Key Concepts

• The null hypothesis is that all the group population means are the same. The alternative hypothesis is that at least one pair of means is different.
• A one-way ANOVA uses variances to help determine if the means are equal or not.
• To perform a one-way ANOVA certain assumptions must be met:
  • Each population from which a sample is taken is assumed to be normal.
  • All samples are randomly selected and independent.
  • The populations are assumed to have equal standard deviations or variances.
  • The factor is a categorical variable. (In the introductory example, type of swimming is the factor).
  • The response is a numerical variable. (In the introductory example, the amount of money is a numerical variable).

Glossary

One-Way ANOVA: a method of testing whether or not the means of three or more populations are equal; The test statistic for analysis of variance is the F-ratio.

Variance: mean of the squared deviations from the mean; the square of the standard deviation. For a set of data, a deviation can be represented as [latex]x- \overline{x}[/latex] where [latex]x[/latex] is a value of the data and [latex]\overline{x}[/latex] is the sample mean. The sample variance is equal to the sum of the squares of the deviations divided by the difference between the sample size and one.