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Sample Size Determination. Everything You Ever Wanted to Know About Sampling Distributions--And More!. Sampling Distribution. A frequency distribution of all the means obtained from all the samples of a given size Example: $$ spent on CD’s at Best Buy Daffy $34.00 Donald $72.00

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sample size determination

Sample Size Determination

Everything You Ever Wanted to Know About Sampling Distributions--And More!

sampling distribution
Sampling Distribution
  • A frequency distribution of all the means obtained from all the samples of a given size
  • Example: $$ spent on CD’s at Best Buy
    • Daffy $34.00
    • Donald $72.00
    • Sylvester $36.00
    • Tweetie Bird $40.00
  • All samples of n=2
your turn
Your Turn:
  • Develop a sampling distribution using n=2
  • Calculate the population mean

CAR

A B C D E

Expected 3 4 5 0 1

Life

sampling distributions
Sampling Distributions
  • The distribution of sample means is skinnier than the distribution of elements
    • Why?
  • The distribution is normal
  • The sampling distribution mean equals the population mean
standard error
Standard Error
  • The variability in the sampling distribution
  • Tells you how reliable your estimate of the population mean is
  • If this is big (good or bad)
  • If this is small (good or bad)
  • WHY?
standard error6
Standard Error

Sxstandard deviation

square root of the sample size

As the samples size gets bigger, the standard error gets __________

confidence intervals
Confidence Intervals
  • CI= Xbar +/- z (standard error)
  • Where:
    • z= _____ for 68% confidence
    • z= _____ for 95% confidence
    • z= _____ for 99.7% confidence
    • (again think Chebychev)
  • What confidence level should you use?
develop a confidence interval
Develop a Confidence Interval
  • Estimate the average number of trips to the beach taken by undergrad students during their 4-6 year career
    • xbar = 5
    • SD = 1.5
    • 95% Confidence Level
    • n=100
slide9
So,
  • There is a 95% chance that if all undergrad students were sampled regarding the number of beach trips that the findings would differ from our results by no more than ____ in either direction.
or maybe better
or, maybe better,
  • If I were to conduct this study 100 times, then I would get _____ different confidence intervals. If I have a 95% confidence interval then ____ of the 100 CI’s will contain the true population mean (mu) and ____ will not.
  • I sure hope that the confidence interval I got is one of the 95 that contains mu!
probably the easiest interpretation
Probably the easiest interpretation:
  • If you have a 95% Confidence Interval - there is a 95% chance that the CI will contain Mu – there is a 5% chance that it won’t.
confidence interval issues
Confidence Interval Issues
  • Reliability (Z)
    • how often we are correct – how often mu falls within the range
  • Precision
    • how wide the confidence interval is
  • The smaller the n, the _____ the CI
  • Given a particular n, the CI will be _______ when we increase the reliability
factors that influence n
Factors that Influence n
  • Precision (H)
    • how skinny must your CI be in order to be able to take action on the results?
  • I will go to a new water park in the area.
    • DWN PWN Maybe PW DW
  • I will pay _____ for a musical card.
  • I will pay _____ for a motorcycle.
more factors that influence n
More Factors That Influence n
  • Confidence level (z)
  • Population SD
  • Time, money and personnel
sample size for interval or ratio data
Sample Size for Interval or Ratio Data

Z2

n= H2 * s2

Where:

z= 1, 1.96, or 3

H= precision (+/-) H

s2= variance (or standard deviation squared)

sample size for nominal or ordinal data
Sample Size for Nominal or Ordinal Data

Z2

n = H2 * (P) (Q)

Where:

Z= 1, 1.96, or 3

H= a percentage (e.g., 0.03--NOT 3)

P = initial estimate of the population proportion

Q= (1-P)

n for proportion of students who read the news paper
n for Proportion of Students Who Read the News Paper
  • Do you read the newsl paper?
      • 1. YES
      • 2. NO
  • Estimate that 60% read the news paper
  • Want a 99 % CI
  • Want a +/- 3% precision
the final sample size
The Final Sample Size
  • Compute n for all nominal, interval and ratio questions
    • most conservative
    • limited resources
non statistical approaches to sample size n
Non-statistical Approaches to Sample Size (n)
  • All you can afford method:
    • subtract costs from budget
    • figure out cost per interview
    • divide leftover budget by cost per interview
  • Rules of thumb