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Sample Size Estimation

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TWO WAYS

EMPIRICAL

ANALYTICAL

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REQUIREMENTS

1 – THE PARAMETERS (PROPORTION OR AVERAGE)

2 – THE DEGREE OF PRECISSION (α)

3 – THE DESIRED CONFIDENCE LEVEL (Z)

4 – THE ESTIMATED DEGREE OF VARIABILITY

OF OBSERVATION (STANDARD DEVIATION)

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EXAMPLE 1ESTIMATING THE MEAN

Q1 WHAT PARAMETER DO YOU WANT TO STUDY

ANSWER I WANT TO ESTIMATE THE AVERAGE INCREASE IN BODY

WTS OF INFANT RATS GIVEN TREATMENT A WITH A CERTAIN

PERIOD OF TIME

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Q2 WHAT IS EXPECTED S.D.• S.D. = 20 GM

• Q 3 HOW MUCH ERROR TOLERABLE

• ANSWER A : 10 GM OR LESS

• ANSWER B 5% OF AVERAGE

• Q 4 WHAT IS AVERAGE

• ANSWER MEAN = 100GM

• HOW CONFIDENT DO YOU WANT TO BE ?

• 95% = {Z}

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IN CASE OF ANS A TO Q3

N= (Z )2 (S)2

e 2

= 1.96 x 1.96 x 20 x 20 = 16 10 x 10

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IN CASE OF ANS B TO Q3

N= (Z )2 (S)2

e2

= 1.96 x 1.96 x 20 x 20 = 62 5X5

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Sample size estimationSample size estimation:

n = Z 2 Pqe2

Z = 1.96 deviant error for .05

P = Prevalence

q = 1 - P

e = Tolerance error (5)(.01 ---> .1)

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IN CASE OF prevalence as 20%

N= (Z )2(pq)

e2

= 1.96 x 1.96 x 20 x 80 = 2465 x5

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IN CASE OF prevalence as 20%

N= (Z )2(pq)

e2

= 1.96 x 1.96 x 20 x 80 = 246 X25 = 1 x1

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Objectives

At the end of session participant will be able to:

Understand the role of standard deviation in estimating sample size in

continuous type of data

Understand the role of proportion in estimating sample size in discrete type of

data

Effect of confidence interval on the sample size

Impact of selecting a lower chance of error on sample size

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TutorialA study has been planned to estimate the Factors effecting the prevalence of hypertension in a community.

The prevalence of hypertension from some previous study in the same area was 10%. Assuming the standard confidence interval as well as level of significance, What sample size should be selected to have an appropriate confidence interval regarding proportion.