3 Statistics assignment
WEAONEweek_3_data_assignment.xlsx
Sheet1
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 | 1.0290833333 | 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: | |||||||
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? | |||||