l stoodialinza
← All topics

Step 2 · Drawing conclusions · Topic 6 of 17 · 7 min

Test assumptions

Assumptions describe the study design and data model. Diagnostics can reveal some problems, but cannot confirm every condition.

In short#

  • Independence depends on how units were sampled and assigned. Repeated measurements and clustered units require dependence to be handled in the model.
  • In many t-tests and ANOVA models, normality concerns model errors within groups, not all values pooled together. Robustness to departures depends on design, sample size and outliers.
  • Shapiro-Wilk and Levene tests are diagnostics. A non-significant p does not prove normality or equal variances. With small n, a test may have little power; with large n, it can detect small departures.
  • Welch's test compares independent-group means and allows unequal variances. It does not handle dependent observations. Rank tests compare distributions; interpreting a result as a difference in medians requires additional conditions.

In plain words#

Assumptions concern how data were collected and how the model is specified. Plots and tests can help find particular violations, but cannot prove that every condition holds. Assess independence from sampling, randomization, repeated measurements and clustering in the study design.

For many t-tests and ANOVA models, normality concerns model errors within groups, not pooled raw values. Strong skew and outliers matter especially with small samples. A logarithm changes the outcome scale, and a rank test answers a different question, so neither is an automatic replacement.

Linza reports available diagnostics for normality, equal variances and calculation warnings. Compare them with the plots and study design: one p-value neither selects a test nor confirms a model.

In Linza#

  1. The Assumption checks panel provides Shapiro-Wilk tests by group, Levene's test and calculation warnings.
  2. The Which test should I choose? guide in Analyses suggests a method based on the goal, design and variance assumption. Check that its recommendation fits your study design.
  3. For positive values with strong right skew, consider a logarithmic transformation. It changes the outcome scale; the source table remains unchanged.
Try it in Linza Opens in a new tab with synthetic data. Work in the original tab remains unchanged.

Common mistakes#

  • Choosing a test only from a normality-test p-value, especially with four observations.
  • Treating a rank test as a test of equal medians without assuming similar distribution shapes.

Check yourself#

Which assumption cannot be established from outcome values alone, without study-design information?

Optional. Your answer is not saved.

Sources#

  • Delacre M., Lakens D., Leys C. (2017) Why psychologists should by default use Welch's t-test instead of Student's t-test. International Review of Social Psychology, 30(1). Open publication Opens in a new tab
  • Ruxton G.D. (2006) The unequal variance t-test is an underused alternative to Student's t-test and the Mann-Whitney U test. Behavioral Ecology, 17(4). Search for publication Opens in a new tab

References are for further reading. A method’s suitability depends on the study design and its assumptions.