StatTools : Differences Between Measurements (Unpaired Groups) Explained

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Related Links:
Sample Size for Unpaired Differences Program Page
Sample Size for Unpaired Differences Tables Page
Unpaired Difference Programs Page

Introduction Parametric Nonparametric Permutation References
Comparing values between groups is a very common research model in the biomedical domain. The model can be used in epidemiology and surveys, such as comparing birth weight between boys and girls, or in randomized controlled trials, such as allocating different medications to groups of patients and compare their responses.

The research models themselves are complex and sophisticated, requiring careful control of bias. This page does not cover these aspects, but focussed only on the statistical procedures. To select the correct procedure, the following issues are addressed.

  • The nature of the data
    • If the measurements are continuous and normally distributed, the powerful parametric statistical procedures can be used. Examples of parametric measurements are height and weight
    • If the measurements are continuous, but not normally distributed, some form of transformation may be needed before parametric statistical procedures can be used. Examples of transformable measurements are ratios and time to events.
    • If the measurements are not continuous, or if they are not normally distributed and cannot be transformed, then the nonparametric statistical procedures can be used. Examples of nonparametric measurements are 5 point Likert items, 10 point semantic differential scales, and many psychometric measurements.
    • If the data are not measurements, such as counts or classifications, then they cannot be analysed as measurements. Examples of non-measurements are number of adverse events, proportion of surgical complications, sex of newborns.
  • The sample size. Programs in the Sample Size for Unpaired Differences Program Page and tables in the Sample Size for Unpaired Differences Tables Page can be used to estimate sample size requirements. For proper statistical inference, the exact sample size required should be calculated and used. Approximations useful in the early stages of research planning are :
    • Pilot studies requires 6 to 20 subjects per group
    • The main study requires 150-200 subjects per group to detect a small effect, 15-20 for a large effect, and in most clinical research situations 60-70 subjects per group for a moderate effect size.
    • Nonparametric tests have approximately 95-99% the power efficiency of the equivalent parametric tests. Approximately, the sample size calculated for parametric tests should increase by 5%-10% for equivalent nonparametric tests.