Review Lecture

histograms, five number summary, one-sample confidence intervals, nonresponse, observational study

Kaiser Foundation Health Plan Company

Description from the Hoover’s Company website, a company that collects information on other companies

• “Kaiser Foundation Health Plan aims to be the emperor of the HMO universe. With more than 8.5 million members in nine states and the District of Columbia, it is one of the largest not-for-profit managed health care companies in the US. Kaiser has an integrated care model, offering both hospital and physician care through a network of hospitals and physician practices operating under the Kaiser Permanente name. Members of Kaiser health plans have access to hospitals and some 400 other health care facilities operated by Kaiser Foundation Hospitals and Permanente Medical Groups, associations consisting of about 13,000 doctors.”

Study of the Birth Weight of Newborns

• data collected on all pregnancies that occurred between 1960 and 1967 among women in the Kaiser Foundation Health Plan in the San Francisco – East Bay Area– 15000 families in the study

• a subset of 1236 chosen for a particular study on smoking and birth weight– born in one year of the study– lived at least 28 days– single birth

Caveats

• What is the reference population?

• Was there any random selection?

• Can a random sample be assumed?

Birth Weight in Ounces

Frequency

1601401201008060

100

80

60

40

20

0

Nonsmokers

Birth Weight in Ounces

Frequency

1601401201008060

70

60

50

40

30

20

10

0

Smokers

Birth Weight in Ounces

Frequency

1601401201008060

100

80

60

40

20

0

Smoking StatusNonsmokerSmokerUnknown

Nonresponse

• tends not to occur for lower birth weights– consequently this may

introduce some bias if the nonrespondents are all or mostly smokers

• only 10 nonrespondents out of 1236 cases– bias, if present, is small

Birth Weight in Ounes

Frequency

1601401201008060

3

2

1

0

Unknown Smoking Status

Smoking Status

Bir

th W

eig

ht

UnknownSmokerNonsmoker

175

150

125

100

75

50

Nonrespondents

Rank

Birth Weight

in Ounces

1 90 Minimum 2 106 3 108 Q1 4 115 5 126 128 Median

6 130 7 141 8 142 Q3 9 151

10 158 Maximum

193511421.5

57511081.5

511.5

34108142

3

1

IQRQ

IQRQ

IQR

IQR

Birth Weight in Ounces

Perc

ent

1601401201008060

14

12

10

8

6

4

2

0

Smoking StatusNonsmokerSmoker

Confidence Intervals

124.1) (122.0, 742

17.401.645123.05 99%

124.3) (121.8, 742

17.401.96123.05 95%

124.7) (121.4, 742

17.402.576123.05 99%

17.40 123.05 742

Nonsmokers

sxn

115.5) (112.8, 484

18.101.645114.11 99%

115.7) (112.5, 484

18.101.96114.11 95%

116.2) (112.0, 484

18.102.576114.11 99%

18.10 114.11 484

Smokers

sxn

90% Confidence Interval for the Proportion of Smokers

0.418) (0.372,

0.0231230

1

1230

744

1230

4861.645

4

)(1*

0.3951230

486

41226

2484

n

ppz

p

~~

~