Statistics for Scientists

Material for Session 6: Comparing groups of numbers

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There are many statistical tests for comparing two or more groups of measured numbers to see if they are different.

The choice of test is determined by the structure of the data (how many groups, etc.), and the nature of the measurements (normally distributed or not).

One method of arranging these tests is as follows:

For Unpaired Data

For Paired Data

Two Groups (e.g.: Drug vs. Placebo)

Normally Distributed Data:

  • Unpaired Student t test

Non-Normally Distributed Data:

  • Transform to Normal (Log, etc.), then use Unpaired Student t test
  • Mann-Whitney U test
  • Wilcoxon Sum-of-Ranks test

Normally Distributed Data:

  • Paired Student t test

Non-Normally Distributed Data:

  • Transform to Normal (Log, etc.), then use Paired Student t test)
  • Sign Test
  • Wilcoxon Signed-Ranks test

More Than Two Groups:

Normally Distributed Data:

  • Factorial Analysis of Variance (ANOVA)

  • Single Basis of Grouping; Any Number of Groups:

    • One-Way Factorial ANOVA

  • Multiple Bases of Grouping:

  • N-Way Factorial ANOVA

Non-Normally Distributed Data:

  • Try to Normalize

Normally Distributed Data:

  • Repeated -Measures ANOVA

  • Single Basis of Grouping; Any Number of Groups:

    • One-Way Repeated-Measures ANOVA

  • Multiple Bases of Grouping:

    • N-Way Repeated-Measures ANOVA

Non-Normally Distributed Data:

  • Try to Normalize

One or More Continuous Variables as Predictors or Confounders:

Normally Distributed Data:

  • Analysis of Covariance (ANCOVA)

Non-Normally Distributed Data:

  • Try to Normalize

More Than One Outcome Variable:

Normally Distributed Data:

  • Multiple Analysis of Variance (MANOVA)

Non-Normally Distributed Data:

  • Try to Normalize

All Possible Combinations of Above:

Normally Distributed Data:

  • General Linear Model

Non-Normally Distributed Data:

  • Try to Normalize