# Chapter 11

Analysis of variance (ANOVA)

a hypothesis test typically used with one or more nominal (and sometimes ordinal) independent variables (with at least three groups overall) and a scale dependent variable

F statistic

a ratio of two measures of variance (1) between-groups variance, which indicates differences among sample means, and (2) within-groups variance, which is essentially an average of the sample variances

Between-groups variance

an estimate of the population variance based on the differences among the means

Within-groups variance

an estimate of the population variance based on the differences within each of the three (or more) sample distributions

one-way ANOVA

a hypothesis test that includes both one nominal independent variable with more than two levels and a scale dependent variable

between-groups ANOVA

a hypothesis test in which there are more than two samples, and each sample is composed of different participants

within-groups ANOVA

a hypothesis test in which there are more than two samples, and each sample is composed of the same participants; also called a repeated-measures ANOVA

Homoscedastic

populations are those that have the same variance; homoscedasticity is also called homogeneity of variance

Heteroscedastic

populations are those that have different variances

two samples

The F statistic, used in an analysis of variance (ANOVA), is essentially an expansion of the z statistic and the t statistic that can be used to compare more than _____ _____

within samples

Like the z statistic and the t statistic, the F statistic is a ratio of difference between group means (in this case, using a measure of variability) to a measure of variability ____ ____

one independent variable

One-way between-groups ANOVA is an analysis in which there is ______ _____ _____ with at least three levels and in which different participants are in each level of the independent variable. A within-groups ANOVA differs in that all participants experienc

same variance

The assumptions for ANOVA are that participants are randomly selected, the populations from which the samples are drawn are normally distributed, and those populations have the ______ _____ (an assumption known as homoscedasticity

source table

presents the important calculations and final results of an ANOVA in a consistent and easy-to-read format

grand mean

the mean of every score in a study, regardless of which sample the score came from

steps 3 and 5

One-way between-groups ANOVA uses the same six steps of hypothesis testing that we learned in Chapter 7, but with a few minor changes in _____ ____ ____ ___

step 3

In _____ ____, we merely state the comparison distribution and provide two different of degrees of freedom, dfbetween for the between-groups variance and dfwithin for the within-groups variance

step 5

In _____ ____, we complete the calculations, using a source table to organize the results. First, we estimate population variance by considering the differences among means (between-groups variance). Second, we estimate population variance by calculating

between-groups variance

We divide ____ _____ _____ by within-groups variance to calculate the F statistic

twice

Before making a decision based on the F statistic, we check to see that the assumption of equal sample variances is met. This assumption is met when the largest sample variance is not more than ____ the amount of the smallest variance

R^2

the proportion of variance in the dependent variable that is accounted for by the independent variable

post hoc test

a statistical procedure frequently carried put after we reject the null hypothesis in an analysis of variance; it allows us to make multiple comparisons among several means; often referred to as a follow-up test

Turkey HSD test

a widely used post hoc test that determines the differences between means in terms of standard error; the HSD is compared to a critical value; sometimes called a q test

effect size

As with other hypothesis tests, it is recommended that we calculate a measure of _____ ____ when we have conducted an ANOVA. The most commonly reported _____ ____ for ANOVA is R^2

pairs of means

If we are able to reject the null hypothesis with ANOVA, we're not finished. We must conduct a post hoc test, such as a Turkey HSD test, to determine exactly which paris of means are significantly different from one another

nominal or ordinal

We use one-way within-groups ANOVA when we have a _____ ___ _____ independent variable with at least three levels, a scale dependent variable, and participants who experience all levels of the independent variable

order effects

Because all participants experience all levels of the independent variable, we reduce the within-groups variability by reducing individual differences; each person serves as a control for him or herself. A possible concern with this design is _____ ____

subjects

One-way within-groups ANOVA uses the same six steps of hypothesis testing that we used for one-way between-groups ANOVA-- with one major exception. We calculate statistics for four sources, rather than three. In addition to between-groups, within-groups,

effect size, R^2,

It is recommended, as with other hypothesis tests, that we calculate a measure of ____ ____, _____, for a one-way within-groups ANOVA

significantly different

As with one-way between-groups ANOVA, if we are able to reject the null hypothesis with a one-way within-groups ANOVA, we're finished. We must conduct a post hoc test, such as a Turkey HSD test, to determine exactly which pairs of means are ______ _____ f