Transcript Population and Sampling Distributions

Chapter Eleven
Sample Size
Determination
Chapter Eleven
Chapter Eleven Objectives
•
Learn the financial and statistical issues in the
determination of sample size
•
Discover methods for determining sample size
•
Gain an appreciation of a normal distribution
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Understand population, sample, and sampling distributions
•
Distinguish between point and interval estimates
•
Recognize problems involving sampling means and
proportions
•
Understand type I and type II errors in statistical
conclusions
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Sample Size for Probability Samples
1. Budget available for survey study
2. Use of “rule of thumb”
3. Number of subgroups to be analyzed
4. Application of traditional statistical methods
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Normal Distribution
Central Limit Theorem:
• A distribution of a large number of sample means or
sample proportions will approximate a normal
distribution, regardless of the distribution of the
population from which they were drawn
Normal Distribution:
• The continuous distribution that is bell shaped and
symmetrical about the mean
• The mean, median, and mode are equal
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Normal Distribution
Proportionate Properties:
• The number of observations falling between the
mean and a given number of standard deviations
from the mean is the same for all normal
distributions
Standard Normal Distribution:
• Normal distribution with a mean of zero and a
standard deviation of one
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Normal Distribution
Standard Deviation:
Standard
Deviation
=
sum
Measure of dispersion calculated by:
1. Subtracting the mean of the series from each value in a
series
2. Squaring each result
3. Summing the results
4. Dividing the sum by the number of observations minus 1,
and taking the square root of this value
(X1- X)
(N-1)
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2
Population and Sampling Distributions
Population Distributions:
• Frequency distribution of all the elements of population
Sampling Distributions:
• Frequency distribution of all elements of an individual sample
Sampling Distribution of the Mean:
• Theoretical frequency distribution of the means of all possible
samples of a given size drawn from a population
• It is normally distributed.
Standard Error of the Mean:
• Standard deviation of a distribution of sample means
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Point and Interval Estimates
Point Estimate:
• Estimate of a population value
Interval Estimate:
• Interval or range of values within which the true population
value is estimated to fall
Confidence Level:
• The probability that a particular interval will include the true
population value
Confidence Interval:
• The interval that, at the specified confidence level, includes the
true population value
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Sampling Distribution of the Proportion
Sampling Distribution of the Proportion:
• Relative frequency distribution of the sample
proportions of many random samples of a given size
drawn from a particular population
• It is normally distributed
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Determining Sample Size
Problems involving means:
o
Chapter Eleven
Determining Sample Size
Problems involving proportions:
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Statistical Power
Probability of not making a type II error
Type I Error:
• The error of concluding something that doesn’t exist
• E.g., concluding that there is a difference in the responses of 2
groups when there is no difference
Type II Error:
• The failure to conclude something when it indeed exists
• E.g., concluding there is no difference in the responses of the
two groups when there is a difference
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Key Sampling Considerations
1.
2.
3.
4.
5.
6.
Time to generate sample
Scope of the research
Budget available
Experience with sampling
Level of accuracy desired
Your knowledge of the
population
Chapter Eleven