Title: Sample Size
2.6: Assumptions to estimate a sample size
Chapter Summary:
In this chapter, we will look at the importance of a sample size, and the assumptions behind
estimating the sample size.
At the end of this chapter:
You should be able to use an online sample size estimator to estimate the sample size for
your study, or provide enough information to a statistician to estimate a sample size for you
You have defined your research question. You have a hypothesis in hand and are now ready
to start research that will either prove or disprove your hypothesis. You have searched the
literature, found evidence to indicate that it is worth the while to pursue your question. You
have then gone about choosing an appropriate design for your study and have decided the
variables to study. You are now reached a very important question
HOW MANY SUBJECTS DO I NEED TO STUDY?
The number of subjects to study is important for several reasons

Ensures that there are enough subjects in the study to minimize the risk of drawing
wrong conclusions

Provides an understanding of the resources needed to complete the study (before
you actually start the study) and gives a very good indication of the study is feasible
within your resources

The sample size assumes particular significance when we do not find any significant
difference between groups- we need to show that this lack of difference is true and
not because we did not study an adequate number of subjects.
Needless to say, the sample size for a study has to be estimated before the study starts.
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Sample size estimations can turn out to be complex, especially for RCTs, and you may be
better off letting a biostatistician do the sample size. However, knowledge of the
assumptions behind sample size estimations will help you provide meaningful information to
the biostatistician, which of course will help the biostatistician estimate sample size easily.
Results of your study
Conclude treatments are not
The Truth
Treatments are not different
Treatment are different
Correct Decision
Type II Error (β)
Type I Error (α)
Correct Decision (1- β)
different
Conclude treatments are
different
POWER
α= probability of a type I error; the probability of concluding that the treatments are
different when actually the treatments do not differ
β= probability of making a type II error; probability of concluding that the treatments do
not differ when actually the treatments do differ
Power= probability of correctly concluding that the treatments do differ; and the probability
of detecting a difference between the treatments if they do differ.
Sample size for a proportion, or descriptive study
Input Data:

Population size

Expected prevalence of the condition of interest or the expected proportion

Confidence limits or the absolute precision (how much deviation are you willing to
tolerate- usually kept between 5-15% but can vary depending on what you are
studying)

Design Effect for complex cluster surveys (used if the selection is not random or
systematic in nature)
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Sample size for an unmatched case control study
Input Data

Two sided confidence interval (1- α)-confidence intervals usually chosen between 9099%, commonly 95%

Power (1- β)- usually, ≥80% chosen as power. The minimum power should be 80%

Ratio of cases to controls

Percent of controls exposed to the factor of interest (between 0 and 99.99)

Percentage of cases with exposure to the factor of interest (between 0 and 99.99)

Odds ratio of interest
Sample Size for cross sectional, cohort and RCT

Two sided confidence interval (1- α)-confidence intervals usually chosen between 9099%, commonly 95%

Power (1- β)- usually, ≥80% chosen as power. The minimum power should be 80%

Ratio of unexposed to exposed in sample

Percent of unexposed with outcome (between 0 and 99.99)

Percentage of exposed with outcome (between 0 and 99.99)

Odds ratio of interest

Risk/Prevalence ratio

Risk/prevalence difference (between -99.99 to 99.99)
Additional parameters of interest for RCT

Effect size of interest

Superiority, non-inferiority or inferiority margin
Note: Can choose a one sided confidence interval if interested only in results in one
direction.
Sample Size for comparing two means

Two sided confidence interval

Power

Ratio of sample size (group 2/group1)

Mean or mean difference

Standard deviation or variance
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These assumptions or input data will help you derive sample sizes for relatively
uncomplicated studies. You may need to consult a biostatistician for more complex sample
size estimations.
THE FOLLOWING LINK IS USEFUL TO ESTIMATE SAMPLE SIZES (AND FOR MANY STATS
TESTS).
http://www.openepi.com/Menu/OpenEpiMenu.htm
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