Definition

Noun: 1. A statistical method for comparing group means: A mathematical procedure used to determine if there are statistically significant differences between the means of two or more independent groups. It tests the hypothesis that the means of these groups are equal. 2. A statistical method for testing relationships between variables: A technique that partitions the total observed variation in a data set into components associated with specific sources of variation (e.g., differences between groups and variation within groups) to test for significant relations.

Usage Examples

• Noun:
  • The researcher used an analysis of variance to determine if the three different fertilizers produced different average crop yields.
  • Before comparing the individual group means, you must first perform an analysis of variance to see if any significant overall difference exists.
  • The results of the analysis of variance indicated a significant effect of training method on performance speed (F(2, 57) = 9.84, p < .01).

Advanced Usage

• "To run an analysis of variance": To perform or execute this statistical test.
  • We will need to run an analysis of variance on the survey data to compare the responses from the four age groups.
• "One-way analysis of variance": The simplest form, used to compare the means of three or more groups based on one independent variable.
  • A one-way analysis of variance was conducted to compare the effect of dosage level on reaction time.
• "Factorial analysis of variance": A more complex form used to analyze the influence of two or more independent variables and their interaction.
  • A 2x3 factorial analysis of variance examined the effects of both gender and anxiety level on test scores.

Variants and Related Words

• ANOVA (n): The common acronym for "analysis of variance."
  • The ANOVA showed a significant main effect.
• Multivariate analysis of variance (MANOVA) (n): An extension of ANOVA used when there are multiple dependent variables.
  • A MANOVA was used to analyze the effects on both reading and math scores simultaneously.
• Analysis of covariance (ANCOVA) (n): A statistical technique that blends ANOVA and regression, used to control for the effect of a continuous confounding variable.
  • An ANCOVA was performed with pretest scores as the covariate.

Synonyms

• F-test: Refers specifically to the statistical test (the F-ratio) that is the core result of an analysis of variance.
• Variance analysis: A less common, direct synonym.

Related Phrases

• Main effect: In ANOVA, the direct effect of an independent variable on the dependent variable.
• Interaction effect: In factorial ANOVA, when the effect of one independent variable depends on the level of another independent variable.
• Within-group variance: The variation of scores within each experimental group.
• Between-group variance: The variation of the mean scores between the different experimental groups.

Noun

1. a statistical method for making simultaneous comparisons between two or more means; a statistical method that yields values that can be tested to determine whether a significant relation exists between variables