One-way ANOVA


One-way analysis of variance is used to test the difference between the means of several subgroups of a variable (multiple testing).

Required input

  • Dependent data: select a continuous variable.

  • Factor: select a categorical or qualitative variable. This variable may either contain character or numeric codes. These codes are used to break-up the data into a one-way classification table.
  • Optionally select a filter to include a subset of cases.


  • Logarithmic transformation: if the data require a logarithmic transformation (e.g. when the data are positively skewed), select the Logarithmic transformation option.
  • Post-hoc test: this is the test used for pairwise comparison of subgroups, when the ANOVA test is positive (i.e. P is less than the selected significance level, see below). offers 3 post-hoc tests (in order of decreasing power): the Student-Newman-Keuls test, the Tukey-Kramer test and Scheffé's test.
  • Significance level: the desired significance level for the post-hoc test. If the ANOVA test results in a P-value less than this significance level, performs the selected post-hoc test.
  • Residuals: you can select a Tests for Normal distribution of the residuals.


Levene's Test for Equality of Variances

Prior to the ANOVA test, Levene's Test for Equality of Variances is performed. If the Levene test is positive (P<0.05) then the variances in the different groups are different (the groups are not homogeneous) and you may need to apply a logarithmic transformation to the data, or use a non-parametric statistic.


The results of the ANOVA are presented in an ANOVA table, followed by the F statistic and associated P value. If the P value is less than 0.05 (or another preselected significance level), then you can accept the hypothesis that there is an influence of the qualitative factor on the dependent data, or that the means of at least two of the subgroups differ significantly.

Post-hoc test

If the ANOVA test is positive (P less than the selected significance level) then performs a post hoc test (using either Student-Newman-Keuls', Tukey-Kramer's or Scheffé's method) for pairwise comparison of subgroups.

Logarithmic transformation

If you selected the Logarithmic transformation option, the program performs the calculations on the logarithms of the dependent variable, but the different means are back-transformed and reported as the geometric means.

Analysis of residuals

See Analysis of residuals.


  • Altman DG (1991) Practical statistics for medical research. London: Chapman and Hall.
  • Armitage P, Berry G, Matthews JNS (2002) Statistical methods in medical research. 4th ed. Blackwell Science.
  • Sheskin DJ (2004) Handbook of parametric and nonparametric statistical procedures. 3rd ed. Boca Raton: Chapman & Hall /CRC.
  • Snedecor GW, Cochran WG (1989) Statistical methods, 8th edition. Ames, Iowa: Iowa State University Press.

See also


Go to One-way ANOVA.