Test 2 Quizes Study Guide

When analyzing mean differences between two samples, doing an independent t test instead of an ANOVA decreases the probability of a Type I error. increases the probability of a Type I error. does not change the probability of a Type I error. cannot be determined from the information provided.

does not change the probability of a Type I error.

How many possible pairwise contrasts are there if J = 5? 5 10 15 20

10

In a two-factor ANOVA, factor A has three levels and factor B has two levels. If each cell has five observations, the FA ratio has degrees of freedom equal to? 2, 24 3, 24 2, 29 3, 29

2, 24

Following a significant omnibus ANOVA F test, a Scheffé MCP is conducted. Which of the following results is never possible? Only one pairwise contrast is significant Only one complex contrast is significant None of the pairwise contrasts are significant None of the linear contrasts are significant

None of the linear contrasts are significant

Which assumption can be examined by Q-Q plots? Independence Homogeneity of variance Normality All of the above

Normality

14. True or false? In ANOVA, each independent variable is known as a level.

True

In a two-factor fixed-effects ANOVA, FA = 2, 𝑑𝑓𝐴 = 3, 𝑑𝑓𝐵= 6, 𝑑𝑓𝐴𝐵 = 18, 𝑑𝑓𝑤𝑖𝑡ℎ = 56. The null hypothesis for factor A can be rejected a. At the .01 level b. At the .05 level, but not at the .01 level c. At the .10 level, but not at the .05 level d. None of the above

d. None of the above

Sampling error increases with larger samples. True or false?

false

After a significant F test, two different pairwise comparison procedures were used to detect the differences between 5 group means. Procedure A detected one significant contrast, whereas procedure B showed that all contrasts are significant. Which procedure is more powerful? procedure A procedure B equally powerful cannot be determined based on the information given

procedure B

Using the same data set (J = 3, K = 2, n = 10), Jane conducted two one-factor ANOVA, whereas Joe conducted a two-factor ANOVA. Which of the following statements is not true? Jane and Joe would get the same dfA. Jane and Joe would get the same dfB. Jane and Joe would get the same dfwith. Jane and Joe would get the same dftotal.

Jane and Joe would get the same dfwith.

In ANOVA, the average deviation of all the scores from their respective group means is estimated by SStotal: SSwith MSwith MStotal MSwith

MSwith

True or false? In contrast-based multiple comparison procedures, alpha is set for each individual contrast.

True

Applying the Dunn procedure, given a nominal family-wise error rate of .10 and two contrasts, what is the per contrast alpha? a. .01 b. .05 c. .10 d. .20

b. .05

True or false? If there is an interaction between the independent variables textbook and time of day, this means that the textbook used has the same effect at different times of the day.

false

True or false? The Dunnett procedure assumes equal numbers of observations per group.

false

True or false? Suppose students in grades 7, 8, 9, 10, 11, and 12 were compared on absenteeism. If ANOVA were used rather than multiple t tests, then the probability of a Type I error will be less.

True

Suppose n1 = 19, n2 = 21, and n3 = 23. For a one-factor ANOVA, the df for the numerator of the F ratio would be which one of the following?a. 2 b. 3 c. 60 d. 62

a. 2

For a one-factor ANOVA comparing three groups with n = 10 in each group, the F ratio has degrees of freedom equal to a. 2, 27 b. 2, 29 c. 3, 27 d. 3, 29

a. 2, 27

In a two-factor ANOVA, one independent variable has five levels and the second has four levels. If each cell has seven observations, what is 𝑑𝑓𝑤𝑖𝑡ℎ? a. 20 b. 120 c. 139 d. 140

b. 120

The mathematic ability of 10 preschool children was measured when they entered their first year of preschool and then again in the spring of their kindergarten year. To test for pre to post mean differences, which of the following tests would be used? a. Independent t test b. Dependent t test c. z test d. None of the above

b. Dependent t test

The number of levels of the independent variable is six. How many orthogonal contrasts can be tested? (J - 1) a. 1 b. 3 c. 5 d. 6

c. 5

Which of the following is NOT an assumption of the independent t test? a. Normality b. Independence c. Equal sample sizes d. Homogeneity of variance

c. Equal sample sizes

Post hoc tests are necessary after an ANOVA given which one of the following? a. H0 is rejected with two groups. b. Fail to reject the null hypothesis and there are more than two groups. c. H0 is rejected and there are more than two groups. d. You should always do post hoc tests after an ANOVA.

c. H0 is rejected and there are more than two groups.

Which of the following is not an alternative to the parametric one-factor fixed effects ANOVA? a. Brown-Forsythe procedure b. Kruskal-Wallis test c. Levene's test d. Welch test

c. Levene's test

MCPs that apply trend analysis are usually conducted sequentially in which order? a. Cubic, linear, quadratic b. Linear, quadratic, cubic c. Linear, cubic, quadratic d. Quadratic, cubic, linear

c. Linear, cubic, quadratic

A priori comparisons are which one of the following? a. Planned in advance of the research b. Often arise out of theory and prior research c. May be done without examining the F ratio d. All of the above

d. All of the above

A researcher finds a statistically significant omnibus F test. For which one of the following will there be at least one statistically significant MCP? a. Kaiser-Bowden b. Dunnett c. Tukey HSD d. Scheffé

d. Scheffé

The number of degrees of freedom for an independent t test with 15 females and 25 males is 40. True or false?

false

How many hypotheses are tested in a one-factor repeated measures ANOVA? 1 2 3 4 It depends

1

In ANOVA, the variability between group means is estimated by SSbetw MSbetw SSwith MSbetw MSwith

MSbetw

For a two-factor fixed-effects model, if the degrees of freedom for testing factor A = 2,24, then I assert that the degrees of freedom for testing factor B will necessarily be = 2,24. Am I correct?

No

Suppose that for a one-factor ANOVA with J = 4 and n = 10, the four sample means are all equal to 15. I assert that the value of 𝑀𝑆𝑤𝑖𝑡ℎ is necessarily equal to zero. Am I correct?

No

When a one-factor fixed-effects ANOVA results in a nonsignificant F ratio for J = 4, one should follow up the ANOVA with which one of the following post-hoc procedures? Scheffé method Tukey HSD method Fisher LSD method None of the above

None of the above

Which of the following is a necessary assumption of the ANOVA model? Observations come from populations with equal means. Observations come from populations with equal variances. Dependent variables are measured on a ratio scale. Sample sizes are equal for each group. Dependent variables are measured on a ratio scale.

Observations come from populations with equal variances.

Which of the following would be appropriate for a factorial ANOVA? One categorical dependent variable and one categorical independent variable One categorical dependent variable and one continuous independent variable One continuous dependent variable and one categorical independent variable One continuous dependent variable and two categorical independent variables

One continuous dependent variable and two categorical independent variables

True or false? Holding the α level and the number of groups constant, as the 𝑑𝑓𝑒𝑟𝑟𝑜𝑟 increases, the critical value of the q decreases.

True

I assert that the critical value of t required for statistical significance is smaller (in absolute value or ignoring the sign) when using a directional rather than a nondirectional test. Am I correct?

Yes

The denominator of the independent t test is known as the standard error of the difference between two means, and may be defined as which one of the following? a. The difference between the two group means b. The amount by which the difference between the two group means differs from the population mean c. The standard deviation of the sampling distribution of the difference between two means d. All of the above e. None of the above

b. The amount by which the difference between the two group means differs from the population mean

The denominator of the dependent t test is known as the standard error of the mean difference, and may be defined as which one of the following? a. The difference between the two group means b. the amount by which the difference between the two group means differs from the population mean c. The standard deviation of the sampling distribution of the mean difference d. All of the abovee. None of the above

c. The standard deviation of the sampling distribution of the mean difference

The results of a two-factor ANOVA (J = 3, K = 2) show that both main effects are significant, but the interaction is not significant. We need to conduct MCPs to examine the two main effects and the interaction effect. conduct MCPs to examine the interaction effect only. conduct MCPs to examine the two main effects. conduct MCPs to examine one main effect only.

conduct MCPs to examine one main effect only.

. Which of the following is not necessary in ANOVA? a. Observations are from random and independent samples. b. The dependent variable is measured on at least the interval scale. c. Populations have equal variances. d. Equal sample sizes are necessary.

d. Equal sample sizes are necessary.

A researcher conducts an independent t test with balanced samples, equal variances, and a total sample size of 12. Which of the following standardized mean differences measures of effect is recommended?a. Cohen's d b. Eta squared c. Glass's d d. Hedge's g

d. Hedge's g

For a one-factor analysis of variance fixed-effects model, which of the following is always true? a. dfbetw + dfwith = dftotal b. SSbetw + SSwith = SStotal c. MSbetw + MSwith = MStotal d. All of the above e. Both a and b

e. Both a and b

True or false? For J = 2 and α = .05, if the result of the independent t test is significant, then the result of the one-factor fixed-effects ANOVA is uncertain.

false

In a two-factor fixed-effects ANOVA, the interaction effect is definitely not present when the effect of one factor is different across levels of the other factor. column effects are not consistent across rows. main effects and residual error do not account for all of the variation in the dependent variable. main effects and residual error have accounted for all of the variation the dependent variable.

main effects and residual error have accounted for all of the variation the dependent variable.

If you find an F ratio of 2 in a one-factor ANOVA (a = .05), you will reject the null hypothesis. not be able to decide because the df and critical value are unknown. fail to reject the null hypothesis. conclude that a mistake has been made.

not be able to decide because the df and critical value are unknown.

In a one-factor repeated measures ANOVA, A (fixed factor) has 4 levels, and each cell has 10 observations. The FA ratio has degrees of freedom equal to what? 4, 9 4, 27 3, 27 3, 36

3, 27

For pairwise post hoc contrasts with unequal group variances, which of the following MCPs is most appropriate? Scheffé Kaiser-Bowden Tukey HSD Games-Howell

Games-Howell

A two-factor experiment means that the design necessarily includes which one of the following? Two independent variables Two dependent variables An interaction between the independent and dependent variables Exactly two separate groups of subjects

Two independent variables

For a design with four factors, how many total interactions will there be? a. 4 b. 8 c. 11 d. 12 e. 16

c. 11

Contrasts can be divided into which two of the following types? a. Contrast and complex b. Nonpairwise and complex c. Pairwise and nonpairwise d. Simple and pairwise

c. Pairwise and nonpairwise

For any pairwise MCP, holding the number of groups and dfwith constant, as the alpha level increases, the critical value will increase decrease not change increase or decrease depending on which MCP is used.

decrease

If you find an F ratio of 0.5 in a one-factor ANOVA (a = .05), you will reject the null hypothesis fail to reject the null hypothesis. not be able to decide because the df and critical value are unknown. conclude that a mistake has been made

fail to reject the null hypothesis.

Which of the following situations would result in the greatest generalizability of the main effect for factor B across the levels of factor A? For factor A, p = .06; for factor B, p = .04; and interaction AB, p = .01. For factor A, p = .06; for factor B, p = .10; and interaction AB, p = .04. For factor A, p = .20; for factor B, p = .02; and interaction AB, p = .10. For factor A, p = .20; for factor B, p = .10; and interaction AB, p = .03.

For factor A, p = .20; for factor B, p = .02; and interaction AB, p = .10.

If the assumption of sphericity (i.e., compound symmetry) is violated, what should the researcher do? Because the effects of assumption violation will be minimal, we should use the results of the usual F test anyway. If H0 is rejected using the usual F test, we should use alternative F tests to verify the results. If H0 is not rejected using the usual F test, we should use alternative F tests to verify the results. Because the usual F test is not valid, we cannot analyze the data using this ANOVA model.

If H0 is rejected using the usual F test, we should use alternative F tests to verify the results.

Ravi conducts a study where randomly selected patients of a clinic are measured on their blood pressure each month over the course of one year. Which ANOVA model is most appropriate for analysis of these data? One-factor random-effects model Two-factor random-effects model Two-factor mixed-effects model One-factor repeated measures design

One-factor repeated measures design

Which of the following statements about post hoc tests is true? We should always do post hoc tests following an omnibus ANOVA F test. We should always do post hoc tests following a significant ANOVA F test. With post hoc comparisons, we can conduct only pairwise tests. We should always do post hoc tests following a significant ANOVA F test and when J > 2.

We should always do post hoc tests following a significant ANOVA F test and when J > 2.

Applying the Dunn procedure, the per contrast alpha is calculated to be 0.01 for five contrasts. What is the nominal family-wise error rate? .002 .005 .01 .05

.05

A researcher used ANOVA to examine the effects of paper colors on reading speed. She prepared reading materials printed on three different colors of paper: white paper, yellow paper, and blue paper. She then randomly assigned 20 readers to each type of paper. How many factors are involved in this experiment, and how many levels are in the factor(s)? 1 factor with 3 levels 1 factor with 20 levels 3 factors with 20 levels 3 factors with 60 levels

1 factor with 3 levels

For a one-factor ANOVA comparing five groups with n = 30 in each group, the F ratio has degrees of freedom equal to 4, 120 4, 145 5, 149 5, 145

4, 145

If 5 orthogonal contrasts can be tested, what is the number of levels of the independent variable? 1 4 5 6

6

For a three-factor fixed-effects ANOVA, how many F tests will there be? 3 4 6 7

7

The homoscedasticity assumption is that the populations from which each of the samples are drawn are normally distributed. True or False?

False

In a study of different instructional methods, if the researcher is interested only in comparing the scores of the class taught by the traditional method against each of the classes taught by the alternative methods, which procedure should she use? Dunnett method Dunn (Bonferroni) method Tukey HSD Trend analysis

Dunn (Bonferroni) method

I assert that rejecting 𝐻0 in a one-factor fixed-effects ANOVA with J = 3 indicates that all three pairs of group means are necessarily statistically significantly different using the Scheffé procedure. Am I correct?

No

In a three-factor fixed-effects ANOVA, the three-way interaction effect is found to be significant. Which of the following statements is always true? All of the two-way interaction effects and main effects are significant. None of the two-way interaction effects or main effects are significant. At least one of the two-way interaction effects or main effects is significant. None of the above.

None of the above.

A researcher finds a p value of .04 for Levene's test. Which of the following can be concluded if the alpha level is .05? The assumption of equal variances has been violated. The assumption of normality has been met. There is a statistically significant main effect for this factor. There is a statistically significant omnibus test.

The assumption of equal variances has been violated.

In a 2 x 2 factorial design, the cell means are given as follows: cell 11 = 10, cell 12 = 20, cell 21 = 10, and cell 22 = 0. Assume that the within-cell variation is small. Which one of the following conclusions seems most probable? All effects are significant. Only the two main effects is significant. Only the interaction is significant. The interaction and one of the main effects are significant.

The interaction and one of the main effects are significant.

Suppose for a one-factor fixed-effects ANOVA with J = 5 and n = 15, the five sample means are all equal to 50. I assert that the F test statistic cannot be significant. Am I correct?

Yes

Suppose n1 = 19, n2 = 21, and n3 = 23. For a one-factor ANOVA, the 𝑑𝑓𝑏𝑒𝑡𝑤 would be a. 2 b. 3 c. 60 d. 62

a. 2

Which of the following conclusions would result in the greatest generalizability of the main effect for factor A across the levels of factor B? The interaction between the independent variables A and B was a. Not significant at the .25 level. b. Significant at the .05 level. c. Significant at the .01 level. d. Significant at the .001 level.

a. Not significant at the .25 level.

A researcher finds a p value of .04 for Levene's test. Which of the following can be concluded if the alpha level is .05? a. The assumption of equal variances has been violated. b. The assumption of normality has been met. c. There is a statistically significant main effect for this factor. d. There is a statistically significant omnibus test

a. The assumption of equal variances has been violated.

A two-factor experiment means that the design necessarily includes which one of the following? a. Two independent variables b. Two dependent variables c. An interaction between the independent and dependent variables d. Exactly two separate groups of subjects

a. Two independent variables

In the absence of random assignment to groups, which one of the following can be used to examine the extent to which the assumption of independence has been met? a. Boxplot of residuals by levels of factor A b. Scatterplot of residuals to categories of the independent variables c. Shapiro-Wilk test d. Spread versus level plot

b. Scatterplot of residuals to categories of the independent variables

Which is not a property of planned orthogonal contrasts? a. The contrasts are independent. b. The contrasts are post hoc. c. The sum of the cross-products of the contrast coefficients = 0. d. If there are J groups, there are J − 1 orthogonal contrasts.

b. The contrasts are post hoc.

When a one-factor fixed-effects ANOVA results in a significant F ratio for J = 2, one should follow the ANOVA with which one of the following procedures? a. Tukey HSD method b. Scheffé method c. Fisher-Hayter method d. None of the above

d. None of the above

When analyzing mean differences between three samples, doing all pairwise independent t tests instead of ANOVA using the same a level decreases the probability of a Type I error. increases the probability of a Type I error. does not change the probability of a Type I error. cannot be determined from the information provided.

increases the probability of a Type I error.

In a one-factor repeated measures model, scores are collected at three different time points (J = 3). The assumption of sphericity basically states that the variance of scores collected at each time point is the same. the variance of the difference scores between the first time point and the second time point is the same as that between the second time point and the third time point. the variance of the difference scores is the same for each of the three pairs of time points. both the variance and covariance of the difference scores are the same for each of the three pairs of time points.

the variance of the difference scores is the same for each of the three pairs of time points.