Week 3 ANOVA and Paired T-test

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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: Average performace ratings are the same for all grades 90 80 100 90 85 70
Alt. Hypothesis: Average performace ratings are not same for all grades 80 75 100 65 100 100
Place B17 in Outcome range box. 100 80 90 75 95 95
Anova: Single Factor 90 70 80 90 55 95
80 95 80 95 90 95
SUMMARY 85 80 95 95
Groups Count Sum Average Variance 65 90 90
90 14 1175 83.9285714286 162.2252747253 70 75
80 6 490 81.6666666667 86.6666666667 95 95
100 4 350 87.5 91.6666666667 60 90
90 4 325 81.25 189.5833333333 90 95
85 11 960 87.2727272727 166.8181818182 75 80
70 5 480 96 5 95
90
100
ANOVA
Source of Variation SS df MS F P-value F crit
Between Groups 789.4426406926 5 157.8885281385 1.1824073728 0.33588804 2.4625482277
Within Groups 5074.1937229437 38 133.5314137617
Total 5863.6363636364 43
Interpretation:
What is the p-value: 0.33588804
Is P-value < 0.05? No
Do we REJ or Not reject the null? Not reject
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: We are not rejecting the null hypothesis in conclusion that there is no significant difference in average performance ratings between grades
<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: Average salaries are the same for all grades If desired, place salaries per grade in these columns
Alt. Hypothesis: Average salaries are not same for all grades A B C D E F
22.8 25.9 42.3 49.6 66.1 78.3
23.3 35.2 40.6 43.7 55.3 78
Place B55 in Outcome range box. 23.6 33.5 37.4 48.9 60.8 76
Anova: Single Factor 21.7 36 42.3 49 57 75.2
21.8 27.5 42.8 57.9 63.6 80.9
SUMMARY 23 28.6 63 75.4
Groups Count Sum Average Variance 25.3 34.8 60.7
A 15 352.4 23.4933333333 1.3378095238 25.8 62.2
B 7 221.5 31.6428571429 17.4095238095 23.3 62.2
C 5 205.4 41.08 4.927 24.2 70.1
D 5 249.1 49.82 26.077 22.4 61.7
E 12 744.1 62.0083333333 14.5026515152 23.6 61.4
F 6 463.8 77.3 4.832 24.3
24.3
23
ANOVA
Source of Variation SS df MS F P-value F crit
Between Groups 18107.3245571429 5 3621.4649114286 369.8016862111 9.33021433190442E-35 2.4270401198
Within Groups 430.8916428571 44 9.7929918831
Total 18538.2162 49
What is the p-value: 9.33021433190442E-35
Is P-value < 0.05? Yes
Do you reject or not reject the null hypothesis: Reject
If the null hypothesis was rejected, what is the effect size value (eta squared): 0.9767565747
Meaning of effect size measure: There is a large effect size
Interpretation: We are rejecting the null hypothesis in conclusion that there is a significant difference in average salaries between grades
<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 1.0290833333 1.075 1.0520416667
0.956 1.000 Variance 0.006686447 0.0065198182 0.0068660417
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 1.0659166667 1.0655833333 1.06575
1.043 0.956 Variance 0.006102447 0.0042128106 0.004933413
1.043 1.129
1.145 1.149 Total
Count 24 24
Sum 25.14 25.687
Average 1.0475 1.0702916667
Variance 0.0064703478 0.0051561286
ANOVA
Source of Variation SS df MS F P-value F crit
Sample 0.0022550208 1 0.0022550208 0.3834821171 0.5389389507 4.0617064601 (This is the row variable or gender.)
Columns 0.0062335208 1 0.0062335208 1.0600539609 0.3088295633 4.0617064601 (This is the column variable or Degree.)
Interaction 0.0064171875 1 0.0064171875 1.0912877664 0.3018915062 4.0617064601
Within 0.25873675 44 0.0058803807
Total 0.2736424792 47
Interpretation:
For Ho: Average compas by gender are equal Ha: Average compas by gender are not equal
What is the p-value: 0.5389389507
Is P-value < 0.05? No
Do you reject or not reject the null hypothesis: Do not reject
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: 0.3088295633
Is P-value < 0.05? No
Do you reject or not reject the null hypothesis: Do not reject
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: 0.3018915062
Is P-value < 0.05? No
Do you reject or not reject the null hypothesis: Do not reject
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: There is no significant difference in compas between genders and degree.
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? 66.1 57
25.9 31
35.2 31
Null Hypothesis: Average salary is not significantly higher than average midpoint 55.3 57
Alt. Hypothesis: Average salary is significantly higher than average midpoint 49.6 48
78.3 67
Statistical test to use: T-test for two sample mean 42.3 40
22.8 23
t-Test: Two-Sample Assuming Unequal Variances 78 67
23.3 23
Salary Midpoint 23.6 23
Mean 44.726 41.76 60.8 57
Variance 378.3309428571 263.4514285714 40.6 40
Observations 50 50 21.7 23
Hypothesized Mean Difference 0 21.8 23
df 95 37.4 40
t Stat 0.8278702134 57 57
P(T<=t) one-tail 0.2049094457 33.5 31
t Critical one-tail 1.6610518173 23 23
P(T<=t) two-tail 0.4098188914 36 31
t Critical two-tail 1.9852510035 76 67
43.7 48
25.3 23
48.9 48
25.8 23
23.3 23
What is the p-value: 2.05E-01 42.3 40
Is P-value < 0.05? No 75.2 67
What else needs to be checked on a 1-tail in order to reject the null? Do not reject 80.9 67
Do we REJ or Not reject the null? 49 48
If the null hypothesis was rejected, what is the effect size value: NA 24.2 23
Meaning of effect size measure: NA 27.5 31
Interpretation: Average salary is not significantly higher than average midpoint 63.6 57
28.6 31
22.4 23
<2 points> 5.   Using the results up thru this week, what are your conclusions about gender equal pay for equal work at this point? 23.6 23
There is sufficient evidence in this week that there is a gender bias. All results indicated no significant difference 24.3 23
between the pay for different genders. 63 57
34.8 31
24.3 23
42.8 40
23 23
75.4 67
60.7 57
57.9 48
62.2 57
62.2 57
70.1 57
61.7 57
61.4 57

Data

ID Salary Compa Midpoint Age Performance Rating Service Gender Raise Degree Gender1 Gr
1 66.1 1.159 57 34 85 8 0 5.7 0 M E
2 25.9 0.834 31 52 80 7 0 3.9 0 M B
3 35.2 1.135 31 30 75 5 1 3.6 1 F B
4 55.3 0.971 57 42 100 16 0 5.5 1 M E
5 49.6 1.033 48 36 90 16 0 5.7 1 M D
6 78.3 1.168 67 36 70 12 0 4.5 1 M F
7 42.3 1.058 40 32 100 8 1 5.7 1 F C
8 22.8 0.990 23 32 90 9 1 5.8 1 F A
9 78 1.164 67 49 100 10 0 4 1 M F
10 23.3 1.014 23 30 80 7 1 4.7 1 F A
11 23.6 1.025 23 41 100 19 1 4.8 1 F A
12 60.8 1.067 57 52 95 22 0 4.5 0 M E
13 40.6 1.014 40 30 100 2 1 4.7 0 F C
14 21.7 0.943 23 32 90 12 1 6 1 F A
15 21.8 0.949 23 32 80 8 1 4.9 1 F A
16 37.4 0.934 40 44 90 4 0 5.7 0 M C
17 57 1.000 57 27 55 3 1 3 1 F E
18 33.5 1.081 31 31 80 11 1 5.6 0 F B
19 23 1.000 23 32 85 1 0 4.6 1 M A
20 36 1.162 31 44 70 16 1 4.8 0 F B
21 76 1.135 67 43 95 13 0 6.3 1 M F
22 43.7 0.911 48 48 65 6 1 3.8 1 F D
23 25.3 1.098 23 36 65 6 1 3.3 0 F A
24 48.9 1.019 48 30 75 9 1 3.8 0 F D
25 25.8 1.122 23 41 70 4 0 4 0 M A
26 23.3 1.013 23 22 95 2 1 6.2 0 F A
27 42.3 1.057 40 35 80 7 0 3.9 1 M C
28 75.2 1.122 67 44 95 9 1 4.4 0 F F
29 80.9 1.208 67 52 95 5 0 5.4 0 M F
30 49 1.020 48 45 90 18 0 4.3 0 M D
31 24.2 1.054 23 29 60 4 1 3.9 1 F A
32 27.5 0.886 31 25 95 4 0 5.6 0 M B
33 63.6 1.115 57 35 90 9 0 5.5 1 M E
34 28.6 0.922 31 26 80 2 0 4.9 1 M B
35 22.4 0.976 23 23 90 4 1 5.3 0 F A
36 23.6 1.026 23 27 75 3 1 4.3 0 F A
37 24.3 1.057 23 22 95 2 1 6.2 0 F A
38 63 1.105 57 45 95 11 0 4.5 0 M E
39 34.8 1.123 31 27 90 6 1 5.5 0 F B
40 24.3 1.057 23 24 90 2 0 6.3 0 M A
41 42.8 1.071 40 25 80 5 0 4.3 0 M C
42 23 0.998 23 32 100 8 1 5.7 1 F A
43 75.4 1.125 67 42 95 20 1 5.5 0 F F
44 60.7 1.065 57 45 90 16 0 5.2 1 M E
45 57.9 1.206 48 36 95 8 1 5.2 1 F D
46 62.2 1.091 57 39 75 20 0 3.9 1 M E
47 62.2 1.091 57 37 95 5 0 5.5 1 M E
48 70.1 1.230 57 34 90 11 1 5.3 1 F E
49 61.7 1.083 57 41 95 21 0 6.6 0 M E
50 61.4 1.077 57 38 80 12 0 4.6 0 M E

Sheet3

ID Salary Compa Midpoint Age Performance Rating Service Gender Raise Degree Gender1 Gr
8 0.990 23 32 90 9 1 5.8 1 F A
10 1.014 23 30 80 7 1 4.7 1 F A
11 1.025 23 41 100 19 1 4.8 1 F A
14 0.943 23 32 90 12 1 6 1 F A
15 0.949 23 32 80 8 1 4.9 1 F A
19 1.000 23 32 85 1 0 4.6 1 M A
23 1.098 23 36 65 6 1 3.3 0 F A
25 1.122 23 41 70 4 0 4 0 M A
26 1.013 23 22 95 2 1 6.2 0 F A
31 1.054 23 29 60 4 1 3.9 1 F A
35 0.976 23 23 90 4 1 5.3 0 F A
36 1.026 23 27 75 3 1 4.3 0 F A
37 1.057 23 22 95 2 1 6.2 0 F A
40 1.057 23 24 90 2 0 6.3 0 M A
42 0.998 23 32 100 8 1 5.7 1 F A
2 0.834 31 52 80 7 0 3.9 0 M B
3 1.135 31 30 75 5 1 3.6 1 F B
18 1.081 31 31 80 11 1 5.6 0 F B
20 1.162 31 44 70 16 1 4.8 0 F B
32 0.886 31 25 95 4 0 5.6 0 M B
34 0.922 31 26 80 2 0 4.9 1 M B
39 1.123 31 27 90 6 1 5.5 0 F B
7 1.058 40 32 100 8 1 5.7 1 F C
13 1.014 40 30 100 2 1 4.7 0 F C
16 0.934 40 44 90 4 0 5.7 0 M C
27 1.057 40 35 80 7 0 3.9 1 M C
41 1.071 40 25 80 5 0 4.3 0 M C
5 1.033 48 36 90 16 0 5.7 1 M D
22 0.911 48 48 65 6 1 3.8 1 F D
24 1.019 48 30 75 9 1 3.8 0 F D
30 1.020 48 45 90 18 0 4.3 0 M D
45 1.206 48 36 95 8 1 5.2 1 F D
1 1.159 57 34 85 8 0 5.7 0 M E
4 0.971 57 42 100 16 0 5.5 1 M E
12 1.067 57 52 95 22 0 4.5 0 M E
17 1.000 57 27 55 3 1 3 1 F E
33 1.115 57 35 90 9 0 5.5 1 M E
38 1.105 57 45 95 11 0 4.5 0 M E
44 1.065 57 45 90 16 0 5.2 1 M E
46 1.091 57 39 75 20 0 3.9 1 M E
47 1.091 57 37 95 5 0 5.5 1 M E
48 1.230 57 34 90 11 1 5.3 1 F E
49 1.083 57 41 95 21 0 6.6 0 M E
50 1.077 57 38 80 12 0 4.6 0 M E
6 1.168 67 36 70 12 0 4.5 1 M F
9 1.164 67 49 100 10 0 4 1 M F
21 1.135 67 43 95 13 0 6.3 1 M F
28 1.122 67 44 95 9 1 4.4 0 F F
29 1.208 67 52 95 5 0 5.4 0 M F
43 1.125 67 42 95 20 1 5.5 0 F F