SAS Output

The SAS System

		Year
		1968	1969	1970	1971	1972
Mortality	Std	0.99	1.40	0.78	1.30	0.95
Mortality	Mean	5.99	5.77	4.91	4.80	4.72

The SAS System

The GLM Procedure

Class Level Information
Class	Levels	Values
Year	5	1968 1969 1970 1971 1972

Number of Observations Read	50
Number of Observations Used	50

The SAS System

The GLM Procedure

Dependent Variable: Mortality

Source	DF	Sum of Squares	Mean Square	F Value	Pr > F
Model	4	14.16280000	3.54070000	2.88	0.0331
Error	45	55.31500000	1.22922222
Corrected Total	49	69.47780000

R-Square	Coeff Var	Root MSE	Mortality Mean
0.203846	21.16653	1.108703	5.238000

Source	DF	Type I SS	Mean Square	F Value	Pr > F
Year	4	14.16280000	3.54070000	2.88	0.0331

Source	DF	Type III SS	Mean Square	F Value	Pr > F
Year	4	14.16280000	3.54070000	2.88	0.0331

The SAS System

The GLM Procedure

t Tests (LSD) for Mortality

Note:

This test controls the Type I comparisonwise error rate, not the experimentwise error rate.

Alpha	0.05
Error Degrees of Freedom	45
Error Mean Square	1.229222
Critical Value of t	2.01410
Least Significant Difference	0.9986

Means with the same letter are not significantly different.
t Grouping		Mean	N	Year
	A	5.9900	10	1968
	A
B	A	5.7700	10	1969
B
B	C	4.9100	10	1970
B	C
B	C	4.8000	10	1971
	C
	C	4.7200	10	1972

The SAS System

The GLM Procedure

Duncan's Multiple Range Test for Mortality

Note:

This test controls the Type I comparisonwise error rate, not the experimentwise error rate.

Alpha	0.05
Error Degrees of Freedom	45
Error Mean Square	1.229222

Number of Means	2	3	4	5
Critical Range	0.999	1.050	1.084	1.108

Means with the same letter are not significantly different.
Duncan Grouping		Mean	N	Year
	A	5.9900	10	1968
	A
B	A	5.7700	10	1969
B
B		4.9100	10	1970
B
B		4.8000	10	1971
B
B		4.7200	10	1972

The SAS System

The GLM Procedure

Bartlett's Test for Homogeneity of Mortality Variance
Source	DF	Chi-Square	Pr > ChiSq
Year	4	3.8867	0.4216

The SAS System

The GLM Procedure

Level of Year	N	Mortality
Level of Year	N	Mean	Std Dev
1968	10	5.99000000	0.98933199
1969	10	5.77000000	1.39845152
1970	10	4.91000000	0.77952977
1971	10	4.80000000	1.30384048
1972	10	4.72000000	0.95078915

The SAS System

The GLM Procedure

Levene's Test for Homogeneity of Mortality Variance ANOVA of Squared Deviations from Group Means
Source	DF	Sum of Squares	Mean Square	F Value	Pr > F
Year	4	10.5638	2.6410	0.97	0.4329
Error	45	122.4	2.7206

The SAS System

The GLM Procedure

Level of Year	N	Mortality
Level of Year	N	Mean	Std Dev
1968	10	5.99000000	0.98933199
1969	10	5.77000000	1.39845152
1970	10	4.91000000	0.77952977
1971	10	4.80000000	1.30384048
1972	10	4.72000000	0.95078915

The SAS System

The GLM Procedure

O'Brien's Test for Homogeneity of Mortality Variance ANOVA of O'Brien's Spread Variable, W = 0.5
Source	DF	Sum of Squares	Mean Square	F Value	Pr > F
Year	4	13.0418	3.2604	0.86	0.4953
Error	45	170.6	3.7918

The SAS System

The GLM Procedure

Level of Year	N	Mortality
Level of Year	N	Mean	Std Dev
1968	10	5.99000000	0.98933199
1969	10	5.77000000	1.39845152
1970	10	4.91000000	0.77952977
1971	10	4.80000000	1.30384048
1972	10	4.72000000	0.95078915

The SAS System

The GLM Procedure

Brown and Forsythe's Test for Homogeneity of Mortality Variance ANOVA of Absolute Deviations from Group Medians
Source	DF	Sum of Squares	Mean Square	F Value	Pr > F
Year	4	1.2788	0.3197	0.60	0.6627
Error	45	23.8750	0.5306

The SAS System

The GLM Procedure

Level of Year	N	Mortality
Level of Year	N	Mean	Std Dev
1968	10	5.99000000	0.98933199
1969	10	5.77000000	1.39845152
1970	10	4.91000000	0.77952977
1971	10	4.80000000	1.30384048
1972	10	4.72000000	0.95078915

The SAS System

The GLM Procedure

Dependent Variable: Mortality

Contrast	DF	Contrast SS	Mean Square	F Value	Pr > F
Linear	1	12.32010000	12.32010000	10.02	0.0028
Quadratic	1	0.75778571	0.75778571	0.62	0.4365

The SAS System

Results from PROC RSREG

The RSREG Procedure

Coding Coefficients for the Independent Variables
Factor	Subtracted off	Divided by
Year	1970.000000	2.000000

Response Surface for Variable Mortality
Response Mean	5.238000
Root MSE	1.095444
R-Square	0.1882
Coefficient of Variation	20.9134

Regression	DF	Type I Sum of Squares	R-Square	F Value	Pr > F
Linear	1	12.320100	0.1773	10.27	0.0024
Quadratic	1	0.757786	0.0109	0.63	0.4308
Crossproduct	0	0	0.0000	.	.
Total Model	2	13.077886	0.1882	5.45	0.0074

Residual	DF	Sum of Squares	Mean Square	F Value	Pr > F
Lack of Fit	2	1.084914	0.542457	0.44	0.6460
Pure Error	45	55.315000	1.229222
Total Error	47	56.399914	1.199998

Parameter	DF	Estimate	Standard Error	t Value	Pr > \|t\|	Parameter Estimate from Coded Data
Intercept	1	286220	359301	0.80	0.4297	5.090857
Year	1	-290.222429	364.772859	-0.80	0.4303	-0.702000
Year*Year	1	0.073571	0.092582	0.79	0.4308	0.294286

Factor	DF	Sum of Squares	Mean Square	F Value	Pr > F
Year	2	13.077886	6.538943	5.45	0.0074

The SAS System

Results from PROC RSREG

The UNIVARIATE Procedure

Variable: Mortality

Year=1968

Moments
N	10	Sum Weights	10
Mean	5.99	Sum Observations	59.9
Std Deviation	0.98933199	Variance	0.97877778
Skewness	0.08853675	Kurtosis	-1.8535056
Uncorrected SS	367.61	Corrected SS	8.809
Coeff Variation	16.5163937	Std Error Mean	0.31285424

Basic Statistical Measures
Location		Variability
Mean	5.990000	Std Deviation	0.98933
Median	6.100000	Variance	0.97878
Mode	4.900000	Range	2.40000
		Interquartile Range	2.00000

Note:

The mode displayed is the smallest of 2 modes with a count of 2.

Tests for Location: Mu0=0
Test	Statistic		p Value
Student's t	t	19.1463	Pr > \|t\|	<.0001
Sign	M	5	Pr >= \|M\|	0.0020
Signed Rank	S	27.5	Pr >= \|S\|	0.0020

Tests for Normality
Test	Statistic		p Value
Shapiro-Wilk	W	0.858614	Pr < W	0.0735
Kolmogorov-Smirnov	D	0.241508	Pr > D	0.0953
Cramer-von Mises	W-Sq	0.079161	Pr > W-Sq	0.1964
Anderson-Darling	A-Sq	0.557215	Pr > A-Sq	0.1139

Quantiles (Definition 5)
Quantile	Estimate
100% Max	7.30
99%	7.30
95%	7.30
90%	7.25
75% Q3	7.00
50% Median	6.10
25% Q1	5.00
10%	4.90
5%	4.90
1%	4.90
0% Min	4.90

Extreme Observations
Lowest		Highest
Value	Obs	Value	Obs
4.9	7	6.3	9
4.9	2	6.4	8
5.0	4	7.0	6
5.0	1	7.2	5
5.9	3	7.3	10

The UNIVARIATE Procedure

Variable: Mortality

The SAS System

Results from PROC RSREG

The UNIVARIATE Procedure

Variable: Mortality

Year=1969

Moments
N	10	Sum Weights	10
Mean	5.77	Sum Observations	57.7
Std Deviation	1.39845152	Variance	1.95566667
Skewness	-0.1466961	Kurtosis	-0.5750493
Uncorrected SS	350.53	Corrected SS	17.601
Coeff Variation	24.2365949	Std Error Mean	0.4422292

Basic Statistical Measures
Location		Variability
Mean	5.770000	Std Deviation	1.39845
Median	5.450000	Variance	1.95567
Mode	7.600000	Range	4.30000
		Interquartile Range	2.10000

Tests for Location: Mu0=0
Test	Statistic		p Value
Student's t	t	13.04753	Pr > \|t\|	<.0001
Sign	M	5	Pr >= \|M\|	0.0020
Signed Rank	S	27.5	Pr >= \|S\|	0.0020

Tests for Normality
Test	Statistic		p Value
Shapiro-Wilk	W	0.943907	Pr < W	0.5972
Kolmogorov-Smirnov	D	0.176548	Pr > D	>0.1500
Cramer-von Mises	W-Sq	0.042347	Pr > W-Sq	>0.2500
Anderson-Darling	A-Sq	0.27439	Pr > A-Sq	>0.2500

Quantiles (Definition 5)
Quantile	Estimate
100% Max	7.60
99%	7.60
95%	7.60
90%	7.60
75% Q3	7.10
50% Median	5.45
25% Q1	5.00
10%	3.90
5%	3.30
1%	3.30
0% Min	3.30

Extreme Observations
Lowest		Highest
Value	Obs	Value	Obs
3.3	12	5.5	14
4.5	13	6.4	18
5.0	15	7.1	20
5.3	19	7.6	16
5.4	11	7.6	17

The UNIVARIATE Procedure

Variable: Mortality

The SAS System

Results from PROC RSREG

The UNIVARIATE Procedure

Variable: Mortality

Year=1970

Moments
N	10	Sum Weights	10
Mean	4.91	Sum Observations	49.1
Std Deviation	0.77952977	Variance	0.60766667
Skewness	0.95670008	Kurtosis	0.0277596
Uncorrected SS	246.55	Corrected SS	5.469
Coeff Variation	15.8763701	Std Error Mean	0.24650896

Basic Statistical Measures
Location		Variability
Mean	4.910000	Std Deviation	0.77953
Median	4.700000	Variance	0.60767
Mode	4.300000	Range	2.40000
		Interquartile Range	0.90000

Tests for Location: Mu0=0
Test	Statistic		p Value
Student's t	t	19.91814	Pr > \|t\|	<.0001
Sign	M	5	Pr >= \|M\|	0.0020
Signed Rank	S	27.5	Pr >= \|S\|	0.0020

Tests for Normality
Test	Statistic		p Value
Shapiro-Wilk	W	0.90363	Pr < W	0.2400
Kolmogorov-Smirnov	D	0.156109	Pr > D	>0.1500
Cramer-von Mises	W-Sq	0.069106	Pr > W-Sq	>0.2500
Anderson-Darling	A-Sq	0.435813	Pr > A-Sq	0.2409

Quantiles (Definition 5)
Quantile	Estimate
100% Max	6.40
99%	6.40
95%	6.40
90%	6.20
75% Q3	5.20
50% Median	4.70
25% Q1	4.30
10%	4.15
5%	4.00
1%	4.00
0% Min	4.00

Extreme Observations
Lowest		Highest
Value	Obs	Value	Obs
4.0	23	4.8	27
4.3	30	5.1	22
4.3	21	5.2	29
4.4	25	6.0	24
4.6	26	6.4	28

The UNIVARIATE Procedure

Variable: Mortality

The SAS System

Results from PROC RSREG

The UNIVARIATE Procedure

Variable: Mortality

Year=1971

Moments
N	10	Sum Weights	10
Mean	4.8	Sum Observations	48
Std Deviation	1.30384048	Variance	1.7
Skewness	1.30609626	Kurtosis	2.73318504
Uncorrected SS	245.7	Corrected SS	15.3
Coeff Variation	27.1633434	Std Error Mean	0.41231056

Basic Statistical Measures
Location		Variability
Mean	4.800000	Std Deviation	1.30384
Median	4.450000	Variance	1.70000
Mode	4.400000	Range	4.80000
		Interquartile Range	1.20000

Tests for Location: Mu0=0
Test	Statistic		p Value
Student's t	t	11.64171	Pr > \|t\|	<.0001
Sign	M	5	Pr >= \|M\|	0.0020
Signed Rank	S	27.5	Pr >= \|S\|	0.0020

Tests for Normality
Test	Statistic		p Value
Shapiro-Wilk	W	0.901446	Pr < W	0.2272
Kolmogorov-Smirnov	D	0.190989	Pr > D	>0.1500
Cramer-von Mises	W-Sq	0.075969	Pr > W-Sq	0.2161
Anderson-Darling	A-Sq	0.473071	Pr > A-Sq	0.1959

Quantiles (Definition 5)
Quantile	Estimate
100% Max	7.80
99%	7.80
95%	7.80
90%	6.80
75% Q3	5.20
50% Median	4.45
25% Q1	4.00
10%	3.45
5%	3.00
1%	3.00
0% Min	3.00

Extreme Observations
Lowest		Highest
Value	Obs	Value	Obs
3.0	33	4.5	37
3.9	40	5.0	34
4.0	36	5.2	31
4.4	39	5.8	35
4.4	38	7.8	32

The UNIVARIATE Procedure

Variable: Mortality

The SAS System

Results from PROC RSREG

The UNIVARIATE Procedure

Variable: Mortality

Year=1972

Moments
N	10	Sum Weights	10
Mean	4.72	Sum Observations	47.2
Std Deviation	0.95078915	Variance	0.904
Skewness	0.89290833	Kurtosis	0.00685603
Uncorrected SS	230.92	Corrected SS	8.136
Coeff Variation	20.1438378	Std Error Mean	0.30066593

Basic Statistical Measures
Location		Variability
Mean	4.720000	Std Deviation	0.95079
Median	4.500000	Variance	0.90400
Mode	3.800000	Range	2.80000
		Interquartile Range	1.50000

Tests for Location: Mu0=0
Test	Statistic		p Value
Student's t	t	15.69849	Pr > \|t\|	<.0001
Sign	M	5	Pr >= \|M\|	0.0020
Signed Rank	S	27.5	Pr >= \|S\|	0.0020

Tests for Normality
Test	Statistic		p Value
Shapiro-Wilk	W	0.893614	Pr < W	0.1862
Kolmogorov-Smirnov	D	0.191493	Pr > D	>0.1500
Cramer-von Mises	W-Sq	0.062287	Pr > W-Sq	>0.2500
Anderson-Darling	A-Sq	0.415674	Pr > A-Sq	>0.2500

Quantiles (Definition 5)
Quantile	Estimate
100% Max	6.6
99%	6.6
95%	6.6
90%	6.2
75% Q3	5.3
50% Median	4.5
25% Q1	3.8
10%	3.8
5%	3.8
1%	3.8
0% Min	3.8

Extreme Observations
Lowest		Highest
Value	Obs	Value	Obs
3.8	50	4.5	48
3.8	47	5.0	41
3.8	45	5.3	49
4.1	44	5.8	42
4.5	48	6.6	43

The UNIVARIATE Procedure

Variable: Mortality