two-way ANOVA

(noun)

an extension of the one-way ANOVA test that examines the influence of different categorical independent variables on one dependent variable

Related Terms

Examples of two-way ANOVA in the following topics:

  • Two-Way ANOVA

    • Two-way ANOVA examines the influence of different categorical independent variables on one dependent variable.
    • As with other parametric tests, we make the following assumptions when using two-way ANOVA:
    • 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.

  • 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.
    • Age would have three levels and gender would have two levels.

  • 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.
    • You will also study the F distribution, used for One-Way ANOVA, and the test of two variances.
    • This is just a very brief overview of One-Way ANOVA.
    • For further information about One-Way ANOVA, use the online link ANOVA2 .

  • ANOVA Design

    • One-way ANOVA is used to test for differences among two or more independent groups.
    • Typically, however, the one-way ANOVA is used to test for differences among at least three groups, since the two-group case can be covered by a $t$-test.
    • When there are only two means to compare, the $t$-test and the ANOVA $F$-test are equivalent.
    • 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 ($xy$, $xz$, $yz$, $xyz$).
    • Differentiate one-way, factorial, repeated measures, and multivariate ANOVA experimental designs; single and multiple factor ANOVA tests; fixed-effect, random-effect and mixed-effect models

  • The One-Way F-Test

    • The $F$-test as a one-way analysis of variance assesses whether the expected values of a quantitative variable within groups differ from each other.
    • Note that when there are only two groups for the one-way ANOVA $F$-test, $F=t^2$ where $t$ is the Student's $t$-statistic.
    • The alternate hypothesis says that at least two of the sorority groups come from populations with different normal distributions.
    • This chart shows example p-values for two F-statistics: p = 0.05 for F = 3.68, and p = 0.00239 for F = 9.27.
    • Explain the purpose of the one-way ANOVA $F$-test and perform the necessary calculations.

  • ANOVA

    • ANOVA is a statistical tool used in several ways to develop and confirm an explanation for the observed data.
    • For hypothesis tests involving more than two averages, statisticians have developed a method called analysis of variance (abbreviated ANOVA).
    • In its simplest form, ANOVA provides a statistical test of whether or not the means of several groups are equal, and therefore generalizes t-test to more than two groups.
    • The calculations of ANOVA can be characterized as computing a number of means and variances, dividing two variances and comparing the ratio to a handbook value to determine statistical significance.
    • In short, ANOVA is a statistical tool used in several ways to develop and confirm an explanation for the observed data.

  • 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:

  • Introduction

    • Analysis of Variance (ANOVA) is a statistical method used to test differences between two or more means.
    • ANOVA is used to test general rather than specific differences among means.
    • 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.

  • Multiple comparisons and controlling Type 1 Error rate

    • We would like to conduct an ANOVA for these data.
    • In this case (like many others) it is difficult to check independence in a rigorous way.
    • This results in a T score of 1.46 on df = 161 and a two-tailed p-value of 0.1462.
    • This results in a T score of 2.60 on df = 161 and a two-tailed p-value of 0.0102.
    • However, this does not invalidate the ANOVA conclusion.

  • Summary

    • A One-Way ANOVA hypothesis test determines if several population means are equal.
    • A Test of Two Variances hypothesis test determines if two variances are the same.
    • The populations from which the two samples are drawn are normally distributed.