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Week 3

ANOVA and Paired T-test

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	1.02908333	1.075	1.052042
			0.956	1.000		Variance	0.00668645	0.00652	0.006866
			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	1.06591667	1.065583	1.06575
			1.043	0.956		Variance	0.00610245	0.004213	0.004933
			1.043	1.129
			1.145	1.149		Total
						Count	24	24
						Sum	25.14	25.687
						Average	1.0475	1.070292
						Variance	0.00647035	0.005156


						ANOVA
						Source of Variation	SS	df	MS	F	P-value	F crit
						Sample	0.00225502	1	0.002255	0.383482	0.538939	4.061706	(This is the row variable or gender.)
						Columns	0.00623352	1	0.006234	1.060054	0.30883	4.061706	(This is the column variable or Degree.)
						Interaction	0.00641719	1	0.006417	1.091288	0.301892	4.061706
						Within	0.25873675	44	0.00588

						Total	0.27364248	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?

At this point we know the following about male and female salaries.

Male and female overall average salaries are not equal in the population.

Male and female overall average compas are equal in the population, but males are a bit more spread out.

The male and female salary range are almost the same, as is their age and service.

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>

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.

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>

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:

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>

The table and analysis below demonstrate a 2-way ANOVA with replication. Please interpret the results.

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

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

Total

1.052

1.087

Male

Female

1.096

1.050

Count

1.025

1.161

Sum

12.349

12.9

25.249

1.000

1.096

Average

1.02908333

1.075

1.052042

0.956

1.000

Variance

0.00668645

0.00652

0.006866

1.000

1.041

1.043

Female

1.043

1.119

Count

1.210

1.043

Sum

12.791

12.787

25.578

1.187

1.000

Average

1.06591667

1.065583

1.06575

1.043

0.956

Variance

0.00610245

0.004213

0.004933

1.043

1.129

1.145

1.149

Total

Count

Sum

25.14

25.687

Average

1.0475

1.070292

Variance

0.00647035

0.005156

ANOVA

Source of Variation

P-value

F crit

Sample

0.00225502

0.002255

0.383482

0.538939

4.061706

(This is the row variable or gender.)

Columns

0.00623352

0.006234

1.060054

0.30883

4.061706

(This is the column variable or Degree.)

Interaction

0.00641719

0.006417

1.091288

0.301892

4.061706

Within

0.25873675

0.00588

Total

0.27364248

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>

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:

Meaning of effect size measure:

Interpretation:

<2 points>

Using the results up thru this week, what are your conclusions about gender equal pay for equal work at this point?

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At this point we know the following about male and female salaries Male and female overall average salaries are not equal in the population.