Deck 11: The T Test for Two Related Samples

Question 1

If the null hypothesis is true, what value is expected on average for the repeated-measures t statistic?

A)0
B)1
C)1.96
D)t > 1.96

Answer 1

A

Question 2

A matched-subjects study and an independent-measures study both produced a t statistic with df = 16.How many individuals participated in each study?

A)17 for matched-subjects and 17 for independent-measures
B)17 for matched-subjects and 18 for independent-measures
C)18 for matched-subjects and 18 for independent-measures
D)34 for matched-subjects and 18 for independent-measures

Answer 2

D

Question 3

For a repeated-measures study comparing two treatment conditions, a researcher obtains a sample of n = 9 difference scores with a mean of M_D = 4 and a variance of s² = 36.What is the value for the repeated-measures t statistic for these data?

A)4/2
B)4/4
C)4/6
D)4/36

Answer 3

A

Question 4

A repeated-measures study and an independent-measures study both produced a t statistic with df = 16.How many individuals participated in each study?

A)18 for repeated-measures and 17 for independent-measures
B)18 for repeated-measures and 18 for independent-measures
C)17 for repeated-measures and 17 for independent-measures
D)17 for repeated-measures and 18 for independent-measures

Question 5

For a repeated-measures study comparing two treatments with a sample of n = 9 participants, the difference scores have a mean of M_D = 4.90 with SS = 288.What is the estimated standard error for the sample mean difference?

A)36
B)36/8 = 4.5
C)4
D)2

Question 6

A repeated?measures study using a sample of n = 20 participants would produce a t statistic with df = ____.

A)9
B)19
C)20
D)39

Question 7

For a repeated-measures study comparing two treatment conditions, a researcher obtains Cohen's d = 0.50 for a sample of n = 4 scores with a variance of s² = 16.What is the value of the sample mean?

A)M_D = 2
B)M_D = 4
C)M_D = 8
D)M_D = 16

Question 8

If a repeated-measures study shows a significant difference between two treatments with α = .01, then you can be sure that _____.

A)the value of Cohen's d is large.
B)the percentage of variance explained (r²) is large
C)both Cohen's d and r² are large
D)A significant effect does not necessarily mean that the effect size will be large.

Question 9

A researcher obtains t(20) = 2.00 and M_D = 9 for a repeated-measures study.If the researcher measures effect size using the percentage of variance accounted for, what value will be obtained for r²?

A)9/20
B)9/29
C)4/13
D)4/24

Question 10

A researcher uses a repeated-measures study to compare two treatment conditions with a set of 20 scores in each treatment.What would be the value of df for the repeated-measures t statistic?

A)df = 18
B)df = 19
C)df = 38
D)df = 39

Question 11

The following data were obtained from a repeated-measures research study.What is the value of M_D for these data?

Question 12

What is the value of the estimated standard error for the following set of D?scores?

A)3 Scores: 2, 2, 10, 2
B) $\surd$ 3
C)4
D)2

Question 13

A repeated-measures study comparing two treatments with a sample of n = 4 participants produces a mean of M = 18 with SS = 24 for the scores in the first treatment, a mean of M = 14 with SS = 18 for the scores in the second treatment, and a mean of M = 4 with SS = 12 for the difference scores.What is the estimated standard error for the sample mean difference?

A)4
B)3
C)2
D)1

Question 14

For the repeated-measures t statistic, df = _____.

A)n₁ + n₂ - 2
B)(n₁ - 1) + (n₂ - 1)
C)n - 1
D)n₁ + n₂ - 1

Question 15

Which of the following is the correct null hypothesis for a repeated-measures t test?

A)M_D = 0
B)µ_D = 0
C)µ₁ = µ₂
D)M₁ = M₂

Question 16

A researcher plans to conduct a research study comparing two treatment conditions with a total of 20 scores in each treatment.Which of the following designs would require only 20 participants?

A)an independent-measures design
B)a repeated-measures design
C)a matched-subjects design
D)all of the other options require only 20 participants

Question 17

A repeated-measures experiment and a matched-subjects experiment each produce a t statistic with df = 10.How many individuals participated in each study?

A)11 for repeated, and 11 for matched
B)11 for repeated, and 12 for matched
C)11 for repeated, and 22 for matched
D)12 for repeated, and 12 for matched

Question 18

The null hypothesis for a repeated-measures test states:

A)Each individual will have a difference score of D = 0.
B)The overall sample will have a mean difference of M_D = 0.
C)The entire population will have a mean difference of μ_D = 0.
D)All of the other options are correct.

Question 19

A researcher conducts a repeated-measures study to evaluate a treatment with a sample of n = 16 participants and obtains a t statistic of t = 1.94.The treatment is expected to increase scores and the sample mean shows an increase.Which of the following is the correct decision for a hypothesis test using α = .05.

A)Reject the null hypothesis with a one-tailed test but fail to reject with two tails.
B)Reject the null hypothesis with either a one-tailed or a two-tailed test.
C)Fail to reject the null hypothesis with either a one-tailed or a two-tailed test.
D)Fail to reject the null hypothesis with a one-tailed test but reject with two tails.

Question 20

For which of the following situations would a repeated-measures research design be appropriate?

A)comparing mathematical skills for girls versus boys at age 10
B)comparing pain tolerance with and without acupuncture needles
C)comparing self-esteem for students who participate in school athletics versus those who do not
D)comparing verbal solving skills for science majors versus art majors at a college

Question 21

If other factors are held constant, which of the following sets of data is most likely to produce a significant value for the repeated-measures t statistic?

A)n = 15 and SS = 10 for the difference scores
B)n = 15 and SS = 100 for the difference scores
C)n = 30 and SS = 10 for the difference scores
D)n = 30 and SS = 100 for the difference scores

Question 22

Assuming that other factors are held constant, which of the following would tend to increase the likelihood of rejecting the null hypothesis?

A)decrease the sample size
B)increase the sample mean difference
C)increase the sample variance
D)None of the other 3 options would increase the likelihood.

Question 23

Compared to an independent-measures design, a repeated-measured study is more likely to find a significant effect because it reduces the contribution of variance due to ______.

A)M_D
B)degrees of freedom
C)the effect of the treatment
D)individual differences

Question 24

A research report describing the results from a repeated-measures t test states, "t(22) = 1.71, p > .05." From this report you can conclude that the outcome of the hypothesis test was ______.

A)to reject the null hypothesis with a sample of n = 23 participants
B)to fail to reject the null hypothesis with a sample of n = 23 participants
C)to reject the null hypothesis with a sample of n = 22 participants
D)to fail to reject the null hypothesis with a sample of n = 22 participants

Question 25

A sample of n = 9 college students is used to evaluate the effectiveness of a new Study Skills Workshop.Each student's grade point average (GPA) is recorded for the semester before the workshop and for the semester after the workshop.The average GPA improved by M_D = 0.60 points with s² = 0.09.The researcher would like to use the sample to estimate how much effect the workshop would have for the entire college population.Which of the following is the 80% confidence interval for these data?

A)µ_D = 0.60 + 0.01(1.397)
B)µ_D = 0.60 + 0.09(1.860)
C)µ_D = 0.60 + 0.10(1.397)
D)µ_D = 0.60 + 0.10(1.860)

Question 26

In a repeated-measures experiment, each individual participates in one treatment condition and then moves on to a second treatment condition.One of the major concerns in this type of study is that participation in the first treatment may influence the participant's score in the second treatment.This problem is called ______.

A)individual differences
B)order effects
C)homogeneity of variance
D)bi-treatment effect

Question 27

For a research study comparing two treatment conditions, a repeated-measures design would require two scores for each participant but an independent-measures design would require only one score for each participant.

Question 28

Which of the following possibilities is a serious concern with a repeated-measures study?

A)You will obtain negative values for the difference scores.
B)The results will be influenced by order effects.
C)The mean difference is due to individual differences rather than treatment differences.
D)All of the other options are major concerns.

Question 29

What value is estimated with a confidence interval using the repeated-measures t statistic?

A)the mean for a sample of difference scores
B)the mean for a population of difference scores
C)the difference between two population means
D)the difference between two sample means

Question 30

A researcher uses a repeated-measures design to compare individuals' performance before treatment with their performance after treatment.If all of the participants show improved performance of 8 or 9 points after treatment, then the researcher should find ______.

A)a sample mean difference near zero
B)a t statistic near zero
C)the variance of the difference scores is near zero
D)None of the other options is correct.

Question 31

A researcher obtains t = 2.35 for a repeated-measures study using a sample of n = 8 participants.Based on this t value, what is the correct decision for a two-tailed test?

A)reject the null hypothesis with α = .05 but not with α = .01
B)reject the null hypothesis with either α = .05 or α = .01
C)fail to reject the null hypothesis with either α = .05 or α = .01
D)cannot make a decision without additional information

Question 32

In general, what is the effect of an increase in the variance for the sample of difference scores?

A)an increase in the standard error and an increase in the value of t
B)an increase in the standard error and a decrease in the value of t
C)a decrease in the standard error and an increase in the value of t
D)a decrease in the standard error and a decrease in the value of t

Question 33

A researcher reports t(12) = 2.86, p < .05 for a repeated-measures research study.How many individuals participated in the study?

A)n = 11
B)n = 13
C)n = 24
D)n = 25

Question 34

In general, what characteristics of the difference scores are most likely to produce a significant t statistic for the repeated-measures hypothesis test?

A)a large number of scores and a large variance
B)a large number of scores and a small variance
C)a small number of scores and a large variance
D)a small number of scores and a small variance

Question 35

If the sample size is held constant, which of the following will produce the widest 90% confidence interval for the population mean difference for a repeated-measures study?

A)M_D = 5 with s² = 5 for the difference scores
B)M_D = 5 with s² = 10 for the difference scores
C)M_D = 3 with s² = 10 for the difference scores
D)M_D = 3 with s² = 20 for the difference scores

Question 36

In general, if the variance of the difference scores increases, then what will happen to the value of the t statistic?

A)It will increase (move farther toward the tail of the distribution).
B)It will decrease (move toward 0 at the center of the distribution).
C)It will stay the same - the t statistic is not affected by the variance of the difference scores.
D)It may increase or may decrease.There is no consistent relationship between variance and the size of the t statistic.

Question 37

For which of the following situations would a repeated-measures design have the maximum advantage over an independent-measures design?

A)when many subjects are available and individual differences are small
B)when very few subjects are available and individual differences are small
C)when many subjects are available and individual differences are large
D)when very few subjects are available and individual differences are large

Question 38

What is indicated by a large variance for a sample of difference scores?

A)a consistent treatment effect and a high likelihood of a significant difference
B)a consistent treatment effect and a low likelihood of a significant difference
C)an inconsistent treatment effect and a high likelihood of a significant difference
D)an inconsistent treatment effect and a low likelihood of a significant difference

Question 39

A researcher is using a repeated-measures study to evaluate the difference between two treatments.If the difference between the treatments is consistent from one participant to another, then the data should produce ______.

A)a small variance for the difference scores and a small standard error
B)a small variance for the difference scores and a large standard error
C)a large variance for the difference scores and a small standard error
D)a large variance for the difference scores and a large standard error

Question 40

A research report describing the results from a repeated-measures study states: The data show no significant difference between the two treatments, t(10) = 1.65, p > .05.Based on this report, you can conclude that a total of ____ individuals participated in the research study .

A)9
B)10
C)11
D)12

Question 41

If all of the 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.

Question 42

For a repeated-measures design, df = n₁ + n₂ - 2 for the t statistic.

Question 43

The estimated standard error in the denominator of the repeated-measures t statistic measures the average mean difference that is expected for a sample when there is a zero mean difference for the population.

Question 44

A repeated-measures research study comparing two treatments with a set of 10 scores in each treatment will produce a t statistic with df = 19.

Question 45

Although a repeated-measures study measures two scores for each participant, the sample mean and variance are computed using only one score for each participant.

Question 46

A repeated-measures study and an independent-measures study both produce a t statistic with df = 20.The repeated-measures study used more subjects than the independent-measures study.

Question 47

If a set of n = 9 difference scores has a mean of M_D = 3.5 and a variance of s² = 36, then the standard error for the sample mean difference is 4 points.

Question 48

For a repeated-measures study, a small variance for the difference scores indicates that the treatment effect is consistent across participants.

Question 49

In a repeated measures study, the null hypothesis says that the mean for the sample of difference scores should be equal to zero.

Question 50

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

Question 51

A repeated-measures study and an independent-measures study both produce t statistics with
df = 20.The independent-measures study used more participants.

Question 52

A researcher reports df = 18 for a repeated-measures t statistic.This research study used a total of n = 19 participants.

Question 53

For the following data from a repeated-measures study, the sample mean difference is M_D = 4.

Question 54

Although the original data for a repeated-measures study consist of two scores for each participant, the calculation of the mean and variance are done with only one score for each participant.

Question 55

In the repeated-measures t statistic, the value for the estimated standard error in the denominator is computed entirely from the sample data.

Question 56

In general, as the variance of the difference scores increases, the likelihood of finding a significant difference also increases.

Question 57

The repeated-measures t statistic is used with a matched-subjects design even though the design uses two separate samples.

Question 58

In a repeated-measures study comparing two treatments with a sample of n = 15 participants, the researcher measures two scores for each individual to obtain a total of 30 scores.The repeated-measures t statistic for this study has df = 29.

Question 59

If a set of n = 9 difference scores has a mean of M_D = 3.5 and a variance of s² = 36, then the sample will produce a repeated-measures t statistic of t = 3.5/2.

Question 60

A researcher would like to compare two treatment conditions with a set of 30 scores in each treatment.If a repeated-measures design is used, the study will require n = 60 participants.

Question 61

One advantage of a repeated-measures design is that it typically requires fewer participants than an independent-measures design.

Question 62

A set of n = 16 difference scores has a mean of M_D = 4 and a variance of s² = 36.Cohen's d for this sample is d = 4/6.

Question 63

A repeated-measures research study uses a total of 20 participants to compare two treatment conditions.If the results are used to construct a 90% confidence interval for the population mean difference, then the t values will be ±1.729.

Question 64

A repeated?measures test usually is more likely to detect a real treatment effect than an independent?measures test because the repeated?measures design typically has a smaller variance and a smaller estimated standard error.

Question 65

Repeated-measures designs are particularly well-suited to research studies examining learning or other changes that occur over time.

Question 66

A repeated-measures study with a sample of n = 16 participants produces a repeated-measures t = 2.00.If effect size is measured using r², then r² = 4/20.

Question 67

Repeated-measures designs are particularly well-suited to research questions concerning the difference between two distinct populations (for example, males versus females).

Question 68

For a repeated-measures study, if other factors are held constant, an increase in the size of the sample will increase the likelihood of finding a significant treatment effect.

Question 69

For a repeated-measures design, the sample mean difference is always located exactly in the center of the confidence interval estimate for the population mean difference.