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Descriptive Statistics

Data
Executive	Salary	Age	Gender	Education	Promotions	Pay
1	79	49	Female	Bachelors	4	Low
2	76	38	Female	Associates	0	Low
3	83	60	Male	Masters	4	High
4	92	63	Male	Masters	6	High
5	80	55	Female	Bachelors	3	Low
6	81	54	Female	Masters	6	High
7	77	42	Male	Masters	4	Low
8	87	59	Male	Masters	6	High
9	69	42	Male	Bachelors	1	Low
10	70	36	Female	Bachelors	1	Low
11	73	48	Male	Associates	2	Low
12	80	53	Male	Associates	2	Low
13	81	46	Female	Associates	2	High
14	87	57	Male	Masters	4	High
15	78	49	Female	Associates	1	Low
16	78	40	Female	Masters	2	Low
17	77	55	Male	Masters	4	Low
18	81	48	Male	Bachelors	5	High
19	75	42	Female	Associates	1	Low
20	83	52	Male	Bachelors	3	High
21	74	41	Female	Bachelors	2	Low
22	85	62	Male	Masters	3	High
23	86	53	Male	Bachelors	5	High
24	73	36	Female	Associates	0	Low
25	70	44	Male	Associates	2	Low
26	81	50	Female	Bachelors	3	High
27	77	50	Male	Bachelors	3	Low
28	85	60	Male	Associates	3	High
29	69	39	Female	Associates	0	Low
30	73	48	Female	Associates	2	Low
31	91	59	Male	Masters	5	High
32	75	44	Male	Bachelors	3	Low
33	90	64	Male	Masters	5	High
34	74	42	Female	Bachelors	0	Low
35	72	46	Female	Bachelors	1	Low
Summary Statistics
	Quantitative Variables				Qualitative Variables
	Salary	Age	Promotions		Gender	Frequency	% Rel. Freq.
N	35.000	35.000	35.000		Female	16	45.7%
Mean	78.914	49.314	2.800		Male	19	54.3%
Standard Deviation	ERROR:#NAME?	ERROR:#NAME?	ERROR:#NAME?			35	100.0%
Variance	ERROR:#NAME?	ERROR:#NAME?	ERROR:#NAME?
Standard Error	ERROR:#NAME?	ERROR:#NAME?	ERROR:#NAME?		Education	Frequency	% Rel. Freq.
Margin of Error (95%)					Associates
					Bachelors
Minimum					Masters
P10	ERROR:#NAME?	ERROR:#NAME?	ERROR:#NAME?
Q1
Median					Pay	Frequency	% Rel. Freq.
Q3					Low
P90					High
Maximum
Mode
Range
Interquartile Range
Coefficient of Variation	ERROR:#NAME?	ERROR:#NAME?	ERROR:#NAME?
Skewness
Kurtosis
Salary
			(by 5)
			Bin
Age
			(by 5)
			Bin
Promotions
			(by 1)
			Bin
Gender
Education
Pay
Salary by Age
Salary by Promotions
Pay by Gender
Pay by Education

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Probability Distributions

Discrete Distributions				Continuous Distributions
(k=8)	(p=.2)	(n=6 p=.2)	(μ=3)	(a=30 b=100)	(μ=50 σ=5)	(μ=1/3)	Seed=		(a=0 b=1)
D. Uniform	Bernoulli	Binomial	Poisson	C. Uniform	Normal	Exponential	x	Pr	C. Uniform
D. Uniform (k=8)
				(by 1)
				Bin
Bernoulli (p=.2)
				(by 1)
				Bin
Binomial (n=6 p=.2)
				(by 1)
				Bin
Poisson (μ=3)
				(by 1)
				Bin
C. Uniform (a=30 b=100)
				(by 10)
				Bin
Normal (μ=50 σ=5)
				(by 5)
				Bin
Exponential (μ=1/3)
				(by .4)
				Bin
Central Limit Theorem
Coin Flip	Set 1	Set 2	Set 3	Set 4	Set 5	Set 6	Set 7	Set 8	Set 9
1
2
3
4
5
6
7
8
9
10
Proportion Heads:
		Proportion Heads			Proportion		Probability
		Sample	Population		Heads	Frequency	Sample	Population
	Mean
	Variance
Central Limit Theorem
	Law of Large Numbers: as the number of sets (300) increases, the sample curve approaches the population curve.
	Central Limit Theorem: as the number of coin flips (10) increases, the curves become more bell-shaped.

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Inferential Statistics

Data
Executive	Salary	Gender	Education	Pay	PayD	Salary2
1	79	Female	Bachelors			81
2	76	Female	Associates			75
3	83	Male	Masters			88
4	92	Male	Masters			95
5	80	Female	Bachelors			83
6	81	Female	Masters			84
7	77	Male	Masters			82
8	87	Male	Masters			90
9	69	Male	Bachelors			81
10	70	Female	Bachelors			71
11	73	Male	Associates			79
12	80	Male	Associates			73
13	81	Female	Associates			78
14	87	Male	Masters			88
15	78	Female	Associates			78
16	78	Female	Masters			80
17	77	Male	Masters			88
18	81	Male	Bachelors			86
19	75	Female	Associates			69
20	83	Male	Bachelors			79
21	74	Female	Bachelors			77
22	85	Male	Masters			89
23	86	Male	Bachelors			93
24	73	Female	Associates			79
25	70	Male	Associates			76
26	81	Female	Bachelors			75
27	77	Male	Bachelors			81
28	85	Male	Associates			81
29	69	Female	Associates			66
30	73	Female	Associates			78
31	91	Male	Masters			93
32	75	Male	Bachelors			75
33	90	Male	Masters			87
34	74	Female	Bachelors			70
35	72	Female	Bachelors			73
Salary
Variable: Salary (Normal)
One Population: All Executives
Unknown variance so use the t distribution; if variance is known use the z distribution.
Two Populations: Male Executives vs. Female Executives
Unknown variances so use the t distribution; if variances are known use the z distribution.
If variances are assumed unequal use the SE with the special DF. If variances are assumed equal use the SE (P) with the regular DF.
		Gender	Gender
	All	Male	Female		Difference in Means
N					Standard Error
Mean					Special DF			29.520 - Use ROUND function with 0 digits.
Variance					Pooled Variance
Standard Error					Standard Error (P)
DF					Regular DF
Confidence Intervals
One Population	Confid.	Alpha	DF	Mean	SE	Critical t	MOE	Lower CL	Upper CL
	90%	0.10
	95%	0.05
	99%	0.01
Two Populations	Confid.	Alpha	DF	Δ Means	SE	Critical t	MOE	Lower CL	Upper CL
(Unequal Variances)	90%	0.10
	95%	0.05
	99%	0.01
Two Populations	Confid.	Alpha	DF	Δ Means	SE	Critical t	MOE	Lower CL	Upper CL
(Equal Variances)	90%	0.10
	95%	0.05
	99%	0.01
Hypothesis Tests
One Population	Null Hypothesis		Alpha	DF	Mean	SE	t-statistic	L Critical t	U Critical t	P-value	Decision
	μ ≥	77	0.10
	μ ≤	77	0.10
	μ =	77	0.10
	μ ≥	77	0.05
	μ ≤	77	0.05
	μ =	77	0.05
	μ ≥	77	0.01
	μ ≤	77	0.01
	μ =	77	0.01
Hypothesis Tests
Two Populations	Null Hypothesis		Alpha	DF	Δ Means	SE	t-statistic	L Critical t	U Critical t	P-value	Decision
(Unequal Variances)	μM - μF ≥	8	0.10
	μM - μF ≤	8	0.10
	μM - μF =	8	0.10
	μM - μF ≥	8	0.05
	μM - μF ≤	8	0.05
	μM - μF =	8	0.05
	μM - μF ≥	8	0.01
	μM - μF ≤	8	0.01
	μM - μF =	8	0.01
Two Populations	Null Hypothesis		Alpha	DF	Δ Means	SE	t-statistic	L Critical t	U Critical t	P-value	Decision
(Equal Variances)	μM - μF ≥	8	0.10
	μM - μF ≤	8	0.10
	μM - μF =	8	0.10
	μM - μF ≥	8	0.05
	μM - μF ≤	8	0.05
	μM - μF =	8	0.05
	μM - μF ≥	8	0.01
	μM - μF ≤	8	0.01
	μM - μF =	8	0.01
Equivalent Two Population Hypothesis Tests
							Salary
							Male	Female
Other Hypothesis Tests
Pay
Variable: PayD (Bernoulli)
One Population: All Executives
It must be that np ≥ 5 and n(1-p) ≥ 5. Use the z distribution.
For HT use the hypothesized value in calculating the SE.
Two Populations: Male Executives vs. Female Executives
It must be that np ≥ 5 and n(1-p) ≥ 5 for both populations. Use the z distribution.
For HT when the hypothesized value is 0, the variances are presumed equal so use the SE (P).
		Gender	Gender
	All	Male	Female
N					Difference in Props
Proportion					Standard Error
Variance					Pooled Variance
Standard Error					Standard Error (P)
Confidence Intervals
One Population	Confid.	Alpha	Proportion	SE	Critical z	MOE	Lower CL	Upper CL
	90%	0.10
	95%	0.05
	99%	0.01
Two Populations	Confid.	Alpha	Δ Props	SE	Critical z	MOE	Lower CL	Upper CL
	90%	0.10
	95%	0.05
	99%	0.01
Hypothesis Tests
One Population	Null Hypothesis		Alpha	Proportion	SE	z-statistic	L Critical z	U Critical z	P-value	Decision
	p ≥	0.50	0.10
	p ≤	0.50	0.10
	p =	0.50	0.10
	p ≥	0.50	0.05
	p ≤	0.50	0.05
	p =	0.50	0.05
	p ≥	0.50	0.01
	p ≤	0.50	0.01
	p =	0.50	0.01
Hypothesis Tests
Two Populations	Null Hypothesis		Alpha	Δ Props	SE	z-statistic	L Critical z	U Critical z	P-value	Decision
(Unequal Variances)	pM - pF ≥	0.15	0.10
	pM - pF ≤	0.15	0.10
	pM - pF =	0.15	0.10
	pM - pF ≥	0.15	0.05
	pM - pF ≤	0.15	0.05
	pM - pF =	0.15	0.05
	pM - pF ≥	0.15	0.01
	pM - pF ≤	0.15	0.01
	pM - pF =	0.15	0.01
Two Populations	Null Hypothesis		Alpha	Δ Props	SE	z-statistic	L Critical z	U Critical z	P-value	Decision
(Equal Variances)	pM - pF ≥	0	0.10
	pM - pF ≤	0	0.10
	pM - pF =	0	0.10
	pM - pF ≥	0	0.05
	pM - pF ≤	0	0.05
	pM - pF =	0	0.05
	pM - pF ≥	0	0.01
	pM - pF ≤	0	0.01
	pM - pF =	0	0.01
Equivalent Two Population Hypothesis Tests
							PayD
							Male	Female
Test of Independence
Test of Independence

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Linear Modeling

Data
Executive	Salary	Age	Gender	Education	Promotions	AgeC	GenD	AgeC*GenD
1	79	49	Female	Bachelors	4
2	76	38	Female	Associates	0
3	83	60	Male	Masters	4
4	92	63	Male	Masters	6
5	80	55	Female	Bachelors	3
6	81	54	Female	Masters	6
7	77	42	Male	Masters	4
8	87	59	Male	Masters	6
9	69	42	Male	Bachelors	1
10	70	36	Female	Bachelors	1
11	73	48	Male	Associates	2
12	80	53	Male	Associates	2
13	81	46	Female	Associates	2
14	87	57	Male	Masters	4
15	78	49	Female	Associates	1
16	78	40	Female	Masters	2
17	77	55	Male	Masters	4
18	81	48	Male	Bachelors	5
19	75	42	Female	Associates	1
20	83	52	Male	Bachelors	3
21	74	41	Female	Bachelors	2
22	85	62	Male	Masters	3
23	86	53	Male	Bachelors	5
24	73	36	Female	Associates	0
25	70	44	Male	Associates	2
26	81	50	Female	Bachelors	3
27	77	50	Male	Bachelors	3
28	85	60	Male	Associates	3
29	69	39	Female	Associates	0
30	73	48	Female	Associates	2
31	91	59	Male	Masters	5
32	75	44	Male	Bachelors	3
33	90	64	Male	Masters	5
34	74	42	Female	Bachelors	0
35	72	46	Female	Bachelors	1
Data (cont.)
	AgeC	Promotions	AgeC*Promos	GenD	EducD1	EducD2	GenD*EducD1	GenD*EducD2
1. Salary by Age
2. Salary by Gender
Equivalent Two Population Hypothesis Tests
							Salary
							Male	Female
3. Salary by Education
Equivalent Three Population Hypothesis Test
							Salary
						Associates	Bachelors	Masters
4. Salary by Promotions
5. Salary by Age, Gender
6. Salary by Age, Gender, Age*Gender
7. Salary by Age, Promotions
8. Salary by Age, Promotions, Age*Promotions
9. Salary by Gender, Education
10. Salary by Gender, Education, Gender*Education
Moving Average (Interval = 3)
Week	Sales	Forecast	Squared Error
1	17
2	21
3	19
4	23
5	18
6	16
7	20
8	18
9	22
10	20
11	15
12	22
Exponential Smoothing (Optimized α)
Week	Sales	Forecast	Squared Error
1	17
2	21
3	19
4	23
5	18
6	16
7	20
8	18
9	22
10	20
11	15
12	22
Multiplicative Model (Trend, Seasonal)
		Moving		Seasonal	Seasonal	Deseasonalized		Squared
Quarter	Sales	Average	Centered MA	Irregular Value	Index	Sales	Forecast	Error
1	4.8
2	4.1
3	6.0
4	6.5
5	5.8
6	5.2
7	6.8
8	7.4
9	6.0
10	5.6
11	7.5
12	7.8
13	6.3
14	5.9
15	8.0
16	8.4
17
18
19
20
Multiplicative Model (Trend, Seasonal)
Year	Quarter
2012	F
	W
	Sp
	Su
2013	F
	W
	Sp
	Su
2014	F
	W
	Sp
	Su
2015	F
	W
	Sp
	Su
2016	F
	W
	Sp
	Su

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