Chapter 12 Introduction to Analysis of Variance

Data Set B or Data Set A

Data Set A

F

The f-ratio

levels of the factor (in ANOVAs)

The individual conditions that make up the factor -ie. if age group is the factor, 16- to 20-year-olds, 21- to 25-year-olds, and ≥ 26-year-olds are the levels of the factor.

n

The number of scores in each treatment

k

The number of treatment conditions

G

The sum of all of the scores in the research study

T

The sum of the scores for each treatment condition

N

The total number of scores in the entire study

Between degrees of freedom

number of groups minus 1

Within degrees of freedom

(The total number of scores in the entire study - 1)(number of scores in the treatment - 1) ??????

Q3. An analysis of variance produces SStotal = 80 and SSwithin = 30. For this analysis, what is SSbetween?

50, because SSbetween= SStotal-SSwithin

Q5. Posttests are needed if the decision from an analysis of variance is "fail to reject the null hypothesis." True/False

False, post hoc tests are needed ONLY if you *reject H0* -(doing this indicates at least one mean difference is significant)

The data that you collect suggest that the between-treatments variance is small, relative to the within-treatment variance, so the F-ratio for your study is likely to be (close to 1.00/ substantially larger than 1.00), suggesting that (the null hypothesis will be rejected/will not be rejected)

The data that you collect suggest that the between-treatments variance is small, relative to the within-treatment variance, so the F-ratio for your study is likely to be close to 1.00, suggesting that will not be rejected

Q6. A report shows ANOVA results: F(2, 27) = 5.36, p < .05. You can conclude that the study used a total of 30 participants. True/False

True bc dfwithin = N - k -therefore, 30 - 1 = (2+27)

Q1. ANOVA allows researchers to compare several treatment conditions without conducting several hypothesis tests. T/F

True: Several conditions can be compared in one test.

Analysis of Variance (ANOVA)

a statistical technique that determines whether three or more means are statistically different from one another

Q4. Which combination of circumstances is most likely to produce a large value for the F-ratio? a. large mean differences and small sample variances b. large mean differences and large sample variances c. small mean differences and large sample variances d. small mean differences and small sample variances

a. large mean differences and small sample variances

ANOVA

analysis of variance

Within-treatments variance

caused by random unsystematic variance caused by individual differences or sampling error

Posttest

refers to measuring the dependent variable after changing the independent variable

Q2. If the null hypothesis is true, the F-ratio for ANOVA is expected (on average) to have a value of 0. T/F

False: If the null hypothesis is true, the F-ratio will have a value near 1.00.

The US Department of Health and Human Services compiles statistics on the consumption of alcohol. An investigator decides to look at the role of age in determining alcohol use. She requests data on the amount of drinking done by three different age groups: 16- to 20-year-olds, 21- to 25-year-olds, and ≥ 26-year-olds. The results come in, and a statistician conducts an analysis of variance. The _____alternative/null hypothesis_____ is that there is no difference between the population means (in other words, there is no treatment effect). The _____alternative/null hypothesis_____ is that at least one of the population means is different from another (in other words, there is an effect of at least one of the treatments). Note: The term "treatment effect" is used even when there is not actually a treatment. The age group is _____(the different levels of the factor/the factor/the dependent variable)_____. The treatments (16- to 20-year-olds, 21- to 25-year-olds, and ≥ 26-year-olds) are _____(_the different levels of the factor/the factor/the dependent variable)____. Which of the following might contribute to between-treatments variance? *Check all that apply.* a. Systematic differences in drinking preference by age group b. Flaws in the questionnaire used to measure the amount of drinking c. Individual differences in the frequency of drinking

The _____null hypothesis_____ is that there is no difference between the population means (in other words, there is no treatment effect). The _____alternative_____ is that at least one of the population means is different from another (in other words, there is an effect of at least one of the treatments). The age group is _____the factor_____. The treatments (16- to 20-year-olds, 21- to 25-year-olds, and ≥ 26-year-olds) are _____the different levels of the factor____. Which of the following might contribute to between-treatments variance? a. Systematic differences in drinking preference by age group b. Flaws in the questionnaire used to measure the amount of drinking c. Individual differences in the frequency of drinking

Between-treatments variance

caused by either systematic age group variance or random unsystematic variance due to individual differences and sampling error

factor (in ANOVAs)

the variable that designates the groups being compared -made up of levels ie. age group