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1

How to Determine Sample Size

1) Heuristics ( 100/group, Minimum of 20 to 50 per subgroup, Disproportionate sampling)
2) Budget constraints( Sample size = total budget/cost per subject)
3) Previous Research
4) Formal Statistics

2

precision

the size of the estimating interval

3

confidence

the degree of certainty that the true value falls within the estimating interval

4

formal statistics

trade off btw precision and confidence

5

Confidence interval for a population mean is:

X + Z* (s / sq. rt n)

6

T =

margin of error you are willing to tolerate, i.e.,
zone around sample mean where population mean lies, or half CI width

7

T = (equation)

z * (s / sq. rt. n)

8

Three pieces of information are needed for estimating for a mean sample size

1. Margin of error T (zone around sample mean where population mean lies)
2. Your confidence level
For 90% confidence, z = 1.645 For 95% confidence, z = 1.96 For 99% confidence, z= 2.575
3. Estimate of the population standard deviation (SD) s

9

Estimating the population SD

Review prior research Conduct a pilot study
Use conservation guesses

10

conservation guess for 5-item rating/Likert scale

use s=1.4

11

conservation guess for 7-item rating/Likert scale

use s=2

12

conservation guess for 9, 10, 11-item rating scale

use s=3

13

conservation guess for responses measured by ratio scales

use s=range/4

14

Three pieces of information are needed for estimating a proportion sample size

1. Margin of error T
2. Confidence level
For 90% confidence, z = 1.645 For 95% confidence, z = 1.96 For 99% confidence, z= 2.575
3. Estimate of the population proportion p

15

Estimating the Population Proportion p

 Review prior research
 Find secondary data (e.g., US census)  Conduct a pilot study
 Make an informed guess
 Use the most conservative guess: p=0.5

16

Sample Size Required for a Survey with Multiple Questions

-calculate ideal sample size for each question
-go with highest among all questions and the most critical questions

17

total sampling elements (TSE) =

n / { (1- BCI) (1-U) (1-R) (1-I) }

18

BCI =

proportion that are expected to have bad contact

19

U =

proportion that are expected to be unreachable

20

R =

proportion that are expected to refuse to participate

21

I =

proportion that are expected to be ineligible

22

assume that the population is

very large