PSY 410 Exam Review

T/F: In a hypothesis test, a large value for the sample variance increases the likelihood that you will find a significant treatment effect.​

False

T/F: ​A repeated-measures study has n = 8 participants and k = 3 treatments. For this study, dferror= 21.

False

T/F: ​A repeated-measures t test produces a t statistic of t = 4.00 with df = 12. If the same data were evaluated with a repeated-measures ANOVA, the F-ratio would have df = 2, 12.

False

T/F: ​A research report presents the results of an independent-measures ANOVA as follows: F(3, 28) = 5.36, p < .01. The research study compared three treatments.

False

T/F: ​A two-factor analysis of variance with 2 levels of factor A and 3 levels of factor B involves six separate hypothesis tests.

False

T/F: ​A two-factor study compares 2 levels of factor A and 3 levels of factor B with a sample of n = 5 participants in each treatment condition. This study uses a total of 25 participants.

False

T/F: ​An independent-measures study produces t(10) = 3.00, p < .05. For this study, if effect size is measured with r2, then r2 = 3/13.

False

T/F: ​Effect size for analysis of variance is measured by η2, which equals SSbetween divided by SSwithin.

False

T/F: ​For a repeated-measures study, a small variance for the difference scores indicates that the treatment has little or no effect.

False

T/F: ​For a two-tailed test with α = .05 and a sample of n = 16, the boundaries for the critical region are t = ±2.120.

False

T/F: ​For the repeated-measures analysis, the F-ratio, on average, is expected to be zero when H0 is true.

False

T/F: ​If the F-ratio for factor A has df = 1, 40 and the F-ratio for factor B has df = 3, 40, then the F-ratio for the interaction must have df = 2, 40.

False

​T/F: One concern for a repeated-measures study is that the participants in one treatment may have different characteristics than the participants in the other treatment.

False

T/F: For the repeated-measures t statistic, the value of the estimated standard error in the denominator is computed entirely from the sample data.​

True

T/F: ​A two-factor study compares three different treatment conditions (factor 1) for males and females (factor 2). In this study, the main effect for gender is determined by the overall mean score for the males (averaged over the three treatments) and the corresponding overall mean score for the females.

True

T/F: ​Because the repeated-measures ANOVA removes variance caused by individual differences, it usually is more likely to detect a treatment effect than the independent-measures ANOVA is.

True

T/F: ​For a repeated-measures study, if other factors are held constant, then an increase in the sample variance will decrease measures of effect size.

True

T/F: ​For an ANOVA, when the null hypothesis is true, the F-ratio is balanced so that the numerator and the denominator are both measuring the same sources of variance.

True

T/F: ​For an analysis of variance comparing three treatment means with a separate sample of n = 10 participants in each treatment, dftotal = 29.

True

T/F: ​For an independent-measures t statistic, the estimated standard error measures how much difference is reasonable to expect between the sample means for two samples selected from the same population.

True

T/F: ​If all participants in a repeated-measures study show roughly the same 10-point difference between treatments, then the data are likely to produce a significant value for the t statistic.

True

T/F: ​If other factors are held constant, the bigger the sample is, the greater the likelihood of rejecting the null hypothesis.

True

T/F: ​Posttests are only needed if H0 is rejected in an ANOVA comparing more than two treatments.

True

T/F: ​SSbetween measures the size of the mean differences from one treatment to another.

True

T/F: ​SSwithin measures the size of the sample variances.

True

T/F: ​The 95% confidence interval for the difference between two treatment means extends from 2.50 to +5.50. Based on this information, you can conclude that there is no significant difference between the treatments at the .05 level of significance.

True

T/F: ​The denominator of the repeated-measures F-ratio is intended to measure differences that exist without any systematic treatment effect or any systematic individual differences.

True

T/F: ​The larger the differences among the sample means, the larger the numerator of the F-ratio will be.

True

An independent-measures study with n = 6 in each sample produces a sample mean difference of 4 points and a pooled variance of 12. What is the value for the t statistic?​ ​a. 2 ​b. 4√8 ​c. 4√2 ​d. 1

a. 2

​An independent-measures research study with n = 5 participants in each treatment produces sample variances of 8 and 10, and a 2-point difference between the two treatment means. What is the value of Cohen's d? a. 2/3 ​b. 2/18 ​c. 2/2 d. ​2/9

a. 2/3

An independent-measures research study uses a total of 40 participants to compare two treatment conditions. What is the df value for the t statistic for this study?​ a. 38 b. 19 c. 39 d. 18

a. 38

​The following data represent the means for each treatment condition in a two-factor experiment. Note that one mean is not given. What value for the missing mean would result in no main effect for factor B? B1 B2 A1 20 10 ​ A2 40 ? a. 50 ​b. 20 ​c. 30 ​d. 40

a. 50

​For the following data, what is SSbetween subjects? ​ Treatments Subject I II III P-totals A 3 4 5 12 B 1 1 4 6 C 2 1 6 9 T = 6 T = 6 T = 15 SS = 2 SS = 6 SS = 2 G = 27 ΣX2 = 109 a. 6 b. 2 c. 3 d. 12

a. 6

​If an analysis of variance is used for the following data, what would be the effect of changing the value of SS1 to 50? Sample Data M1 = 10 M2 = 20 SS1 = 90 SS2 = 70 a. Decrease SSwithin and increase the size of the F-ratio b. ​Increase SSwithin and decrease the size of the F-ratio c. ​Increase SSwithin and increase the size of the F-ratio d. ​Decrease SSwithin and decrease the size of the F-ratio

a. Decrease SSwithin and increase the size of the F-ratio

​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? a. You cannot make any conclusion about the significance of the interaction b. ​There probably is a significant interaction c. ​There must be a significant interaction d. ​The interaction cannot be significant

a. You cannot make any conclusion about the significance of the interaction

​What is the sample variance and the estimated standard error for a sample of n = 9 scores with SS = 72? a. s2 = 9 and sM = 1 b. s2 = 3 and sM = 1 c. ​s2 = 9 and sM = 3 d. ​s2 = 3 and sM = 3

a. s2 = 9 and sM = 1

​Which of the following is the correct null hypothesis for a repeated-measures t test? a. µD = 0 b. MD = 0 ​c. M1 = M2 ​d. µ1 = µ2

a. µD = 0

​For the independent-measures t statistic, what is the effect of increasing the difference between sample means? a. ​Increase the likelihood of rejecting H0 and increase measures of effect size b. ​Decrease the likelihood of rejecting H0 and increase measures of effect size c. ​Decrease the likelihood of rejecting H0 and decrease measures of effect size d. ​Increase the likelihood of rejecting H0 and decrease measures of effect size

a. ​Increase the likelihood of rejecting H0 and increase measures of effect size

​A sample of n = 25 scores produces a t statistic of t = 2.062. If the researcher is using a two-tailed test, which of the following is the correct statistical decision? a. ​The researcher must fail to reject the null hypothesis with either α = .05 or α = .01. b. ​It is impossible to make a decision about H0 without more information. c. ​The researcher can reject the null hypothesis with either α = .05 or α = .01. d. ​The researcher can reject the null hypothesis with α = .05 but not with α = .01.

a. ​The researcher must fail to reject the null hypothesis with either α = .05 or α = .01.

Which of the following is the correct way to report the results of a hypothesis test and a measure of effect size using a t statistic?​ a. ​t(19) = 2.30, p < .05, r2 = 0.42 b. r2 = 0.42, t(19) = 2.30 , p < .05 c. t = 2.30, df = 19, p < .05, r2 = 0.42 d. ​t(19) = 2.30, r2 = 0.42, p < .05

a. ​t(19) = 2.30, p < .05, r2 = 0.42

An independent-measures study comparing two treatment conditions produces a t statistic with df = 18. If the two samples are the same size, how many participants were in each of the samples?​ a. 19 b. 10 c. 9 d. 20

b. 10

​A research report describing the results from a repeated-measures study states that the data show no significant difference between the two treatments, t(10) = 1.65, p > .05. Based on this report, how many individuals participated in the research study? a. 9 b. 11 c. 10 d. 12

b. 11

​For the following data, what is SStotal? Treatments Subject I II III P-totals A 3 4 5 12 B 1 1 4 6 C 2 1 6 9 T = 6 T = 6 T = 15 SS = 2 SS = 6 SS = 2 G = 27 ΣX2 = 109 a. 6 b. 28 c. 10 d. 18

b. 28

​For a repeated-measures study comparing three treatment conditions with a sample of n = 4 participants, the participant totals (the P values) are 3, 6, 9, and 6. What is the value for SSbetween subjects? a. 3 b. 6 c. 2 d. 10

b. 6

​The following table shows the results of an analysis of variance comparing three treatment conditions with a sample of n = 10 participants in each treatment. Note that several values are missing in the table. What is the missing value for SStotal? Source SS df MS Between 20 xx xx F = 5.00 Within xx xx xx Total xx xx ​a. 30 b. 74 ​c. 54 ​d. 22

b. 74

​What is assumed by the homogeneity of variance assumption? a. The two population variances are not equal. b. The two populations have equal variances. c. ​The two sample variances are not equal. d. ​The two samples have equal variances.

b. The two populations have equal variances.

​In a two-factor analysis of variance, a main effect is defined as _____. ​a. the mean difference between the two factors b. the mean differences among the levels of one factor ​c. the mean differences among all treatment conditions ​d. the difference between the largest treatment mean and the smallest treatment mean

b. the mean differences among the levels of one factor

One sample of n = 8 scores has a variance of s2 = 6 and a second sample of n = 8 scores has a variance of s2 = 10. If the pooled variance is computed for these two samples, then the value obtained will be ______.​ a. ​closer to 6 than to 10 b. ​exactly halfway between 6 and 10 c. ​closer to 10 than to 6 d. ​cannot be determined without more information

b. ​exactly halfway between 6 and 10

​For a repeated-measures study comparing two treatments with a sample of n = 9 participants, the difference scores have a mean of MD = 4.90 with SS = 72. What is the estimated standard error for the sample mean difference? a. 3 ​b. 9 c. 1 d. ​√8/3

c. 1

The following table shows the results of an analysis of variance comparing four treatment conditions with a sample of n = 5 participants in each treatment. Note that several values are missing in the table. What is the missing value for MSwithin? Source SS df MS Between 30 xx xx F = xx Within xx xx xx Total 62 xx a. 48 b. 32 c. 2 d. 16

c. 2

​A repeated-measures ANOVA produced an F-ratio of F = 4.00 with df = 1, 14. If the same data were analyzed with a repeated-measures t test, what value would be obtained for the t statistic? a. ​Cannot determine without more information b. 4 c. 2 d. 16

c. 2

​A repeated-measures study comparing two treatments with n = 4 participants produces MD = 2 and SS = 75 for the difference scores. What is the estimated standard error for the sample mean difference? ​a. 5 ​b. 25/4 = 6.25 c. 2.5​ ​d. 25

c. 2.5​

​What is the pooled variance for the following two samples? Sample 1: n = 8 and SS = 168 Sample 2: n = 6 and SS = 120 a. 7 b. ​​√7 c. 24 d. 20.57

c. 24

A research study produces a t statistic with df = 14. For this study, which of the following designs would require a total of 30 participants?​ a. An independent-measures design ​b. None of the other options would require a total of 30 participants. c. A matched-subjects design ​d. A repeated-measures design

c. A matched-subjects design

​In analysis of variance, what is measured by the MS values? a. The total variability for the set of N scores ​b. Population variance c. Sample variance ​d. The average distance from one mean to another

c. Sample variance

​For an ANOVA comparing three treatment conditions, what is stated by the null hypothesis (H0)? a. At least one of the three population means is different from another mean. ​b. None of the other choices is correct. c. There are no differences between any of the population means. d. ​All three of the population means are different from each other.

c. There are no differences between any of the population means.

For the repeated-measures t statistic, df = _____. a. n1 + n2 - 1 b. ​(n1 - 1) + (n2 - 1) c. n - 1 d. ​n1 + n2 - 2

c. n - 1

​On average, what value is expected for the t statistic when the null hypothesis is true? a. t = 1.96 b. t = 1 c. t = 0 d. t > 1.96

c. t = 0

If an analysis of variance is used for the following data, what would be the effect of changing the value of M1 to 20? Sample Data M1 = 15 M2 = 25 SS1 = 90 SS2 = 70 a. Decrease SSbetween and increase the F-ratio b. ​Increase SSbetween and decrease the F-ratio c. ​Decrease SSbetween and decrease the F-ratio d. Increase SSbetween and increase the F-ratio

c. ​Decrease SSbetween and decrease the F-ratio

​If an analysis of variance is used for the following data, what would be the effect of changing the value of M2 to 25? Sample Data M1 = 10 M2 = 20 SS1 = 90 SS2 = 70 a. Decrease SSbetween and decrease the F-ratio b. ​Increase SSbetween and decrease the F-ratio c. ​Increase SSbetween and increase the F-ratio d. ​Decrease SSbetween and increase the F-ratio

c. ​Increase SSbetween and increase the F-ratio

If other factors are held constant, what is the effect of increasing the sample variance? a. ​It will increase the estimated standard error and increase the likelihood of rejecting H0. b. ​It will decrease the estimated standard error and increase the likelihood of rejecting H0. c. ​It will increase the estimated standard error and decrease the likelihood of rejecting H0. d. ​It will decrease the estimated standard error and decrease the likelihood of rejecting H0.

c. ​It will increase the estimated standard error and decrease the likelihood of rejecting H0.

​A researcher reports an F-ratio with df = 1, 24 for an independent-measures experiment. If all the treatments had the same number of participants, then how many individuals were in each treatment? a. 12 ​b. 11 ​c. 14 d. 13

d. 13

​An independent-measures study comparing two treatment conditions with n = 6 in each sample produces t = 4.00. What is the value of r2 for this study? ​a. 4/26 ​b. 4/28 c. ​16/28 d. 16/26

d. 16/26

​A researcher reports an F-ratio with df = 2, 40 from a repeated-measures ANOVA. How many treatment conditions were compared in this experiment? a. 4 b. 2 c. 41 d. 3

d. 3

​A researcher reports an F-ratio with df = 2, 18 from an independent-measures research study. Based on the df values, how many treatments were compared in the study, and what was the total number of subjects participating in the study? a. 3 treatments and 22 subjects b. ​2 treatments and 19 subjects ​c. 2 treatments and 20 subjects d. 3 treatments and 21 subjects

d. 3 treatments and 21 subjects

With α = .01, the two-tailed critical region for a t test using a sample of n = 16 subjects would have boundaries of ______.​ a. t = ±2.583 ​b. t = ±2.921 ​c. t = ±2.602 d. t = ±2.947

d. t = ±2.947

​For the following data, what are the df values for the repeated-measures F-ratio? ​ Treatments Subject I II III P-totals A 3 4 5 12 B 1 1 4 6 C 2 1 6 9 T = 6 T = 6 T = 15 SS = 2 SS = 6 SS = 2 G = 27 ΣX2 = 109 ​a. 2, 6 b. ​3, 4 ​c. 3, 6 d. ​2, 4

d. ​2, 4

​Which of the following describes what a confidence interval does? a. ​It uses a population mean to predict a sample mean. b. ​It uses the sample mean to determine a level of confidence. c. ​It uses a level of confidence to estimate a sample mean. d. ​It uses a sample mean to estimate the corresponding population mean.

d. ​It uses a sample mean to estimate the corresponding population mean.

​Why are t statistics more variable than z-scores? a. ​The extra variability is caused by variations in the sample mean. b. ​The extra variability is caused by variations in the df value. c. ​None of the other options explains the extra variability for t statistics. d. ​The extra variability is caused by variations in the sample variance.

d. ​The extra variability is caused by variations in the sample variance.

​A repeated-measures study uses a total of n = 10 participants to compare two treatment conditions. How many scores are measured in this study, and how many scores are actually used to compute the sample mean and the sample variance? a. 10 measured and 20 used ​b. 20 measured and 10 used ​c. 20 measured and 20 used ​d. 10 measured and 10 used

​b. 20 measured and 10 used