BUS 308 Week 3 Assignment

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Week 3

Week 3 Paired T-test and ANOVA
For this week's work, again be sure to state the null and alternate hypotheses and use alpha = 0.05 for our decision
value in the reject or do not reject decision on the null hypothesis.
1 Many companies consider the grade midpoint to be the "market rate" - the salary needed to hire a new employee. Salary Midpoint Diff
Does the company, on average, pay its existing employees at or above the market rate?
Use the data columns at the right to set up the paired data set for the analysis.
Null Hypothesis:
Alt. Hypothesis:
Statistical test to use:
What is the p-value:
Is P-value < 0.05 (one tail test) or 0.25 (two tail test)?
What else needs to be checked on a 1-tail test 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:
If calculated, what is the meaning of effect size measure:
Interpretation of test results:
Let's look at some other factors that might influence pay - education(degree) and performance ratings.
2 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.) Here are the data values sorted by grade level.
The rating values sorted by grade have been placed in columns I - N for you. A B C D E F
Null Hypothesis: Ho: means equal for all grades 90 80 100 90 85 70
Alt. Hypothesis: Ha: at least one mean is unequal 80 75 100 65 100 100
Place B17 in Outcome range box. 100 80 90 75 95 95
90 70 80 90 55 95
80 95 80 95 90 95
85 80 95 95
65 90 90
70 75
95 95
60 90
90 95
75 80
95
90
100
Interpretation of test results:
What is the p-value: 0.57 If the ANVOA was done correctly, this is the p-value shown.
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:
3 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?
Use the input table to the right to list salaries under each grade level.
(Assume equal variance, and use the analysis toolpak function ANOVA.)
Null Hypothesis: If desired, place salaries per grade in these columns
Alt. Hypothesis: A B C D E F
Place B51 in Outcome range box.
Note: Sometimes we see a p-value in the format of 3.4E-5; this means move the decimal point left 5 places. In this example, the p-value is 0.000034
What is the p-value:
Is P-value < 0.05?
Do we REJ or Not reject the null?
If the null hypothesis was rejected, calculate the effect size value (eta squared):
If calculated, what is the meaning of effect size measure:
Interpretation:
4 The table and analysis below demonstrate a 2-way ANOVA with replication. Please interpret the results.
Note: These values are not the same as the data the assignment uses. The purpose of this question is to analyze the result of a 2-way ANOVA test rather than directly answer our equal pay question.
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 three decisions mean in terms of our equal pay question:
Place data values in these columns
5.   Using the results up thru this week, what are your conclusions about gender equal pay for equal work at this point? Dif