Sampling for Estimation. Instructor: Ron S. Kenett Email: ron@kpa.co.il Course Website: www.kpa.co.il/biostat Course textbook: MODERN INDUSTRIAL STATISTICS, Kenett and Zacks, Duxbury Press, 1998. Course Syllabus. Understanding Variability Variability in Several Dimensions
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
Instructor: Ron S. Kenett
Email: ron@kpa.co.il
Course Website: www.kpa.co.il/biostat
Course textbook: MODERN INDUSTRIAL STATISTICS,
Kenett and Zacks, Duxbury Press, 1998
(c) 2001, Ron S. Kenett, Ph.D.
(c) 2001, Ron S. Kenett, Ph.D.
(c) 2001, Ron S. Kenett, Ph.D.
(c) 2001, Ron S. Kenett, Ph.D.
Probability, or Scientific, Samples: Each element to be sampled has a known (or calculable) chance of being selected.
(c) 2001, Ron S. Kenett, Ph.D.
Probability, or Scientific, Samples: Each element to be sampled has a known (or calculable) chance of being selected.
(c) 2001, Ron S. Kenett, Ph.D.
Nonprobability Samples: Not every element has a chance to be sampled. Selection process usually involves subjectivity.
(c) 2001, Ron S. Kenett, Ph.D.
Nonprobability Samples: Not every element has a chance to be sampled. Selection process usually involves subjectivity.
(c) 2001, Ron S. Kenett, Ph.D.
s
=
.
x
n
Distribution of the Mean
(c) 2001, Ron S. Kenett, Ph.D.
n

m
m
sample
mean
x
–
=
=
z
s
standard
error
n
The Standardized Mean
Standardized sample mean
(c) 2001, Ron S. Kenett, Ph.D.
(c) 2001, Ron S. Kenett, Ph.D.
s
=
.
x
n
Distribution of the Mean
(c) 2001, Ron S. Kenett, Ph.D.
Distribution of the Proportion
(c) 2001, Ron S. Kenett, Ph.D.
׳
p
(
1
–
)
s
=
.
p
n
Distribution of the Proportion
(c) 2001, Ron S. Kenett, Ph.D.
׳
p
(
1
–
)
s
=
p
n

p
sample
proportion
p
p
–
=
=
z
p
׳
p
(
1
–
)
standard
error
n
Distribution of the Proportion
Standardized sample proportion
(c) 2001, Ron S. Kenett, Ph.D.
(c) 2001, Ron S. Kenett, Ph.D.
i
x
x
=
n
2
(
x
–
x
)
2
2
i
=
s
s
n
–
1
x
successes
p
p
=
n
trials
Unbiased Point Estimates
Population Sample
Parameter Statistic Formula
(c) 2001, Ron S. Kenett, Ph.D.
z
:
–
z
0
z
s
s
׳
+
׳
x
:
x
–
z
x
x
z
n
n
Confidence Intervals: µ, s Known
where = sample mean ASSUMPTION:
s = population standard infinite population
deviation
n = sample size
z = standard normal score
for area in tail = a/2
(c) 2001, Ron S. Kenett, Ph.D.
t
:
–
t
0
t
s
s
׳
+
׳
x
:
x
–
t
x
x
t
n
n
Confidence Intervals: µ, s Unknown
where = sample mean ASSUMPTION:
s = sample standard Population
deviation approximately
n = sample size normal and
t = tscore for area infinite
in tail = a/2
df = n– 1
(c) 2001, Ron S. Kenett, Ph.D.
(
1
–
p
)
p
(
1
–
p
)
׳
+
׳
p
:
p
–
z
p
p
z
Confidence Intervals on p
where p = sample proportion ASSUMPTION:
n = sample size n•p > 5,
z = standard normal score n•(1–p) >5,
for area in tail = a/2 and population
infinite
(c) 2001, Ron S. Kenett, Ph.D.
n
n
Interpretation of Confidence Intervals
OR
(c) 2001, Ron S. Kenett, Ph.D.
=
׳
e
z
n
2
2
׳
s
z
=
n
2
e
Sample Size Determination for
Infinite Populations
(c) 2001, Ron S. Kenett, Ph.D.
Finite Populations
where n = required sample size
N = population size
z = zscore for (1–a)% confidence
(c) 2001, Ron S. Kenett, Ph.D.
(
1
–
p
)
=
׳
e
z
n
2
z
p
(
1
–
p
)
=
n
2
e
Sample Size Determination of p for Infinite Populations
(c) 2001, Ron S. Kenett, Ph.D.
(
1
–
p
)
n
=
2
p
(
1
–
p
)
e
+
N
2
z
Sample Size Determination of p for
Finite Populations
where n = required sample size
N = population size
z = zscore for (1–a)% confidence
p = sample estimator of p
(c) 2001, Ron S. Kenett, Ph.D.