STATS exam 4 (HW 8&9)

On average, what value is expected for the F-ratio if the null hypothesis, H0 is false?

Much greater than 1.00.

Which of the following accurately describes a shape of F distribution?

Positively skewed with all values greater than or equal to zero

A one-way ANOVA is used to evaluate the mean differences between three experimental groups, with n = 10 participants in each group. If the data produce an F= 4.74, which of the following is the correct statistical decision?

Reject the null hypothesis with α = .05 but not with α = .01.

In one-factor ANOVA, what is measured by the MSwithin?

The average (i.e., mean) variance within samples (i.e., within groups).

In one-factor ANOVA, what is measured by the MSbetween?

The average difference between sample means.

For a one-factor ANOVA comparing four treatment conditions, what is stated by the null hypothesis (H0)?

There are no differences between any of the population means.

What is the purpose of post-hoc tests such as Scheffe's test or Tukey's test?

To determine exactly which treatment groups significantly differ from other groups.

A one-factor ANOVA produces SStotal = 150 and SSwithin = 40. For this analysis, what is SSbetween?

110

How many separate groups of participants would be needed for an independent samples, two-factor experiment with 3 levels of factor A and 4 levels of factor B?

12

The following table shows the results of a two-factor ANOVA. Based on this table, what is the value of eta2 for Factor A (i.e., the effect size produced by Factor A)? Source: SS df MS Between 36 3 Factor A 12 1 12 Factor B 3 1 3 Interaction AxB 21 1 21 Within 84 28 3 Total 120 31

12/96 = 0.13

For a research study with 3 levels of factor A, 3 levels of factor B, and n = 5 in each treatment condition, what are the df values for the F-ratio evaluating the main effect for factor A?

2, 36

The following table represents a two-factor experiment, with each factor having two levels. The numbers in each cell represent the means of performance scores that were computed for each group after the experimental treatment. Note that one mean value is not given. What value of the missing mean would result in no main effect for factor B? B1 B2 A1 15 10 A2 30 ?

35

A researcher reports outcomes of one-factor ANOVA as F(3, 40) = 3.24, p > .05. Based on the df values, how many groups were compared in the study, and what was the total number of subjects participating in the study?

4 groups & total of 44 participants.

The following table shows the results of a two-factor ANOVA. Based on this table, what is the F statistic value for the main effect of Factor A? Source: SS df MS Between 36 3 Factor A 12 1 12 Factor B 3 1 3 Interaction AxB 21 1 21 Within 84 28 3 Total 120 31

4.0

The following table represents a two-factor experiment, with both factors A and B having two levels each. The numbers in each cell are the mean performance scores computed for each group after the experimental treatment. Note that one mean value is not given. What value of the missing mean would result in no interaction between factor A and factor B? B1 B2 A1 10 30 A2 25 ?

45

A one-factor ANOVA is used to evaluate the mean differences among 3 treatment conditions with a sample of n = 20 participants in each group. For this study, what is dfwithin treatments?

57

A one-factor ANOVA produces SSbetween = 30, SSwithin = 60, and an F-ratio with df = 5, 30. For this analysis, what is the F-ratio?

6/2 = 3

A two-factor study with 3 levels of factor A and 2 levels of factor B uses a separate group of n =10 participants in each treatment condition. How many participants are needed for the entire study?

60

A researcher conducted a t-test for independent samples to evaluate the mean difference between two treatment conditions and obtained t(48) = 3.00. If the researcher decides to used a one-actor ANOVA to evaluate outcomes of this study, what would be the computed F statistic value?

9.00

A two-factor research study is used to evaluate the effectiveness of a new blood-pressure medication. In this two-factor study, Factor A - Medication, has 2 levels (i.e., receiving medication versus no medication condition) and Factor B - Gender, has also two levels (i.e., males versus females) Overall, the medication is expected to significantly reduce blood pressure for both - males and females, but it is expected to have a much greater effect for males than females. What pattern of results should be obtained in this study, if the medication works as predicted?

A significant main effect for Factor A-Medication, and a significant interaction between Factor A (Medication) and Factor B (Gender)

A two-factor ANOVA for independent samples produced F(3, 36) = 6.34 for a main effect of factor A and F(1, 36) = 4.75 for a main effect of factor B. Which of the following accurately describes the experiment producing these F-ratios?

An experiment with 4 levels of factor A and 2 levels of factor B.

For a one-factor ANOVA comparing five treatment conditions, what is stated by the alternative hypothesis (H1)?

At least one of the five population means is different from another mean.

In a one-factor ANOVA, the mean differences between-groups caused by a treatment effect contribute to which of the following variances?

Between-treatments variance

A one-way ANOVA is used to evaluate the mean differences in BMI (i.e., body mass index) between three groups of adults - young adults, middle age adults and elderly. Each age group had n = 15 participants. If the data produced an F-ratio of F = 3.18, which of the following is the correct conclusion from this study (assume p <. 05)?

Fail to reject the null hypothesis and conclude that there are no significant differences in mean BMI.

The results from a two-factor analysis of variance show a significant main effect for factor A and a significant main effect for factor B. Based on this information, what can you conclude about the interaction of factor A & factor B?

You cannot make any conclusion about the significance of the interaction (i.e., all three effects are independent from each other).

A researcher conducts a 2-factor ANOVA on results of a study that compares a new teaching strategy relative to the old strategy. It is predicted that the new teaching strategy will increase test scores for highly motivated students but will decrease scores for students with low motivation. This researcher is predicting

a significant interaction between teaching strategy and student motivation.

A researcher examines the effect of gender and special training on task performance using a 2-factor ANOVA for independent samples. He predicts that a special training course will be equally effective for males and females. That means the researcher is expecting to find

a significant main effect of special training.

On average, what value is expected for the F-ratio if the null hypothesis, H0 is true?

around 1.00

A researcher uses one-factor ANOVA to test the statistical significance of differences among three treatments, with a sample of n = 20 in each treatment group. The F-ratio for this analysis would have what df values?

df = 2, 57

The results of testing the significance of a main effect of Factor A in the two-factor ANOVA for independent samples are reported as F(2, 24) = 3.21. Based on this result, the correct conclusion is (assume p < .05)

fail to reject null hypothesis and conclude that there is no evidence of significant effect of Factor A.

Two independent variables (i.e., factors) are said to interact when

the effect of one independent variable depends on the levels of the second independent variable.

If the results of a two-factor ANOVA are presented in a line graph, then an interaction between the two factors can be seen whenever

the lines are not parallel.

In a two-factor analysis of variance, a main effect is defined as

the mean differences among different levels of one factor

The results of testing the significance of an interaction effect between mood (i.e., factor A) and reward size (i.e., factor B) on test performance in the two-factor ANOVA for independent samples are reported as F(6, 48) = 2.45. Based on this result the correct conclusion is that

there is a significant effect of interaction between factor A and factor B with p <. 05.

A 2-factor ANOVA for independent groups produces

three separate F-ratios.

In one-factor ANOVA, the score differences cause by random factors (i.e., chance factor) contribute to which component of F ratio?

to both, the numerator and denominator (i.e., both between-treatments variance and within-treatments variance)