Chapter 12

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When the null hypothesis is true, the F test statistic is

within-treatments variance

measure of how much difference exists inside each treatment condition - caused by random unsystematic variance caused by individual differences or sampling error - provides a measure of how big the differences are when H₀ is true

error term

measure of the variance caused by random, unsystematic differences

experimentwise alpha level

total probability of a Type I error accumulated from all individual tests in the experiment - alpha level is substantially greater than the value of alpha used for any one of the individual tests

simply two different ways of doing exactly the same job: - testing for mean differences

ANOVA and t tests are both

large values

In general, you should reject the null hypothesis for ______ values of the F test statistic .

When the study is comparing more than two treatments

When is the distinction between the "testwise" alpha level and the "experimentwise" alpha level important?

mean square

average of the squared deviations

treatment effect

cause of differences between treatments

total

entire set of scores

analysis of variance (ANOVA)

hypothesis-testing procedure used to evaluate mean differences between two or more treatments or populations

level

individual condition or value that makes up a variable

It is called the "F test statistic" because it

it follows an F distribution with parameters equal to the degrees of freedom of its numerator and denominator when the assumptions underlying ANOVA are true.

null: There really are no differences between the populations (or treatments). The observed differences between the sample means are caused by random, unsystematic factors (sampling error) that differentiate one sample from another. alt: The populations (or treatments) really do have different means, and these population mean differences are responsible for causing systematic differences between the sample means.

two interpretations/ two hypotheses (null and alternative) that are part of the general hypothesis-testing procedure for ANOVA

factor

variable that designates the groups being compared

formula for within-treatments degrees of freedom

E(N - 1) = Edfineachtreatment

formula for within-treatments sum of squares

ESS

formula for total sum of squares

Ex2- (G2/N)

the testwise alpha and experimentalwise alpha are the same - only 1 hypothesis is perfromed for ANOVA

If an ANOVA is performed, the alpha level tests

- substantially larger than 1.00 - the null hypothesis will be rejected

The data that you collect suggest that the between-treatments variance is large, relative to the within-treatment variance, so the F-ratio for your study is likely to be ______ , suggesting that __________ .

large

When the null hypothesis is false, the F test statistic is most likely

eta squared

percentage of variance accounted for by the treatment effect in published reports of ANOVA results

testwise alpha level

risk of a Type I error for an individual hypothesis test

two-factor design/ factorial design

study that combines two variables

single-factor design

study that has only one independent variable

researchers perform more than one hypothesis test with α - occurs because they have multiple chances of making this error

the experimentwise alpha level increases when

2

How many levels are there in a single-factor independent-measures design comparing depression scores of participants with and without treatment?

formula for total degrees of freedom

N-1

an ANOVA avoids the problem of an inflated experimentwise alpha level.

Why should he perform an analysis of variance (ANOVA) with α = 0.05 instead of simply using multiple t tests with α = 0.05 to compare the six pairs of group means?

Scheffé test

method using an F-ratio to evaluate the significance of the difference between two treatment conditions

situations in which there are only two treatments to compare

t tests are limited to

between-treatments

term referring to differences from one condition to another

The F test statistic is the

the ratio of the between-treatments variance (MSbetween) to the within-treatments variance (MSwithin) - MSbetween/ MSwithin

The F-ratio is a ratio of two variances.

Which of the following accurately describes the F-ratio in an analysis of variance?

The within-treatments variance measures random, unsystematic differences within each of the samples assigned to each of the treatments. These differences are not due to treatment effects because everyone within each sample received the same treatment; therefore, the differences are sometimes referred to as "error."

Which of the following reasons best explains why the within-treatments variance is sometimes referred to as the "error variance"?

within-treatments

term referring to differences that exist inside the individual conditions - produced only by differences caused by chance

k- The number of treatment conditions n- The number of scores in each treatment N- The total number of scores in the entire study T- The sum of the scores for each treatment condition G- The sum of all of the scores in the research study F- The F-ratio

1. The number of treatment conditions 2. The number of scores in each treatment 3. The total number of scores in the entire study 4. The sum of the scores for each treatment condition 5. The sum of all of the scores in the research study 6. The F-ratio

determines the greatest acceptable risk of making a Type I error - α= 0.05, this means they want to limit their overall risk of making a Type I error, that is, they want the experimentwise alpha level to be α= 0.05

Researchers select a significance level, α, that

formula for between-treatments sum of squares

SStotal - SSwithin

post hoc test

additional hypothesis test done after an ANOVA to determine whether mean differences are significant

distribution of F-ratios

all possible F values that can be obtained when the null hypothesis is true

F-ratio

comparison between how much difference exists versus how big the differences are between treatment conditions - calculated by dividing the between-treatments variance by the within-treatment variance - When the numerator and denominator are roughly equal, the F-ratio should have a value around 1.00 - An F-ratio near 1.00, you can conclude that there is no evidence to suggest that the treatment has any effect -- differences between treatments are random and unsystematic - A large F-ratio is evidence for the existence of systematic treatment effects -- There are significant differences between treatments (allowing you to reject the null hypothesis)

pairwise comparison

comparison of individual treatments two at a time

Tukey's HSD test

computation of single value that determines the minimum difference between treatment means necessary for significance

ANOVA summary table

diagram showing the source of variability

formula for between-treatments degrees of freedom

k - 1

that it can be used to compare two or more treatments - Thus, ANOVA provides researchers with much greater flexibility in designing experiments and interpreting results

major advantage of ANOVA is

between-treatments variance

measure of how much difference exists between treatment conditions - caused by either systematic age group variance or random unsystematic variance due to individual differences and sampling error