    1.086    23    24    90    2    0    6.3    0    M    A
2    27    0.870    31    52    80    7    0    3.9    0    M    B
32    28    0.903    31    25    95    4    0    5.6    0    M    B
34    28    0.903    31    26    80    2    0    4.9    1    M    B
16    47    1.175    40    44    90    4    0    5.7    0    M    C
27    40    1.000    40    35    80    7    0    3.9    1    M    C
41    43    1.075    40    25    80    5    0    4.3    0    M    C
5    47    0.979    48    36    90    16    0    5.7    1    M    D
30    49    1.020    48    45    90    18    0    4.3    0    M    D
1    58    1.017    57    34    85    8    0    5.7    0    M    E
4    66    1.157    57    42    100    16    0    5.5    1    M    E
12    60    1.052    57    52    95    22    0    4.5    0    M    E
33    64    1.122    57    35    90    9    0    5.5    1    M    E
38    56    0.982    57    45    95    11    0    4.5    0    M    E
44    60    1.052    57    45    90    16    0    5.2    1    M    E
46    65    1.140    57    39    75    20    0    3.9    1    M    E
47    62    1.087    57    37    95    5    0    5.5    1    M    E
49    60    1.052    57    41    95    21    0    6.6    0    M    E
50    66    1.157    57    38    80    12    0    4.6    0    M    E
6    76    1.134    67    36    70    12    0    4.5    1    M    F
9    77    1.149    67    49    100    10    0    4    1    M    F
21    76    1.134    67    43    95    13    0    6.3    1    M    F
29    72    1.074    67    52    95    5    0    5.4    0    M    F

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