ANOVA Model

(noun)

Analysis of variance model; used to analyze the differences between group means and their associated procedures in which the observed variance in a particular variable is partitioned into components attributable to different sources of variation.

Related Terms

  • ANCOVA model
  • concomitant
  • covariance
  • qualitative variable

(noun)

Analysis of variance; used to analyze the differences between group means and their associated procedures (such as "variation" among and between groups), in which the observed variance in a particular variable is partitioned into components attributable to different sources of variation.

Related Terms

  • ANCOVA model
  • concomitant
  • covariance
  • qualitative variable

Examples of ANOVA Model in the following topics:

  • Qualitative Variable Models

    • Dummy variables are "proxy" variables, or numeric stand-ins for qualitative facts in a regression model.
    • Analysis of variance (ANOVA) models are a collection of statistical models used to analyze the differences between group means and their associated procedures (such as "variation" among and between groups).
    • One type of ANOVA model, applicable when dealing with qualitative variables, is a regression model in which the dependent variable is quantitative in nature but all the explanatory variables are dummies (qualitative in nature).
    • This type of ANOVA modelcan have differing numbers of qualitative variables.
    • Graph showing the regression results of the ANOVA model example: Average annual salaries of public school teachers in 3 regions of a country.
  • ANOVA Design

    • It is also common to apply ANOVA to observational data using an appropriate statistical model.
    • 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 ($xy$, $xz$, $yz$, $xyz$).
    • Random effects models are used when the treatments are not fixed.
    • The fixed-effects model would compare a list of candidate texts.
    • 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
  • 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.
    • Another term for the two-way ANOVA is a factorial ANOVA.
    • 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 ( $xy$, $xz$, $yz$, $xyz$).
    • 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.
  • ANOVA Assumptions

    • The results of a one-way ANOVA can be considered reliable as long as certain assumptions are met.
    • The results of a one-way ANOVA can be considered reliable as long as the following assumptions are met:
    • Kempthorne uses the randomization-distribution and the assumption of unit-treatment additivity to produce a derived linear model, very similar to the one-way ANOVA discussed previously.
    • The test statistics of this derived linear model are closely approximated by the test statistics of an appropriate normal linear model, according to approximation theorems and simulation studies.
    • In summary, the normal model based ANOVA analysis assumes the independence, normality and homogeneity of the variances of the residuals.
  • ANOVA

    • A consumer looking for a new car might compare the average gas mileage of several models.
    • ANOVA is a collection of statistical models used to analyze the differences between group means and their associated procedures (such as "variation" among and between groups).
    • 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 .
    • Recognize how ANOVA allows us to test variables in three or more groups.
  • An alternative test statistic

    • The analysis of variance (ANOVA) technique introduced in Section 5.5 uses this general principle.
    • ANOVA can be further employed in advanced regression modeling to evaluate the inclusion of explanatory variables, though we leave these details to a later course.
  • Introduction

    • Discuss two uses for the F distribution: One-Way ANOVA and the test of two variances.
    • A consumer looking for a new car might compare the average gas mileage of several models.
    • 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.
    • For further information about One-Way ANOVA, use the online link ANOVA2 .
  • Further Discussion of ANOVA

    • Due to the iterative nature of experimentation, preparatory and follow-up analyses are often necessary in ANOVA.
    • Power analysis is often applied in the context of ANOVA in order to assess the probability of successfully rejecting the null hypothesis if we assume a certain ANOVA design, effect size in the population, sample size and significance level.
    • Eta-squared is a biased estimator of the variance explained by the model in the population (it estimates only the effect size in the sample).
    • It is prudent to verify that the assumptions of ANOVA have been met.
    • Residuals should have the appearance of (zero mean normal distribution) noise when plotted as a function of anything including time and modeled data values.
  • 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.
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