Chapter 12

between-groups ANOVA

A between-groups ANOVA is a hypothesis test in which there are more than two samples, and each sample is composed of different participants.

source table

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

Analysis of Variance (ANOVA)

Analysis of variance (ANOVA) is 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.

How do you find the DF and CV of an ANOVA

Between k-1 within N-k

between-groups variance

Between-groups variance is an estimate of the population variance, based on the differences among the means.

Which distribution allows various types of statistical analyses to be made and is the most complex?

F

Rousseau visually inspects her data before analyzing it only to find that the populations that she sampled appear to have very different variances although her sample sizes are equal. Which assumption of ANOVA has she violated and what should she do?

Homoscedasticity; she should proceed as long as the largest variance is not greater than two times the smallest variance and report it with her statistics.

Henry is examining the effectiveness of using scare tactics to manipulate the behaviors of people living on the same island but in different regions, categorized as the beach, the valley, and the mountains. What is the first step Henry should follow for hypothesis testing?

Identify population 1 as all beach inhabitants on the island, population 2 as all valley inhabitants on the island, and population 3 as all mountain inhabitants on the island. He should also use an F distribution with a one-way between-groups ANOVA.

A researcher found a significant result using a one-way ANOVA to compare the mean of four age groups (3 years old, 5 years old, 8 years old, and 12 years old) on a test of language ability. What specific conclusions can the researcher draw from this result?

Language ability of 3-, 5-, 8-, and 12-year-olds was not the same.

A researcher rejects the null hypothesis after using an F table to determine the significance value. What can be concluded?

Reject the null hypothesis since her F statistic is beyond the cutoff, and perform a post hoc test to determine between which groups the significant difference occurs.

Grand Mean

The grand mean is the mean of every score in a study, regardless of which sample the score came from.

Which statement is NOT an assumption of an ANOVA?

The samples should be from a population with a known mean and standard deviation.

A Tukey HSD is computed to compare two groups following an ANOVA that compared five groups. The within-groups degrees of freedom for the test are 7, and the computed HSD value is 6.24. What could be concluded about this analysis if evaluated at a p level of 0.05?

The test statistic is significant, revealing a statistical difference between the two groups.

For the three statistics F, z, and t, divide _____ variability by _____ variability to analyze the relation between variables.

between-groups; within-groups

homoscedastic

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

The Bonferroni test

(also sometimes called the Dunn Multiple Comparison test) is a post hoc test that provides a more strict critical value for every comparison of means

one-way ANOVA

A one-way ANOVA is a hypothesis test that includes both one nominal independent variable with more than two levels and a scale-dependent variable.

post hoc test

A post hoc test is a statistical procedure frequently carried out after the null hypothesis has been rejected in an analysis of variance; it allows us to make multiple comparisons among several means; often referred to as a follow-up test.

within-groups ANOVA

A within-groups ANOVA is 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.

Tilbe wants to compare young children's verbal test scores across three experimental conditions (different levels of instruction from low to high) and one control group (no instruction). What type of test should she use?

ANOVA

Which symbol is NOT a type of sum of squares ( SS) listed in a source table?

SSdegrees of freedom

Bernard thinks some college students spend more money during the semester than others, and that this difference is related to the students' majors. He wants to compare the total amount of money spent at the end of one semester by American college students who major in psychology to that spent by history or physics majors. What is the second step Bernard should follow for testing his hypothesis?

State the null hypothesis as college students majoring in psychology, history, or physics spend about the same amount of money during one semester on average. State the research hypothesis as college students majoring in psychology, history, or physics do not spend the same amount of money during one semester on average.

When researchers use ANOVAs to report results of case studies that include only one participant, they typically violate the assumption of random selection. How does this action affect the conclusions of the study?

The external validity is low, and they cannot generalize their results beyond the sample.

Clara works for an advertising firm and needs to understand how an individual's levels of experience with cooking (novice, intermediate, or expert) affect how he or she will rate a new group of cookware advertisements. What type of design would be best for Clara to use?

one-way between-groups ANOVA

heteroscedastic

populations are those that have different variances.

After a researcher _____ the null hypothesis, the researcher should conduct a _____ to determine which means are statistically significantly different from each other.

rejects; post hoc test

Malcolm found a statistically significant difference between means using an ANOVA that he had not previously predicted. To identify where the differences between means lie, which test should he run?

Tukey HSD or Bonferroni test

within-groups variance

Within-groups variance is an estimate of the population variance, based on the differences within each of the three (or more) sample distributions.

Does the F distribution take into account individual differences when comparing sample means?

Yes; as the variability within the individual samples decreases, the F statistic becomes larger since the distributions are not overlapping very much.

A researcher compares bone density in retired professional athletes across three different sports. He computes a series of three t tests to examine all between-group differences, running each test with a p level of 0.01. What is the probability of a Type I error when making these comparisons?

0.03 or a 3 percent chance

For an F distribution with 2 degrees of freedom between and 27 degrees of freedom within, how many groups are being compared and how many participants are in each group, assuming equal numbers of participants per group?

3 groups, 10 participants in each group

f statistic

The F statistic is 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.

tukey HSD test

The Tukey HSD test is 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 the q test.