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Sample Size and Power

NRSA Trainees Research Conference Slide Presentation (Text Version)

By Paula Diehr

On June 5, 2004, Paula Diehr made a presentation at the 10th Annual National Research Service Award (NRSA) Trainees Research Conference. This is the text version of her presentation. Select to access the PDF file (335 KB). Plugin Software Help.

Page 1

Sample Size and Power

Paula Diehr
5-6-2004

Before the study, estimate the approximate number of subjects required to achieve a specified goal.

Approximate because:

  • Poor data for estimates of parameters.
  • Normality assumptions (rarely a problem).
  • Murphy's Law.
  • Etc.

Outline

I. Easy part: the formulas:

  • Hypothesis Testing.
  • Estimation.
  • Software.
  • Simulation.
II. Harder part: the data to put into the formulas.
III. Sample size for Cluster Randomized Trials.
IV. Summary.

Page 3

Simple part, the formulas

Review of the normal distribution.

Figure of a bell curve, with apex at 0.

The area to the left of Zc is c.

The area to the left of Z1-α is 1-α.

Z.975 = 1.96
Z.95 = 1.645
Z.80 = .84

Zc = -Z1-c

Page 1

Review of Hypothesis Testing

H0 Null Hypothesis μ1 = μ2
H1 Alternative Hypothesis μ1 . μ2

Errors:

  Truth = H0 Truth = H1
Conclusion:    
H0 - Type II (β)
H1 Type I (α) -

Pr (Type I error) =α (we can select,.05)

(multiple comparisons?)

Pr (Type II error)=β (we can select by making N large enough, .8)

1-β = power = probability that we detect an effect (reject H0) when there really is one.

This is why sample size is important.

Cohen says mean power~.4 in studies (β=.6), so most were hopeless from the start.

Page 4

The idea

Figure of a bell curve, with apex at 0.

N(0,1)

Figure of two bell curves, one with its apex at 0, the other with its apex at 0.5.

N(0,1) Null
N(.5,1)
Alternative (N=1)

Figure of two bell curves, one with its apex at 0, the other with its apex at 0.5.

dist'n of
x sub1 - x sub2 over s/ divided by N
(N=10)

(N=50)

(N=100)

Page 5

Magic Formula:

2 groups

D = μ1 - μ2

(Z1-α + Z1-β)2 = D2
___________
s12      s22
____ + ____
N1      N2

(use 1-α/2 for 2-tailed tests)

Example Data

Number of visits in 14 months in a combined population of an HMO (GHC) and an indemnity plan (KCM) in the early 1970's. (1689 subjects).

  Pop Sample
mean = 4.5 μ x¯
sd = 6.3 σ s

Proportion of people hospitalized in one year
variance = p(1-p)

GHC   .05   Var=.05*.95, sd=.22
KCM   .10   Var=.10*.90, sd=.30

Page 6

Examples

Continuous Variable: Plan a new study to look for differences in Visits/year between a new HMO and a new indemnity plan. Want enough power to detect small but important differences in visits between the two plans.

What's an "important" difference?
1 visit per year?   D=1

GH vs KC : = 5 :=4 F=6.3 (estimated from old data) Magic Formula (one-tailed test): If N1 = N2 = N, (Equal #'s in each group), solve for N as: Want 80% power $=.2 (why 80%?) Z1-$ = Z.80=.8416

Current as of September 2004

Internet Citation:

Sample Size and Power. Text Version of a Slide Presentation at a National Research Service Award (NRSA) Trainees Research Conference. Agency for Healthcare Research and Quality, Rockville, MD. http://www.ahrq.gov/fund/training/diehrtxt.htm

 
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