ANOVA

(noun)

Analysis of variance—a collection of statistical models used to analyze the differences between group means and their associated procedures (such as "variation" among and between groups).

Related Terms

Examples of ANOVA in the following topics:

  • F Distribution and One-Way ANOVA: Purpose and Basic Assumptions of One-Way ANOVA

    • The purpose of a One-Way ANOVA test is to determine the existence of a statistically significant difference among several group means.
    • In order to perform a One-Way ANOVA test, there are five basic assumptions to be fulfilled:

  • Reading an ANOVA table from software

    • The calculations required to perform an ANOVA by hand are tedious and prone to human error.
    • An ANOVA can be summarized in a table very similar to that of a regression summary, which we will see in Chapters 7 and 8.
    • Table 5.30 shows an ANOVA summary to test whether the mean of on-base percentage varies by player positions in the MLB.
    • ANOVA summary for testing whether the average on-base percentage differs across player positions.

  • Two-Way ANOVA

    • The two-way analysis of variance (ANOVA) test is an extension of the one-way ANOVA test that examines the influence of different categorical independent variables on one dependent variable.
    • While the one-way ANOVA measures the significant effect of one independent variable (IV), the two-way ANOVA is used when there is more than one IV and multiple observations for each IV.
    • Another term for the two-way ANOVA is a factorial ANOVA.
    • Caution is advised when encountering interactions in a two-way ANOVA.
    • Distinguish the two-way ANOVA from the one-way ANOVA and point out the assumptions necessary to perform the test.

  • Introduction

    • ANOVA is used to test general rather than specific differences among means.
    • ANOVA tests the non-specific null hypothesis that all four population means are equal.
    • The Tukey HSD is therefore preferable to ANOVA in this situation.
    • Some textbooks introduce the Tukey test only as a follow-up to an ANOVA.
    • A second is that ANOVA is by far the most commonly-used technique for comparing means, and it is important to understand ANOVA in order to understand research reports.

  • Introduction

    • Discuss two uses for the F distribution: One-Way ANOVA and the test of two variances.
    • In this chapter, you will study the simplest form of ANOVA called single factor or One-Way ANOVA.
    • This is just a very brief overview of One-Way ANOVA.
    • One-Way ANOVA, as it is presented here, relies heavily on a calculator or computer.
    • For further information about One-Way ANOVA, use the online link ANOVA2 .

  • ANOVA

    • ANOVA is a statistical tool used in several ways to develop and confirm an explanation for the observed data.
    • ANOVA is the synthesis of several ideas and it is used for multiple purposes.
    • ANOVA with a very good fit and ANOVA with no fit are shown, respectively, in and .
    • This graph is a representation of a situation with a very good fit in terms of ANOVA statistics
    • Recognize how ANOVA allows us to test variables in three or more groups.

  • ANOVA Design

    • There are several types of ANOVA.
    • Some popular designs use the following types of ANOVA.
    • ANOVA generalizes to the study of the effects of multiple factors.
    • The use of ANOVA to study the effects of multiple factors has a complication.
    • In a 3-way ANOVA with factors $x$, $y$, and $z$, the ANOVA model includes terms for the main effects ($x$, $y$, $z$) and terms for interactions ($xy$, $xz$, $yz$, $xyz$).

  • Analysis of Variance Designs

    • There are many types of experimental designs that can be analyzed by ANOVA.
    • In describing an ANOVA design, the term factor is a synonym of independent variable.
    • An ANOVA conducted on a design in which there is only one factor is called a one-way ANOVA.
    • If an experiment has two factors, then the ANOVA is called a two-way ANOVA.

  • Graphical diagnostics for an ANOVA analysis

    • There are three conditions we must check for an ANOVA analysis: all observations must be independent, the data in each group must be nearly normal, and the variance within each group must be approximately equal.
    • Sometimes in ANOVA there are so many groups or so few observations per group that checking normality for each group is not reasonable.
    • Independence is always important to an ANOVA analysis.

  • Introduction to comparing many means with ANOVA

    • In this section, we will learn a new method called analysis of variance (ANOVA) and a new test statistic called F.
    • ANOVA uses a single hypothesis test to check whether the means across many groups are equal:
    • Generally we must check three conditions on the data before performing ANOVA:
    • When these three conditions are met, we may perform an ANOVA to determine whether the data provide strong evidence against the null hypothesis that all the µi are equal.
    • Strong evidence favoring the alternative hypothesis in ANOVA is described by un- usually large differences among the group means.