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

Answer 1

t = 0

Question 2

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

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

Answer 2

19

Question 3

The following data were obtained from a repeated-measures research study.What is the value of MD for these data? $$\begin{array} { c r r } \text { Subject } & \text { 1st } & 2 \text { nd } \\\hline \# 1 & 10 & 15 \\\# 2 & 4 & 8 \\\# 3 & 7 & 5 \\\# 4 & 6 & 11\end{array}$$

A)3
B)3.5
C)4
D)4.5

Answer 3

3

Question 4

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 5

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 MD = 0.
C)the entire population will have a mean difference of μD = 0.
D)All of the other options are correct.

Question 6

A matched-subjects study and an independent-measures study both produced a t statistic with df = 10.How many individuals participated in each study?

A)11 for matched-subjects and 11 for independent-measures
B)11 for matched-subjects and 12 for independent-measures
C)12 for matched-subjects and 12 for independent-measures
D)22 for matched-subjects and 12 for independent-measures

Question 7

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)A repeated-measures design
C)A matched-subjects design
D)None of the other options would require a total of 30 participants.

Question 8

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)20 measured and 10 used
B)20 measured and 20 used
C)10 measured and 10 used
D)10 measured and 20 used

Question 9

For a repeated-measures study,if the null hypothesis is true,then what value should be obtained for the sample mean?

A)MD = 0
B)MD > 0
C)MD < 0
D)MD near 0

Question 10

A repeated-measures study comparing two treatments with a sample of n = 4 participants produces a mean of M₁ = 18 with SS = 24 for the scores in the first treatment,a mean of M₂ = 14 with SS = 18 for the scores in the second treatment,and a mean of MD = 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 11

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

A)MD = 0
B)µD = 0
C)µ1 = µ2
D)M1 = M2

Question 12

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)25
B)25/4 = 6.25
C)5
D)2.5

Question 13

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

A)An independent-measures design
B)A repeated-measures design
C)A matched-subjects design
D)All of the other options would produce 20 scores in each treatment.

Question 14

A repeated-measures study and an independent-measures study both produced a t statistic with df = 10.How many individuals participated in each study?

A)12 for repeated-measures and 11 for independent-measures
B)12 for repeated-measures and 12 for independent-measures
C)11 for repeated-measures and 11 for independent-measures
D)11 for repeated-measures and 12 for independent-measures

Question 15

What is the value of the estimated standard error for the following set of D-scores? Scores: 2,2,10,2

A)3
B)√3
C)4
D)2

Question 16

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 17

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 18

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

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

Question 19

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)9
B)3
C)1
D)√8/3

Question 20

The following data were obtained from a repeated-measures research study.What is the value of SS for the difference scores? $$\begin{array} { l c c } \text { Subject } & 1 \text { st } & 2 \text { nd } \\\hline \# 1 & 10 & 11 \\\# 2 & 4 & 6 \\\# 3 & 7 & 9 \\\# 4 & 6 & 5\end{array}$$

A)10
B)6
C)4
D)1

Question 21

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 22

A repeated-measures study comparing two treatments with a sample of n = 4 participants produces MD = 3 with SS = 48 for the set of difference scores.What is the repeated-measures t statistic for these data?

A)3/√3 = 1.73
B)3/2 = 1.50
C)3/4 = 0.75
D)3/16 = 0.19

Question 23

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 24

A sample of difference scores has a mean of MD = 5 with a variance of s² = 100.If effect size is measured using Cohen's d,what is the value of d?

A)5/10
B)5/100
C)25/100
D)Cannot determine without knowing the sample size

Question 25

For a repeated-measures study comparing two treatment conditions,a researcher obtains a sample of n = 9 difference scores with a mean of MD = 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

Question 26

A researcher obtains t = 2.25 for a repeated-measures study using a sample of n = 10 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 both α = .05 and α = .01
C)Fail to reject the null hypothesis with both α = .05 and α = .01
D)Cannot make a decision without additional information

Question 27

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 28

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

A)It will increase in magnitude (move farther toward the tail of the distribution).
B)It will decrease in magnitude (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 29

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 30

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)10
C)11
D)12

Question 31

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 32

If a repeated-measures study shows a significant difference between two treatments with α = .01,then what can you conclude about measures of effect size?

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 33

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 MD = 2
B)n = 15 and MD = 4
C)n = 30 and MD = 2
D)n = 30 and MD = 4

Question 34

A researcher obtains t(20)= 2.00 and MD = 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 35

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)MD = 2
B)MD = 4
C)MD = 8
D)MD = 16

Question 36

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 37

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 38

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 39

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

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

Question 40

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

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

Question 41

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 and the repeated-measures t statistic has df = 29.

Question 42

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 43

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 44

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 45

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 MD = 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)µD = 0.60 + 0.01(1.397)
B)µD = 0.60 + 0.09(1.860)
C)µD = 0.60 + 0.10(1.397)
D)µD = 0.60 + 0.10(1.860)

Question 46

Which of the following will not increase the width of a confidence interval?

A)Increase the percentage of confidence from 80% to 90%
B)Reduce the sample size from n = 25 to n = 16
C)Increase the sample mean from MD = 2 to MD = 4
D)All of the other options will increase the width of a confidence interval.

Question 47

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

Question 48

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 49

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

Question 50

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

Question 51

Which of the following describes the effect of an increase in the variance of the difference scores in a repeated-measures design?

A)Measures of effect size and the likelihood of rejecting the null hypothesis both decrease.
B)Measures of effect size increase, but the likelihood of rejecting the null hypothesis decreases.
C)There is little or no effect on measures of effect size, but the likelihood of rejecting the null hypothesis increases.
D)There is little or no effect on measures of effect size, but the likelihood of rejecting the null hypothesis decreases.

Question 52

Which of the following describes the effect of increasing sample size in a repeated-measures design?

A)Measures of effect size and the likelihood of rejecting the null hypothesis both increase.
B)Measure of effect size increase, but the likelihood of rejecting the null hypothesis decreases.
C)There is little or no effect on measures of effect size, but the likelihood of rejecting the null hypothesis increases.
D)There is little or no effect on measures of effect size, but the likelihood of rejecting the null hypothesis decreases.

Question 53

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.What is this problem is called?

A)Individual differences
B)Order effects
C)Homogeneity of variance
D)Bi-treatment effect

Question 54

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.

Question 55

A repeated-measures study and matched-subjects study both produce t statistics with df = 20.The repeated-measures study used more participants than the matched-subjects study.

Question 56

The estimated standard error in the denominator of the repeated-measures t statistic measures the typical mean difference that is expected for a sample selected from a population with a zero mean difference.

Question 57

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

A)time-related factors
B)order effects
C)the effect of the treatment
D)individual differences

Question 58

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 59

For the following data from a repeated-measures study,the sample mean difference is MD = 1.
$$\begin{array} { c r r } \text { Participant } & X _ { 1 } & X _ { 2 } \\\hline \mathrm { A } & 1 & 5 \\\mathrm {~B} & 4 & 6 \\\mathrm { C } & 5 & 2\end{array}$$

Question 60

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 61

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

Question 62

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

Question 63

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

Question 64

One concern for a repeated-measures study is that a participant's score in one treatment may be influenced by practice or experience gained in a previous treatment.

Question 65

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

Question 66

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

Question 67

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

Question 68

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 69

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 70

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

Question 71

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

Question 72

For a repeated-measures study,if other factors are held constant,then an increase in sample size will lead to an increase in measures of effect size.

Question 73

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

Question 74

For a repeated-measures study,as the variance of the difference scores increases,the likelihood of finding a significant difference also increases.

Question 75

A repeated-measures research study comparing two treatments with a set of 10 scores in each treatment will produce a t statistic with df = 18.

Question 76

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 77

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

Question 78

For a repeated-measures study,as the sample mean difference increases,the likelihood of rejecting the null hypothesis also increases.

Question 79

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.

Question 80

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.