Statics

BUS308Week234Assignment.xlsx

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Data

ID	Salary	Compa-ratio	Midpoint	Age	Performance Rating	Service	Gender	Raise	Degree	Gender1	Grade	Do not manipuilate Data set on this page, copy to another page to make changes
1	58	1.018	57	34	85	8	0	5.7	0	M	E	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)?
2	28	0.902	31	52	80	7	0	3.9	0	M	B	Note: to simplfy the analysis, we will assume that jobs within each grade comprise equal work.
3	33.8	1.089	31	30	75	5	1	3.6	1	F	B
4	64.8	1.137	57	42	100	16	0	5.5	1	M	E	The column labels in the table mean:
5	48.7	1.014	48	36	90	16	0	5.7	1	M	D	ID – Employee sample number	Salary – Salary in thousands
6	75.4	1.126	67	36	70	12	0	4.5	1	M	F	Age – Age in years	Performance Rating - Appraisal rating (employee evaluation score)
7	41.6	1.039	40	32	100	8	1	5.7	1	F	C	Service – Years of service (rounded)	Gender – 0 = male, 1 = female
8	23.6	1.028	23	32	90	9	1	5.8	1	F	A	Midpoint – salary grade midpoint	Raise – percent of last raise
9	73.8	1.102	67	49	100	10	0	4	1	M	F	Grade – job/pay grade	Degree (0= BS\BA 1 = MS)
10	22.5	0.980	23	30	80	7	1	4.7	1	F	A	Gender1 (Male or Female)	Compa-ratio - salary divided by midpoint
11	24.1	1.046	23	41	100	19	1	4.8	1	F	A
12	58.3	1.023	57	52	95	22	0	4.5	0	M	E
13	41.4	1.035	40	30	100	2	1	4.7	0	F	C
14	23.2	1.008	23	32	90	12	1	6	1	F	A
15	22.5	0.978	23	32	80	8	1	4.9	1	F	A
16	44.7	1.117	40	44	90	4	0	5.7	0	M	C
17	63.8	1.120	57	27	55	3	1	3	1	F	E
18	34.9	1.127	31	31	80	11	1	5.6	0	F	B
19	24.9	1.083	23	32	85	1	0	4.6	1	M	A
20	33.4	1.076	31	44	70	16	1	4.8	0	F	B
21	73.5	1.097	67	43	95	13	0	6.3	1	M	F
22	51.4	1.071	48	48	65	6	1	3.8	1	F	D
23	25.1	1.090	23	36	65	6	1	3.3	0	F	A
24	48.6	1.013	48	30	75	9	1	3.8	0	F	D
25	24.4	1.062	23	41	70	4	0	4	0	M	A
26	24.3	1.058	23	22	95	2	1	6.2	0	F	A
27	39.2	0.980	40	35	80	7	0	3.9	1	M	C
28	75.8	1.131	67	44	95	9	1	4.4	0	F	F
29	76.3	1.139	67	52	95	5	0	5.4	0	M	F
30	48.6	1.012	48	45	90	18	0	4.3	0	M	D
31	23.4	1.018	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	58	1.018	57	35	90	9	0	5.5	1	M	E
34	27	0.871	31	26	80	2	0	4.9	1	M	B
35	23	0.998	23	23	90	4	1	5.3	0	F	A
36	23	1.001	23	27	75	3	1	4.3	0	F	A
37	23.6	1.026	23	22	95	2	1	6.2	0	F	A
38	60.8	1.066	57	45	95	11	0	4.5	0	M	E
39	35	1.129	31	27	90	6	1	5.5	0	F	B
40	24.3	1.056	23	24	90	2	0	6.3	0	M	A
41	40.5	1.013	40	25	80	5	0	4.3	0	M	C
42	22.6	0.982	23	32	100	8	1	5.7	1	F	A
43	76	1.134	67	42	95	20	1	5.5	0	F	F
44	63.1	1.107	57	45	90	16	0	5.2	1	M	E
45	52.9	1.103	48	36	95	8	1	5.2	1	F	D
46	59.1	1.036	57	39	75	20	0	3.9	1	M	E
47	62.6	1.099	57	37	95	5	0	5.5	1	M	E
48	67.4	1.183	57	34	90	11	1	5.3	1	F	E
49	58.4	1.025	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

Week 1

Week 1: Descriptive Statistics, including Probability

Salary

Gender1

While the lectures will examine our equal pay question from the compa-ratio viewpoint, our weekly assignments will focus on

33.8

examining the issue using the salary measure.

41.6

23.6

The purpose of this assignmnent is two fold:

22.5

1. Demonstrate mastery with Excel tools.

24.1

2. Develop descriptive statistics to help examine the question.

41.4

3. Interpret descriptive outcomes

23.2

22.5

The first issue in examining salary data to determine if we - as a company - are paying males and females equally for doing equal work is to develop some

63.8

descriptive statistics to give us something to make a preliminary decision on whether we have an issue or not.

34.9

33.4

Descriptive Statistics: Develop basic descriptive statistics for Salary

51.4

The first step in analyzing data sets is to find some summary descriptive statistics for key variables.

25.1

Suggestion: Copy the gender1 and salary columns from the Data tab to columns T and U at the right.

48.6

Then use Data Sort (by gender1) to get all the male and female salary values grouped together.

24.3

75.8

Use the Descriptive Statistics function in the Data Analysis tab

Place Excel outcome in Cell K19

23.4

to develop the descriptive statistics summary for the overall

Column1

group's overall salary. (Place K19 in output range.)

Highlight the mean, sample standard deviation, and range.

Mean

44.364

23.6

Standard Error

2.6490133088

Median

41.5

22.6

Mode

23.6

Using Fx (or formula) functions find the following (be sure to show the formula

Standard Deviation

18.7313527411

52.9

and not just the value in each cell) asked for salary statistics for each gender:

Sample Variance

350.8635755102

67.4

Male

Female

Male

Female

Kurtosis

-1.3765917226

Mean:

51.252

37.476

24.300

76.300

=AVERAGE(T27:T51)

=AVERAGE(T2:T26)

Skewness

0.2827691781

Sample Standard Deviation:

17.4001465511

17.7408727707

22.500

=STDEV.S(T27:T51)

=STDEV.S(T2:T26)

Range

53.8

64.8

Range:

52.000

53.500

=H28-G28

=H29-G29

Minimum

22.5

48.7

Maximum

76.3

75.4

Sum

2218.2

73.8

Count

58.3

44.7

Develop a 5-number summary for the overall, male, and female SALARY variable.

24.9

For full credit, use the excel formulas in each cell rather than simply the numerical answer.

73.5

Overall

Males

Females

Overall

Males

Females

24.4

Max

76.300

76.000

=QUARTILE(T$2:T$51,4)

=QUARTILE($T$27:$T$51,4)

=QUARTILE($T$2:$T$26,4)

39.2

3rd Q

60.375

62.600

48.600

=QUARTILE(T$2:T$51,3)

=QUARTILE($T$27:$T$51,3)

=QUARTILE($T$2:$T$26,3)

76.3

Midpoint

41.500

58.000

33.400

=QUARTILE(T$2:T$51,2)

=QUARTILE($T$27:$T$51,2)

=QUARTILE($T$2:$T$26,2)

48.6

1st Q

24.525

39.200

23.400

=QUARTILE(T$2:T$51,1)

=QUARTILE($T$27:$T$51,1)

=QUARTILE($T$2:$T$26,1)

27.5

Min

22.500

24.300

22.500

=QUARTILE(T$2:T$51,0)

=QUARTILE($T$27:$T$51,0)

=QUARTILE($T$2:$T$26,0)

Location Measures: comparing Male and Female midpoints to the overall Salary data range.

60.8

For full credit, show the excel formulas in each cell rather than simply the numerical answer.

24.3

Using the entire Salary range and the M and F midpoints found in Q2

Male

Female

Male

Female

40.5

a. What would each midpoint's percentile rank be in the overall range?

0.645

0.42

Use Excel's =PERCENTRANK.EXC function

=PERCENTRANK.EXC(E38:E42,F40)

=PERCENTRANK.EXC(E38:E42,G40)

63.1

b. What is the normal curve z value for each midpoint within overall range?

0.7280

-0.5853

Use Excel's =STANDARDIZE function

=STANDARDIZE(F40,L21,L25)

=STANDARDIZE(G40,L21,L25)

59.1

62.6

Probability Measures: comparing Male and Female midpoints to the overall Salary data range

58.4

For full credit, show the excel formulas in each cell rather than simply the numerical answer.

61.4

Using the entire Salary range and the M and F midpoints found in Q2, find

Male

Female

Male

Female

a. The Empirical Probability of equaling or exceeding (=>) that value for

0.36

0.64

Show the calculation formula = value/50 or =countif(range,">="&cell)/50

=COUNTIF(T2:T51,">="&F40)/50

=COUNTIF(T2:T51,">="&G40)/50

b. The Normal curve Prob of => that value for each group

0.233313734430809

0.720836669337808

Use "=1-NORM.S.DIST" function

=1-NORM.S.DIST(I48, TRUE)

=1-NORM.S.DIST(J48, TRUE)

Note: be sure to use the ENTIRE salary range for part a when finding the probability.

Conclusions: What do you make of these results?

Be sure to include findings from this week's lectures as well.

In comparing the overall, male, and female outcomes, what relationship(s) see, to exist between the data sets?

Your findings:

Although with a lower mean, females end up making more in the long run, with a higher empiical probability as well.

The lecture's related findings: From the lecture, the found the same, females tend to have a higher average of pay than males.

Overall conclusion: Males tend to start off with a higher salary, but females end up with a higher salary in the peak of their careers.

What does this suggest about our equal pay for equal work question? It suggests, that equal pay is given for both genders.

Looking at the mean, standard deviation, and the range the numbers are close, we can say that the pay is pretty much equal.

Week 2

Week 2: Identifying Significant Differences - part 1
To Ensure full credit for each question, you need to show how you got your results. This involves either showing where the data you used is located
or showing the excel formula in each cell.			Be sure to copy the appropriate data columns from the data tab to the right for your use this week.
As with our examination of compa-ratio in the lecture, the first question we have about salary between the genders involves equality - are they the same or different?
What we do, depends upon our findings.
1	As with the compa-ratio lecture example, we want to examine salary variation within the groups - are they equal?				Use Cell K10 for the Excel test outcome location.
	a	What is the data input ranged used for this question:
	b	Which is needed for this question: a one- or two-tail hypothesis statement and test ?
		Answer:
		Why:
	c. Step 1:	Ho:
		Ha:
	Step 2:	Significance (Alpha):
	Step 3:	Test Statistic and test:
		Why this test?
	Step 4:	Decision rule:
	Step 5:	Conduct the test - place test function in cell k10
	Step 6:	Conclusion and Interpretation
			What is the p-value:
			What is your decision: REJ or NOT reject the null?
			Why?
	What is your conclusion about the variance in the population for male and female salaries?
2	Once we know about variance quality, we can move on to means: Are male and female average salaries equal?				Use Cell K35 for the Excel test outcome location.
	(Regardless of the outcome of the above F-test, assume equal variances for this test.)
	a	What is the data input ranged used for this question:
	b	Does this question need a one or two-tail hypothesis statement and test?
		Why:
	c. Step 1:	Ho:
		Ha:
	Step 2:	Significance (Alpha):
	Step 3:	Test Statistic and test:
		Why this test?
	Step 4:	Decision rule:
	Step 5:	Conduct the test - place test function in cell K35
	Step 6:	Conclusion and Interpretation
			What is the p-value:
			What is your decision: REJ or NOT reject the null?
			Why?
What is your conclusion about the means in the population for male and female salaries?
3	Education is often a factor in pay differences.
	Do employees with an advanced degree (degree = 1) have higher average salaries?			Use Cell K60 for the Excel test outcome location.
	Note: assume equal variance for the salaries in each degree for this question.
	a	What is the data input ranged used for this question:
	b	Does this question need a one or two-tail hypothesis statement and test?
		Why:
	c. Step 1:	Ho:
		Ha:
	Step 2:	Significance (Alpha):
	Step 3:	Test Statistic and test:
		Why this test?
	Step 4:	Decision rule:
	Step 5:	Conduct the test - place test function in cell K60
	Step 6:	Conclusion and Interpretation
			What is the p-value:
	Is the t value in the t-distribution tail indicated by the arrow in the Ha claim?
What is your decision: REJ or NOT reject the null?
			Why?
What is your conclusion about the impact of education on average salaries?
4	Considering both the compa-ratio information from the lectures and your salary information, what conclusions can you reach about equal pay for equal work?
	Your findings:
	The lecture's related findings:
	Overall conclusion:
	Why - what statistical results support this conclusion?

Week 3

Week 3: Identifying Significant Differences - part 2

Data Input Table:

Salary Range Groups

Group name:

To Ensure full credit for each question, you need to show how you got your results. This involves either showing where the data you used is located

List salaries within each grade

or showing the excel formula in each cell.

Be sure to copy the appropriate data columns from the data tab to the right for your use this week.

A good pay program will have different average salaries by grade. Is this the case for our company?

What is the data input ranged used for this question:

Use Cell K08 for the Excel test outcome location.

Note: assume equal variances for each grade, even though this may not be accurate, for purposes of this question.

b. Step 1:

Ho:

Ha:

Step 2:

Significance (Alpha):

Step 3:

Test Statistic and test:

Why this test?

Step 4:

Decision rule:

Step 5:

Conduct the test - place test function in cell K08

Step 6:

Conclusion and Interpretation

What is the p-value:

What is your decision: REJ or NOT reject the null?

Why?

What is your conclusion about the means in the population for grade salaries?

If the null hypothesis in question 1 was rejected, which pairs of means differ?

(Use the values from the ANOVA table to complete the follow table.)

Groups Compared

Mean Diff.

T value used

+/- Term

Low

High

Difference Significant?

Why?

A-B

A-C

A-D

A-E

A-F

B-C

B-D

B-E

C-D

C-E

C-F

D-E

D-F

E-F

One issue in salary is the grade an employee is in - higher grades have higher salaries.

This suggests that one question to ask is if males and females are distributed in a similar pattern across the salary grades?

What is the data input ranged used for this question:

Use Cell K54 for the Excel test outcome location.

b. Step 1:

Ho:

Ha:

Step 2:

Significance (Alpha):

Step 3:

Test Statistic and test:

Place the actual distribution in the table below.

Why this test?

Sum

Step 4:

Decision rule:

Male

Step 5:

Conduct the test - place test function in cell K54

Female

Sum:

Step 6:

Conclusion and Interpretation

Place the expected distribution in the table below.

What is the p-value:

What is your decision: REJ or NOT reject the null?

Male

Why?

Female

What is your conclusion about the means in the population for male and female salaries?

Sum:

What implications do this week's analysis have for our equal pay question?

Your findings:

The lecture's related findings:

Overall conclusion:

Why - what statistical results support this conclusion?

Week 4

Week 4: Identifying relationships - correlations and regression
To Ensure full credit for each question, you need to show how you got your results. This involves either showing where the data you used is located
or showing the excel formula in each cell.					Be sure to copy the appropriate data columns from the data tab to the right for your use this week.
1	What is the correlation between and among the interval/ratio level variables with salary? (Do not include compa-ratio in this question.)
	a. Create the correlation table.									Use Cell K08 for the Excel test outcome location.
	i.					What is the data input ranged used for this question:
	ii.	Create a correlation table in cell K08.
	b. Technically, we should perform a hypothesis testing on each correlation to determine
	if it is significant or not. However, we can be faithful to the process and save some
	time by finding the minimum correlation that would result in a two tail rejection of the null.
	We can then compare each correlation to this value, and those exceeding it (in either a
	positive or negative direction) can be considered statistically significant.
	i. What is the t-value we would use to cut off the two tails?						T =
	ii. What is the associated correlation value related to this t-value? r =
	c. What variable(s) is(are) significantly correlated to salary?
	d. Are there any surprises - correlations you though would be significant and are not, or non significant correlations you thought would be?
	e. Why does or does not this information help answer our equal pay question?
2	Perform a regression analysis using salary as the dependent variable and all of the variables used in Q1. Add the
	two dummy variables - gender and education - to your list of independent variables. Show the result, and interpret your findings by answering the following questions.
	Suggestion: Add the dummy variables values to the right of the last data columns used for Q1.
	What is the multiple regression equation predicting/explaining salary using all of our possible variables except compa-ratio?
	a.	What is the data input ranged used for this question:
	b.	Step 1: State the appropriate hypothesis statements:								Use Cell M34 for the Excel test outcome location.
		Ho:
		Ha:
		Step 2:	Significance (Alpha):
		Step 3:	Test Statistic and test:
			Why this test?
		Step 4:	Decision rule:
		Step 5:	Conduct the test - place test function in cell M34
		Step 6:	Conclusion and Interpretation
				What is the p-value:
				What is your decision: REJ or NOT reject the null?
				Why?
What is your conclusion about the factors influencing the population salary values?
	c.	If we rejected the null hypothesis, we need to test the significance of each of the variable coefficients.
		Step 1: State the appropriate coefficient hypothesis statements:						(Write a single pair, we will use it for each variable separately.)
		Ho:
		Ha:
		Step 2:	Significance (Alpha):
		Step 3:	Test Statistic and test:
			Why this test?
		Step 4:	Decision rule:
		Step 5:	Conduct the test
			Note, in this case the test has been performed and is part of the Regression output above.
		Step 6:	Conclusion and Interpretation
			Place the t and p-values in the following table
			Identify your decision on rejecting the null for each variable. If you reject the null, place the coefficient in the table.
			Midpoint	Age	Perf. Rat.	Seniority	Raise	Gender	Degree
		t-value:
		P-value:
		Rejection Decision:
If Null is rejected, what is the variable's coefficient value?
		Using the intercept coefficient and only the significant variables, what is the equation?
		Salary =
	d.	Is gender a significant factor in salary?
	e.	Regardless of statistical significance, who gets paid more with all other things being equal?
	f.	How do we know?
3	After considering the compa-ratio based results in the lectures and your salary based results, what else would you like to know
	before answering our question on equal pay? Why?
4	Between the lecture results and your results, what is your answer to the question
	of equal pay for equal work for males and females? Why?
	Your findings:
	The lecture's related findings:
	Overall conclusion:
5	What does regression analysis show us about analyzing complex measures?