BUS 308

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Ashford 4: - Week 3 - Discussion 1

Your initial discussion thread is due on Day 3 (Thursday) and you have until Day 7 (Monday) to respond to your classmates. Your grade will reflect both the quality of your initial post and the depth of your responses. Reference the Discussion Forum Grading Rubric for guidance on how your discussion will be evaluated.

ANOVA

In many ways, comparing multiple sample means is simply an extension of what we covered last week. Just as we had 3 versions of the t-test (1 sample, 2 sample (with and without equal variance), and paired; we have several versions of ANOVA – single factor, factorial (called 2-factor with replication in Excel), and within-subjects (2-factor without replication in Excel). What examples (professional, personal, social) can you provide on when we might use each type? What would be the appropriate hypotheses statements for each example?

Guided Response: Review several of your classmates’ posts. Respond to at least two classmates by commenting on why you agree or disagree with the statistical test that your peers have described as appropriate in this scenario.

Ashford 4: - Week 3 - Discussion 2

Effect Size

Several statistical tests have a way to measure effect size. What is this, and when might you want to use it in looking at results from these tests on job related data?

Ashford 4: - Week 3 - Assignment

Problem Set Week Three 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.

Carefully review the Grading Rubric for the criteria that will be used to evaluate your assignment.

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	Salary – Salary in thousands
23	23	1.000	23	36	65	6	1	3.3	1	F	A	Age – Age in years		Performance Rating – Appraisal rating (Employee evaluation score)
26	24	1.043	23	22	95	2	1	6.2	1	F	A	Service – Years of service (rounded)	Gender: 0 = male, 1 = female
31	24	1.043	23	29	60	4	1	3.9	0	F	A	Midpoint – salary grade midpoint	Raise – percent of last raise
35	24	1.043	23	23	90	4	1	5.3	1	F	A	Grade – job/pay grade	Degree (0= BS\BA 1 = MS)
36	23	1.000	23	27	75	3	1	4.3	1	F	A	Gender1 (Male or Female)	Compa - salary divided by midpoint
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

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?
		was rejected, what is the effect size value (eta squared):
		If the null hypothesis				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? ANOVA.)
		(Assume equal variance, and use the analysis toolpak function
		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

						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
							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
		Columns
		Total					0.27364248	47


		Interpretation:

		If the null hypothesis was rejected, what				What is the p-value:
						Is P-value < 0.05?
						Do you reject or not reject the null hypothesis:
		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:
		s the effect size value (eta squared):
		If the null hypothesis was rejected, what i				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:
		ect size value (eta squared):
		If the null hypothesis was rejected, what is the eff				Meaning of effect size measure:

		What do these decisions mean in terms of our equal pay				n in terms of our equal pay question:


													Place data values in these columns
<1 point>	4			Salary	Midpoint

		Many companies consider the grade midpoint to be the "market rate" - what is needed to hire a new employee.
		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 t?
		equal pay for equal work at this poin