Results: 2101f17senic1.sas

Open SENIC Data

The FREQ Procedure

Table mschool * mdschl

Cross-Tabular Freq Table

Frequency

Table of mschool by mdschl
mschool	mdschl(Medical school affiliation)
mschool		No	Yes	Total
.	4	0	0	4
0	0	80	0	80
1	0	0	16	16
Total	4	80	16	100

Open SENIC Data

The FREQ Procedure

Table nc * region

Cross-Tabular Freq Table

Frequency

Table of nc by region
nc	region(Region of U.S.A.)
nc	NorthCentral	Northeast	South	West	Total
0	0	24	30	15	69
1	31	0	0	0	31
Total	31	24	30	15	100

Table ne * region

Cross-Tabular Freq Table

Frequency

Table of ne by region
ne	region(Region of U.S.A.)
ne	NorthCentral	Northeast	South	West	Total
0	31	0	30	15	76
1	0	24	0	0	24
Total	31	24	30	15	100

Table s * region

Cross-Tabular Freq Table

Frequency

Table of s by region
s	region(Region of U.S.A.)
s	NorthCentral	Northeast	South	West	Total
0	31	24	0	15	70
1	0	0	30	0	30
Total	31	24	30	15	100

Table w * region

Cross-Tabular Freq Table

Frequency

Table of w by region
w	region(Region of U.S.A.)
w	NorthCentral	Northeast	South	West	Total
0	31	24	30	0	85
1	0	0	0	15	15
Total	31	24	30	15	100

Open SENIC Data

Frequency distributions of categorical variables

The FREQ Procedure

Table region

One-Way Frequencies


Region of U.S.A.
region	Frequency	Percent	Cumulative Frequency	Cumulative Percent
NorthCentral	31	31.00	31	31.00
Northeast	24	24.00	55	55.00
South	30	30.00	85	85.00
West	15	15.00	100	100.00

Table mdschl

One-Way Frequencies


Medical school affiliation
mdschl	Frequency	Percent	Cumulative Frequency	Cumulative Percent
Frequency Missing = 4
No	80	83.33	80	83.33
Yes	16	16.67	96	100.00

Open SENIC Data

Table of means and standard deviations

The MEANS Procedure

Summary statistics


Variable	Label	N	Mean	Std Dev	Minimum	Maximum
census nbeds nurses lngstay age xratio culratio infpercent	Aver # patients in hospital per day Average # beds during study period Aver # nurses during study period Av length of hospital stay, in days Average patient age # x-rays / # no signs of pneumonia # cultures / # no hosp acq infect Percent acquiring infection in hospital	100 100 97 100 100 100 100 96	192.4100000 252.8800000 175.3505155 9.6921000 53.2070000 81.6200000 15.6300000 4.3135417	158.2452447 197.9572589 138.1400287 1.9905663 4.4436143 19.8599948 10.4661793 1.3521616	20.0000000 29.0000000 14.0000000 6.7000000 38.8000000 39.6000000 1.6000000 1.3000000	791.0000000 835.0000000 656.0000000 19.5600000 65.9000000 133.5000000 60.5000000 7.8000000

Open SENIC Data

Detailed descriptive statistics with boxplots and histograms

The UNIVARIATE Procedure

Variable: census (Aver # patients in hospital per day)

The UNIVARIATE Procedure

census

Moments


Moments
N	100	Sum Weights	100
Mean	192.41	Sum Observations	19241
Std Deviation	158.245245	Variance	25041.5575
Skewness	1.39173874	Kurtosis	1.67673694
Uncorrected SS	6181275	Corrected SS	2479114.19
Coeff Variation	82.2437736	Std Error Mean	15.8245245

Basic Measures of Location and Variability


Basic Statistical Measures
Location		Variability
Mean	192.4100	Std Deviation	158.24524
Median	142.0000	Variance	25042
Mode	113.0000	Range	771.00000
		Interquartile Range	182.50000

Tests For Location


Tests for Location: Mu0=0
Test	Statistic		p Value
Student's t	t	12.15898	Pr > \|t\|	<.0001
Sign	M	50	Pr >= \|M\|	<.0001
Signed Rank	S	2525	Pr >= \|S\|	<.0001

Quantiles


Quantiles (Definition 5)
Level	Quantile
100% Max	791.0
99%	693.0
95%	546.5
90%	427.0
75% Q3	250.0
50% Median	142.0
25% Q1	67.5
10%	47.0
5%	39.5
1%	28.5
0% Min	20.0

Extreme Observations


Extreme Observations
Lowest		Highest
Value	Obs	Value	Obs
20	35	547	51
37	70	581	81
37	14	591	75
38	87	595	10
39	98	791	66

Plots for census

Open SENIC Data

Detailed descriptive statistics with boxplots and histograms

The UNIVARIATE Procedure

Histogram 1

Panel 1

Open SENIC Data

Detailed descriptive statistics with boxplots and histograms

The UNIVARIATE Procedure

Variable: nbeds (Average # beds during study period)

nbeds

Moments


Moments
N	100	Sum Weights	100
Mean	252.88	Sum Observations	25288
Std Deviation	197.957259	Variance	39187.0764
Skewness	1.40255597	Kurtosis	1.26471665
Uncorrected SS	10274350	Corrected SS	3879520.56
Coeff Variation	78.2811052	Std Error Mean	19.7957259

Basic Measures of Location and Variability


Basic Statistical Measures
Location		Variability
Mean	252.8800	Std Deviation	197.95726
Median	185.0000	Variance	39187
Mode	298.0000	Range	806.00000
		Interquartile Range	206.00000

Tests For Location


Tests for Location: Mu0=0
Test	Statistic		p Value
Student's t	t	12.77447	Pr > \|t\|	<.0001
Sign	M	50	Pr >= \|M\|	<.0001
Signed Rank	S	2525	Pr >= \|S\|	<.0001

Quantiles


Quantiles (Definition 5)
Level	Quantile
100% Max	835.0
99%	834.0
95%	696.0
90%	582.0
75% Q3	309.0
50% Median	185.0
25% Q1	103.0
10%	78.0
5%	66.0
1%	40.5
0% Min	29.0

Extreme Observations


Extreme Observations
Lowest		Highest
Value	Obs	Value	Obs
29	35	752	10
52	14	768	75
56	25	831	81
60	96	833	51
64	65	835	66

Plots for nbeds

Open SENIC Data

Detailed descriptive statistics with boxplots and histograms

The UNIVARIATE Procedure

Histogram 1

Panel 1

Open SENIC Data

Detailed descriptive statistics with boxplots and histograms

The UNIVARIATE Procedure

Variable: nurses (Aver # nurses during study period)

nurses

Moments


Moments
N	97	Sum Weights	97
Mean	175.350515	Sum Observations	17009
Std Deviation	138.140029	Variance	19082.6675
Skewness	1.42905145	Kurtosis	1.79391854
Uncorrected SS	4814473	Corrected SS	1831936.08
Coeff Variation	78.7793685	Std Error Mean	14.0259948

Basic Measures of Location and Variability


Basic Statistical Measures
Location		Variability
Mean	175.3505	Std Deviation	138.14003
Median	136.0000	Variance	19083
Mode	35.0000	Range	642.00000
		Interquartile Range	145.00000

Tests For Location


Tests for Location: Mu0=0
Test	Statistic		p Value
Student's t	t	12.50182	Pr > \|t\|	<.0001
Sign	M	48.5	Pr >= \|M\|	<.0001
Signed Rank	S	2376.5	Pr >= \|S\|	<.0001

Quantiles


Quantiles (Definition 5)
Level	Quantile
100% Max	656
99%	656
95%	469
90%	392
75% Q3	218
50% Median	136
25% Q1	73
10%	49
5%	35
1%	14
0% Min	14

Extreme Observations


Extreme Observations
Lowest		Highest
Value	Obs	Value	Obs
14	25	469	99
19	57	497	7
32	16	519	51
35	85	629	81
35	70	656	75

Missing Values


Missing Values
Missing Value	Count	Percent Of
Missing Value	Count	All Obs	Missing Obs
.	3	3.00	100.00

Plots for nurses

Open SENIC Data

Detailed descriptive statistics with boxplots and histograms

The UNIVARIATE Procedure

Histogram 1

Panel 1

Open SENIC Data

Detailed descriptive statistics with boxplots and histograms

The UNIVARIATE Procedure

Variable: lngstay (Av length of hospital stay, in days)

lngstay

Moments


Moments
N	100	Sum Weights	100
Mean	9.6921	Sum Observations	969.21
Std Deviation	1.99056628	Variance	3.96235413
Skewness	2.01995349	Kurtosis	7.50112548
Uncorrected SS	9785.9533	Corrected SS	392.273059
Coeff Variation	20.5380287	Std Error Mean	0.19905663

Basic Measures of Location and Variability


Basic Statistical Measures
Location		Variability
Mean	9.692100	Std Deviation	1.99057
Median	9.515000	Variance	3.96235
Mode	7.140000	Range	12.86000
		Interquartile Range	2.41500

Tests For Location


Tests for Location: Mu0=0
Test	Statistic		p Value
Student's t	t	48.69016	Pr > \|t\|	<.0001
Sign	M	50	Pr >= \|M\|	<.0001
Signed Rank	S	2525	Pr >= \|S\|	<.0001

Quantiles


Quantiles (Definition 5)
Level	Quantile
100% Max	19.560
99%	18.750
95%	12.425
90%	11.635
75% Q3	10.725
50% Median	9.515
25% Q1	8.310
10%	7.650
5%	7.140
1%	6.890
0% Min	6.700

Extreme Observations


Extreme Observations
Lowest		Highest
Value	Obs	Value	Obs
6.70	5	12.78	61
7.08	39	13.59	90
7.13	34	13.95	95
7.14	70	17.94	66
7.14	57	19.56	64

Plots for lngstay

Open SENIC Data

Detailed descriptive statistics with boxplots and histograms

The UNIVARIATE Procedure

Histogram 1

Panel 1

Open SENIC Data

Detailed descriptive statistics with boxplots and histograms

The UNIVARIATE Procedure

Variable: age (Average patient age)

age

Moments


Moments
N	100	Sum Weights	100
Mean	53.207	Sum Observations	5320.7
Std Deviation	4.4436143	Variance	19.7457081
Skewness	-0.1620192	Kurtosis	1.40735388
Uncorrected SS	285053.31	Corrected SS	1954.8251
Coeff Variation	8.35155958	Std Error Mean	0.44436143

Basic Measures of Location and Variability


Basic Statistical Measures
Location		Variability
Mean	53.20700	Std Deviation	4.44361
Median	53.20000	Variance	19.74571
Mode	52.80000	Range	27.10000
		Interquartile Range	5.05000

Note: The mode displayed is the smallest of 3 modes with a count of 4.

Tests For Location


Tests for Location: Mu0=0
Test	Statistic		p Value
Student's t	t	119.7381	Pr > \|t\|	<.0001
Sign	M	50	Pr >= \|M\|	<.0001
Signed Rank	S	2525	Pr >= \|S\|	<.0001

Quantiles


Quantiles (Definition 5)
Level	Quantile
100% Max	65.90
99%	65.00
95%	59.75
90%	58.10
75% Q3	56.05
50% Median	53.20
25% Q1	51.00
10%	48.40
5%	45.10
1%	40.40
0% Min	38.80

Extreme Observations


Extreme Observations
Lowest		Highest
Value	Obs	Value	Obs
38.8	38	59.9	64
42.0	80	62.2	7
43.7	52	63.9	37
44.2	48	64.1	56
45.0	15	65.9	95

Plots for age

Open SENIC Data

Detailed descriptive statistics with boxplots and histograms

The UNIVARIATE Procedure

Histogram 1

Panel 1

Open SENIC Data

Detailed descriptive statistics with boxplots and histograms

The UNIVARIATE Procedure

Variable: xratio (# x-rays / # no signs of pneumonia)

xratio

Moments


Moments
N	100	Sum Weights	100
Mean	81.62	Sum Observations	8162
Std Deviation	19.8599948	Variance	394.419394
Skewness	0.01412329	Kurtosis	-0.2433795
Uncorrected SS	705229.96	Corrected SS	39047.52
Coeff Variation	24.3322651	Std Error Mean	1.98599948

Basic Measures of Location and Variability


Basic Statistical Measures
Location		Variability
Mean	81.62000	Std Deviation	19.85999
Median	82.15000	Variance	394.41939
Mode	59.20000	Range	93.90000
		Interquartile Range	24.80000

Note: The mode displayed is the smallest of 7 modes with a count of 2.

Tests For Location


Tests for Location: Mu0=0
Test	Statistic		p Value
Student's t	t	41.09769	Pr > \|t\|	<.0001
Sign	M	50	Pr >= \|M\|	<.0001
Signed Rank	S	2525	Pr >= \|S\|	<.0001

Quantiles


Quantiles (Definition 5)
Level	Quantile
100% Max	133.50
99%	128.15
95%	115.30
90%	107.00
75% Q3	95.00
50% Median	82.15
25% Q1	70.20
10%	55.95
5%	46.75
1%	40.00
0% Min	39.60

Extreme Observations


Extreme Observations
Lowest		Highest
Value	Obs	Value	Obs
39.6	34	116.9	61
40.4	85	116.9	99
42.6	55	122.0	75
45.7	57	122.8	46
46.5	16	133.5	95

Plots for xratio

Open SENIC Data

Detailed descriptive statistics with boxplots and histograms

The UNIVARIATE Procedure

Histogram 1

Panel 1

Open SENIC Data

Detailed descriptive statistics with boxplots and histograms

The UNIVARIATE Procedure

Variable: culratio (# cultures / # no hosp acq infect)

culratio

Moments


Moments
N	100	Sum Weights	100
Mean	15.63	Sum Observations	1563
Std Deviation	10.4661793	Variance	109.540909
Skewness	1.73027606	Kurtosis	4.24048245
Uncorrected SS	35274.24	Corrected SS	10844.55
Coeff Variation	66.9621196	Std Error Mean	1.04661793

Basic Measures of Location and Variability


Basic Statistical Measures
Location		Variability
Mean	15.63000	Std Deviation	10.46618
Median	13.05000	Variance	109.54091
Mode	6.90000	Range	58.90000
		Interquartile Range	11.25000

Tests For Location


Tests for Location: Mu0=0
Test	Statistic		p Value
Student's t	t	14.93382	Pr > \|t\|	<.0001
Sign	M	50	Pr >= \|M\|	<.0001
Signed Rank	S	2525	Pr >= \|S\|	<.0001

Quantiles


Quantiles (Definition 5)
Level	Quantile
100% Max	60.50
99%	56.45
95%	36.50
90%	26.70
75% Q3	19.50
50% Median	13.05
25% Q1	8.25
10%	5.45
5%	3.20
1%	1.90
0% Min	1.60

Extreme Observations


Extreme Observations
Lowest		Highest
Value	Obs	Value	Obs
1.6	37	36.7	2
2.2	25	42.0	68
2.5	85	46.0	61
2.6	70	52.4	52
2.6	48	60.5	18

Plots for culratio

Open SENIC Data

Detailed descriptive statistics with boxplots and histograms

The UNIVARIATE Procedure

Histogram 1

Panel 1

Open SENIC Data

Detailed descriptive statistics with boxplots and histograms

The UNIVARIATE Procedure

Variable: infpercent (Percent acquiring infection in hospital)

infpercent

Moments


Moments
N	96	Sum Weights	96
Mean	4.31354167	Sum Observations	414.1
Std Deviation	1.35216161	Variance	1.82834101
Skewness	-0.1127617	Kurtosis	-0.0831037
Uncorrected SS	1959.93	Corrected SS	173.692396
Coeff Variation	31.3469003	Std Error Mean	0.13800442

Basic Measures of Location and Variability


Basic Statistical Measures
Location		Variability
Mean	4.313542	Std Deviation	1.35216
Median	4.450000	Variance	1.82834
Mode	4.500000	Range	6.50000
		Interquartile Range	1.85000

Tests For Location


Tests for Location: Mu0=0
Test	Statistic		p Value
Student's t	t	31.25655	Pr > \|t\|	<.0001
Sign	M	48	Pr >= \|M\|	<.0001
Signed Rank	S	2328	Pr >= \|S\|	<.0001

Quantiles


Quantiles (Definition 5)
Level	Quantile
100% Max	7.80
99%	7.80
95%	6.40
90%	5.80
75% Q3	5.25
50% Median	4.45
25% Q1	3.40
10%	2.50
5%	1.80
1%	1.30
0% Min	1.30

Extreme Observations


Extreme Observations
Lowest		Highest
Value	Obs	Value	Obs
1.3	25	6.4	44
1.4	57	6.5	64
1.6	62	6.6	95
1.7	11	7.7	61
1.8	85	7.8	52

Missing Values


Missing Values
Missing Value	Count	Percent Of
Missing Value	Count	All Obs	Missing Obs
.	4	4.00	100.00

Plots for infpercent

Open SENIC Data

Detailed descriptive statistics with boxplots and histograms

The UNIVARIATE Procedure

Histogram 1

Panel 1

The SGPLOT Procedure

The SGPlot Procedure

The SGPLOT Procedure

The SGPlot Procedure

Open SENIC Data

Detailed descriptive statistics with boxplots and histograms

The BOXPLOT Procedure

infpercent

Panel 1

Open SENIC Data

Relationship between region and medical school affiliation

The FREQ Procedure

Table mdschl * region

Cross-Tabular Freq Table

Frequency Col Pct

Table of mdschl by region
mdschl(Medical school affiliation)	region(Region of U.S.A.)
mdschl(Medical school affiliation)	NorthCentral	Northeast	South	West	Total
No	24 80.00	19 79.17	24 88.89	13 86.67	80
Yes	6 20.00	5 20.83	3 11.11	2 13.33	16
Total	30	24	27	15	96
Frequency Missing = 4

Statistics for Table of mdschl by region

Chi-Square Tests


Statistic	DF	Value	Prob
WARNING: 38% of the cells have expected counts less than 5. Chi-Square may not be a valid test.
Chi-Square	3	1.2600	0.7387
Likelihood Ratio Chi-Square	3	1.3029	0.7284
Mantel-Haenszel Chi-Square	1	0.7978	0.3718
Phi Coefficient		0.1146
Contingency Coefficient		0.1138
Cramer's V		0.1146

Effective Sample Size = 96
Frequency Missing = 4

The TTEST Procedure

Percent acquiring infection in hospital

Open SENIC Data

Less risk at Hospitals with Med School Affiliation?

Compare t = -2.542

The TTEST Procedure

Variable: infpercent (Percent acquiring infection in hospital)

Statistics


mdschl	N	Mean	Std Dev	Std Err	Minimum	Maximum
No	79	4.2051	1.3314	0.1498	1.3000	7.8000
Yes	14	5.1714	1.1815	0.3158	2.9000	7.7000
Diff (1-2)		-0.9664	1.3110	0.3802

Confidence Limits


mdschl	Method	Mean	95% CL Mean		Std Dev	95% CL Std Dev
No		4.2051	3.9069	4.5033	1.3314	1.1513	1.5788
Yes		5.1714	4.4892	5.8536	1.1815	0.8566	1.9035
Diff (1-2)	Pooled	-0.9664	-1.7215	-0.2112	1.3110	1.1451	1.5336
Diff (1-2)	Satterthwaite	-0.9664	-1.6970	-0.2357

T-Tests


Method	Variances	DF	t Value	Pr > \|t\|
Pooled	Equal	91	-2.54	0.0127
Satterthwaite	Unequal	19.345	-2.76	0.0122

Equality of Variances


Equality of Variances
Method	Num DF	Den DF	F Value	Pr > F
Folded F	78	13	1.27	0.6585

Summary Panel

Q-Q Plots

Open SENIC Data

Regional differences in average infection risk?

Compare F = 2.674, p = 0.0519

The GLM Procedure

Data

Class Levels


Class Level Information
Class	Levels	Values
region	4	NorthCentral Northeast South West

Number of Observations


Number of Observations Read	100
Number of Observations Used	96

Open SENIC Data

Regional differences in average infection risk?

Compare F = 2.674, p = 0.0519

The GLM Procedure

Dependent Variable: infpercent Percent acquiring infection in hospital

Analysis of Variance

infpercent

Overall ANOVA


Source	DF	Sum of Squares	Mean Square	F Value	Pr > F
Model	3	13.9285440	4.6428480	2.67	0.0519
Error	92	159.7638519	1.7365636
Corrected Total	95	173.6923958

Fit Statistics


R-Square	Coeff Var	Root MSE	infpercent Mean
0.080191	30.55001	1.317787	4.313542

Type I Model ANOVA


Source	DF	Type I SS	Mean Square	F Value	Pr > F
region	3	13.92854398	4.64284799	2.67	0.0519

Type III Model ANOVA


Source	DF	Type III SS	Mean Square	F Value	Pr > F
region	3	13.92854398	4.64284799	2.67	0.0519

Box Plot

Fit Plot for Percent acquiring infection in hospital by Region of U.S.A.

Open SENIC Data

Regional differences in average infection risk?

Compare F = 2.674, p = 0.0519

The GLM Procedure

Means

region

infpercent

Distribution of infpercent by region

Means


Level of region	N	infpercent
Level of region	N	Mean	Std Dev
NorthCentral	27	4.35925926	1.44175621
Northeast	24	4.83333333	1.33633720
South	30	3.82000000	1.35351395
West	15	4.38666667	0.90700974

Open SENIC Data

Regional differences in average infection risk?

Compare F = 2.674, p = 0.0519

The MEANS Procedure

Summary statistics


Analysis Variable : infpercent Percent acquiring infection in hospital
Region of U.S.A.	N Obs	N	Mean	Std Dev	Minimum	Maximum
NorthCentral	31	27	4.3592593	1.4417562	1.3000000	7.8000000
Northeast	24	24	4.8333333	1.3363372	2.5000000	7.7000000
South	30	30	3.8200000	1.3535139	1.4000000	6.2000000
West	15	15	4.3866667	0.9070097	2.6000000	5.6000000

Open SENIC Data

Correlation matrix of quantitative variables

The CORR Procedure

Variables Information


8 Variables:	census nbeds nurses lngstay age xratio culratio infpercent

Simple Statistics


Simple Statistics
Variable	N	Mean	Std Dev	Sum	Minimum	Maximum	Label
census	100	192.41000	158.24524	19241	20.00000	791.00000	Aver # patients in hospital per day
nbeds	100	252.88000	197.95726	25288	29.00000	835.00000	Average # beds during study period
nurses	97	175.35052	138.14003	17009	14.00000	656.00000	Aver # nurses during study period
lngstay	100	9.69210	1.99057	969.21000	6.70000	19.56000	Av length of hospital stay, in days
age	100	53.20700	4.44361	5321	38.80000	65.90000	Average patient age
xratio	100	81.62000	19.85999	8162	39.60000	133.50000	# x-rays / # no signs of pneumonia
culratio	100	15.63000	10.46618	1563	1.60000	60.50000	# cultures / # no hosp acq infect
infpercent	96	4.31354	1.35216	414.10000	1.30000	7.80000	Percent acquiring infection in hospital

Pearson Correlations


Pearson Correlation Coefficients Prob > \|r\| under H0: Rho=0 Number of Observations
	census	nbeds	nurses	lngstay	age	xratio	culratio	infpercent
census Aver # patients in hospital per day	1.00000 100	0.98195 <.0001 100	0.90850 <.0001 97	0.47231 <.0001 100	-0.03164 0.7546 100	0.07998 0.4289 100	0.13834 0.1699 100	0.39311 <.0001 96
nbeds Average # beds during study period	0.98195 <.0001 100	1.00000 100	0.92421 <.0001 97	0.39942 <.0001 100	-0.05066 0.6167 100	0.05150 0.6108 100	0.13622 0.1766 100	0.35675 0.0004 96
nurses Aver # nurses during study period	0.90850 <.0001 97	0.92421 <.0001 97	1.00000 97	0.34813 0.0005 97	-0.01104 0.9146 97	0.11666 0.2551 97	0.22487 0.0268 97	0.42388 <.0001 93
lngstay Av length of hospital stay, in days	0.47231 <.0001 100	0.39942 <.0001 100	0.34813 0.0005 97	1.00000 100	0.19790 0.0484 100	0.38600 <.0001 100	0.33667 0.0006 100	0.53491 <.0001 96
age Average patient age	-0.03164 0.7546 100	-0.05066 0.6167 100	-0.01104 0.9146 97	0.19790 0.0484 100	1.00000 100	-0.02332 0.8178 100	-0.21189 0.0343 100	0.00061 0.9953 96
xratio # x-rays / # no signs of pneumonia	0.07998 0.4289 100	0.05150 0.6108 100	0.11666 0.2551 97	0.38600 <.0001 100	-0.02332 0.8178 100	1.00000 100	0.43979 <.0001 100	0.48001 <.0001 96
culratio # cultures / # no hosp acq infect	0.13834 0.1699 100	0.13622 0.1766 100	0.22487 0.0268 97	0.33667 0.0006 100	-0.21189 0.0343 100	0.43979 <.0001 100	1.00000 100	0.59210 <.0001 96
infpercent Percent acquiring infection in hospital	0.39311 <.0001 96	0.35675 0.0004 96	0.42388 <.0001 93	0.53491 <.0001 96	0.00061 0.9953 96	0.48001 <.0001 96	0.59210 <.0001 96	1.00000 96

Open SENIC Data

Simple regression (One explanatory variable)

The REG Procedure

Model: MODEL1

Dependent Variable: infpercent Percent acquiring infection in hospital

The REG Procedure

MODEL1

Fit

infpercent

Number of Observations


Number of Observations Read	100
Number of Observations Used	93
Number of Observations with Missing Values	7

Analysis of Variance


Analysis of Variance
Source	DF	Sum of Squares	Mean Square	F Value	Pr > F
Model	1	30.13246	30.13246	19.93	<.0001
Error	91	137.57033	1.51176
Corrected Total	92	167.70280

Fit Statistics


Root MSE	1.22954	R-Square	0.1797
Dependent Mean	4.32688	Adj R-Sq	0.1707
Coeff Var	28.41624

Parameter Estimates


Parameter Estimates
Variable	Label	DF	Parameter Estimate	Standard Error	t Value	Pr > \|t\|
Intercept	Intercept	1	3.60779	0.20542	17.56	<.0001
nurses	Aver # nurses during study period	1	0.00436	0.00097605	4.46	<.0001

Open SENIC Data

Just the hospital size variables

The REG Procedure

Model: MODEL1

Dependent Variable: infpercent Percent acquiring infection in hospital

The REG Procedure

MODEL1

Fit

infpercent

Number of Observations


Number of Observations Read	100
Number of Observations Used	93
Number of Observations with Missing Values	7

Analysis of Variance


Analysis of Variance
Source	DF	Sum of Squares	Mean Square	F Value	Pr > F
Model	3	41.01065	13.67022	9.60	<.0001
Error	89	126.69215	1.42351
Corrected Total	92	167.70280

Fit Statistics


Root MSE	1.19311	R-Square	0.2445
Dependent Mean	4.32688	Adj R-Sq	0.2191
Coeff Var	27.57432

Parameter Estimates


Parameter Estimates
Variable	Label	DF	Parameter Estimate	Standard Error	t Value	Pr > \|t\|
Intercept	Intercept	1	3.75658	0.20919	17.96	<.0001
census	Aver # patients in hospital per day	1	0.01159	0.00442	2.62	0.0102
nbeds	Average # beds during study period	1	-0.01083	0.00395	-2.75	0.0073
nurses	Aver # nurses during study period	1	0.00631	0.00236	2.67	0.0090

Open SENIC Data

All the quantitative explanatory variables

Compare F-test for size: F = 2.7662

The REG Procedure

Model: MODEL1

Dependent Variable: infpercent Percent acquiring infection in hospital

The REG Procedure

MODEL1

Fit

infpercent

Number of Observations


Number of Observations Read	100
Number of Observations Used	93
Number of Observations with Missing Values	7

Analysis of Variance


Analysis of Variance
Source	DF	Sum of Squares	Mean Square	F Value	Pr > F
Model	7	91.90340	13.12906	14.72	<.0001
Error	85	75.79940	0.89176
Corrected Total	92	167.70280

Fit Statistics


Root MSE	0.94433	R-Square	0.5480
Dependent Mean	4.32688	Adj R-Sq	0.5108
Coeff Var	21.82471

Parameter Estimates


Parameter Estimates
Variable	Label	DF	Parameter Estimate	Standard Error	t Value	Pr > \|t\|
Intercept	Intercept	1	0.14786	1.29129	0.11	0.9091
census	Aver # patients in hospital per day	1	0.00197	0.00404	0.49	0.6274
nbeds	Average # beds during study period	1	-0.00244	0.00338	-0.72	0.4710
nurses	Aver # nurses during study period	1	0.00342	0.00200	1.71	0.0907
lngstay	Av length of hospital stay, in days	1	0.16418	0.07190	2.28	0.0249
age	Average patient age	1	0.01065	0.02403	0.44	0.6589
xratio	# x-rays / # no signs of pneumonia	1	0.01085	0.00622	1.74	0.0849
culratio	# cultures / # no hosp acq infect	1	0.05332	0.01347	3.96	0.0002

Open SENIC Data

All the quantitative explanatory variables

Compare F-test for size: F = 2.7662

The REG Procedure

Model: MODEL1

Test size

Results


Test size Results for Dependent Variable infpercent
Source	DF	Mean Square	F Value	Pr > F
Numerator	3	2.46678	2.77	0.0468
Denominator	85	0.89176

Open SENIC Data

Full model including categorical variables

Reference category for region is South

The REG Procedure

Model: MODEL1

Dependent Variable: infpercent Percent acquiring infection in hospital

The REG Procedure

MODEL1

Fit

infpercent

Number of Observations


Number of Observations Read	100
Number of Observations Used	90
Number of Observations with Missing Values	10

Analysis of Variance


Analysis of Variance
Source	DF	Sum of Squares	Mean Square	F Value	Pr > F
Model	11	97.85727	8.89612	10.92	<.0001
Error	78	63.56596	0.81495
Corrected Total	89	161.42322

Fit Statistics


Root MSE	0.90274	R-Square	0.6062
Dependent Mean	4.36556	Adj R-Sq	0.5507
Coeff Var	20.67881

Parameter Estimates


Parameter Estimates
Variable	Label	DF	Parameter Estimate	Standard Error	t Value	Pr > \|t\|
Intercept	Intercept	1	-0.11995	1.31182	-0.09	0.9274
census	Aver # patients in hospital per day	1	0.00574	0.00405	1.42	0.1605
nbeds	Average # beds during study period	1	-0.00524	0.00335	-1.56	0.1220
nurses	Aver # nurses during study period	1	0.00401	0.00199	2.01	0.0474
lngstay	Av length of hospital stay, in days	1	0.23396	0.07470	3.13	0.0024
age	Average patient age	1	0.00241	0.02396	0.10	0.9200
xratio	# x-rays / # no signs of pneumonia	1	0.00803	0.00612	1.31	0.1930
culratio	# cultures / # no hosp acq infect	1	0.05869	0.01335	4.40	<.0001
mschool		1	-0.61275	0.36491	-1.68	0.0971
nc		1	0.27366	0.26670	1.03	0.3080
ne		1	-0.23615	0.30624	-0.77	0.4430
w		1	0.91236	0.31735	2.87	0.0052

Open SENIC Data

Full model including categorical variables

Reference category for region is South

The REG Procedure

Model: MODEL1

Test region

Results


Test region Results for Dependent Variable infpercent
Source	DF	Mean Square	F Value	Pr > F
Numerator	3	3.32245	4.08	0.0096
Denominator	78	0.81495

Open SENIC Data

Full model including categorical variables

Reference category for region is South

The REG Procedure

Model: MODEL1

Test size

Results


Test size Results for Dependent Variable infpercent
Source	DF	Mean Square	F Value	Pr > F
Numerator	3	2.92209	3.59	0.0174
Denominator	78	0.81495

Open SENIC Data

Full model with proc glm

Compare tests of region (F=4.0769) and size (F=3.5856)

The GLM Procedure

Data

Class Levels


Class Level Information
Class	Levels	Values
region	4	NorthCentral Northeast South West
mdschl	2	No Yes

Number of Observations


Number of Observations Read	100
Number of Observations Used	90

Open SENIC Data

Full model with proc glm

Compare tests of region (F=4.0769) and size (F=3.5856)

The GLM Procedure

Dependent Variable: infpercent Percent acquiring infection in hospital

Analysis of Variance

infpercent

Overall ANOVA


Source	DF	Sum of Squares	Mean Square	F Value	Pr > F
Model	11	97.8572672	8.8961152	10.92	<.0001
Error	78	63.5659550	0.8149481
Corrected Total	89	161.4232222

Fit Statistics


R-Square	Coeff Var	Root MSE	infpercent Mean
0.606216	20.67881	0.902745	4.365556

Type I Model ANOVA


Source	DF	Type I SS	Mean Square	F Value	Pr > F
census	1	24.26002343	24.26002343	29.77	<.0001
nbeds	1	5.01192754	5.01192754	6.15	0.0153
nurses	1	9.46557912	9.46557912	11.61	0.0010
lngstay	1	22.81251810	22.81251810	27.99	<.0001
age	1	1.18913635	1.18913635	1.46	0.2307
xratio	1	10.95890568	10.95890568	13.45	0.0004
culratio	1	13.17951843	13.17951843	16.17	0.0001
mdschl	1	1.01229942	1.01229942	1.24	0.2685
region	3	9.96735912	3.32245304	4.08	0.0096

Type III Model ANOVA


Source	DF	Type III SS	Mean Square	F Value	Pr > F
census	1	1.63641831	1.63641831	2.01	0.1605
nbeds	1	1.99234241	1.99234241	2.44	0.1220
nurses	1	3.30794395	3.30794395	4.06	0.0474
lngstay	1	7.99424249	7.99424249	9.81	0.0024
age	1	0.00826770	0.00826770	0.01	0.9200
xratio	1	1.40499417	1.40499417	1.72	0.1930
culratio	1	15.74157137	15.74157137	19.32	<.0001
mdschl	1	2.29791789	2.29791789	2.82	0.0971
region	3	9.96735912	3.32245304	4.08	0.0096

Contrasts


Contrast	DF	Contrast SS	Mean Square	F Value	Pr > F
Test of Region	3	9.96735912	3.32245304	4.08	0.0096
Test of size	3	8.76625610	2.92208537	3.59	0.0174

Solution


Parameter	Estimate		Standard Error	t Value	Pr > \|t\|
Intercept	0.179655379	B	1.32949565	0.14	0.8929
census	0.005744689		0.00405401	1.42	0.1605
nbeds	-0.005241114		0.00335202	-1.56	0.1220
nurses	0.004008682		0.00198970	2.01	0.0474
lngstay	0.233958891		0.07469919	3.13	0.0024
age	0.002413362		0.02396046	0.10	0.9200
xratio	0.008030024		0.00611568	1.31	0.1930
culratio	0.058689788		0.01335376	4.40	<.0001
mdschl No	0.612754961	B	0.36490900	1.68	0.0971
mdschl Yes	0.000000000	B	.	.	.
region NorthCentral	-0.638704083	B	0.31379278	-2.04	0.0452
region Northeast	-1.148515886	B	0.35673940	-3.22	0.0019
region South	-0.912364558	B	0.31734800	-2.87	0.0052
region West	0.000000000	B	.	.	.

Note:The X'X matrix has been found to be singular, and a generalized inverse was used to solve the normal equations. Terms whose estimates are followed by the letter 'B' are not uniquely estimable.

Open SENIC Data

Full model with proc glm

Compare tests of region (F=4.0769) and size (F=3.5856)

The GLM Procedure

Least Squares Means

region

infpercent

LSMeans


region	infpercent LSMEAN
NorthCentral	4.26001145
Northeast	3.75019964
South	3.98635097
West	4.89871553

region Mean Plot

Plot of infpercent least-squares means for region.

Open SENIC Data

Try lsmeans another way

The GLM Procedure

Data

Class Levels


Class Level Information
Class	Levels	Values
region	4	NorthCentral Northeast South West

Number of Observations


Number of Observations Read	100
Number of Observations Used	90

Open SENIC Data

Try lsmeans another way

The GLM Procedure

Dependent Variable: infpercent Percent acquiring infection in hospital

Analysis of Variance

infpercent

Overall ANOVA


Source	DF	Sum of Squares	Mean Square	F Value	Pr > F
Model	11	97.8572672	8.8961152	10.92	<.0001
Error	78	63.5659550	0.8149481
Corrected Total	89	161.4232222

Fit Statistics


R-Square	Coeff Var	Root MSE	infpercent Mean
0.606216	20.67881	0.902745	4.365556

Type I Model ANOVA


Source	DF	Type I SS	Mean Square	F Value	Pr > F
census	1	24.26002343	24.26002343	29.77	<.0001
nbeds	1	5.01192754	5.01192754	6.15	0.0153
nurses	1	9.46557912	9.46557912	11.61	0.0010
lngstay	1	22.81251810	22.81251810	27.99	<.0001
age	1	1.18913635	1.18913635	1.46	0.2307
xratio	1	10.95890568	10.95890568	13.45	0.0004
culratio	1	13.17951843	13.17951843	16.17	0.0001
mschool	1	1.01229942	1.01229942	1.24	0.2685
region	3	9.96735912	3.32245304	4.08	0.0096

Type III Model ANOVA


Source	DF	Type III SS	Mean Square	F Value	Pr > F
census	1	1.63641831	1.63641831	2.01	0.1605
nbeds	1	1.99234241	1.99234241	2.44	0.1220
nurses	1	3.30794395	3.30794395	4.06	0.0474
lngstay	1	7.99424249	7.99424249	9.81	0.0024
age	1	0.00826770	0.00826770	0.01	0.9200
xratio	1	1.40499417	1.40499417	1.72	0.1930
culratio	1	15.74157137	15.74157137	19.32	<.0001
mschool	1	2.29791789	2.29791789	2.82	0.0971
region	3	9.96735912	3.32245304	4.08	0.0096

Open SENIC Data

Try lsmeans another way

The GLM Procedure

Least Squares Means at census=197.2903, nbeds=258.9247, nurses=175.3656, lngstay=9.748065, age=53.25699, xratio=81.46882, culratio=15.4129, mschool=0

Least Squares Means

region

infpercent

LSMeans


region	infpercent LSMEAN
NorthCentral	4.60096012
Northeast	4.09114832
South	4.32729964
West	5.23966420

region Mean Plot

Open SENIC Data

Just hospitals with no medical school affiliation

The REG Procedure

Model: MODEL1

Dependent Variable: infpercent Percent acquiring infection in hospital

The REG Procedure

MODEL1

Fit

infpercent

Number of Observations


Number of Observations Read	80
Number of Observations Used	76
Number of Observations with Missing Values	4

Analysis of Variance


Analysis of Variance
Source	DF	Sum of Squares	Mean Square	F Value	Pr > F
Model	10	87.58091	8.75809	12.67	<.0001
Error	65	44.92685	0.69118
Corrected Total	75	132.50776

Fit Statistics


Root MSE	0.83137	R-Square	0.6609
Dependent Mean	4.21711	Adj R-Sq	0.6088
Coeff Var	19.71432

Parameter Estimates


Parameter Estimates
Variable	Label	DF	Parameter Estimate	Standard Error	t Value	Pr > \|t\|
Intercept	Intercept	1	-0.47528	1.27065	-0.37	0.7096
census	Aver # patients in hospital per day	1	0.01067	0.00526	2.03	0.0464
nbeds	Average # beds during study period	1	-0.00748	0.00386	-1.94	0.0571
nurses	Aver # nurses during study period	1	0.00348	0.00225	1.55	0.1264
lngstay	Av length of hospital stay, in days	1	0.23184	0.07421	3.12	0.0027
age	Average patient age	1	0.00103	0.02312	0.04	0.9647
xratio	# x-rays / # no signs of pneumonia	1	0.00807	0.00648	1.25	0.2173
culratio	# cultures / # no hosp acq infect	1	0.05596	0.01423	3.93	0.0002
nc		1	0.61038	0.27128	2.25	0.0278
ne		1	0.07650	0.30622	0.25	0.8035
w		1	1.45341	0.33465	4.34	<.0001