Deck 11: The T Test for Two Related Samples

Question 1

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_D = 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

Answer 1

D

Question 2

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

Answer 2

A

Question 3

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

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

Answer 3

A

Question 4

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

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

Question 5

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 6

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 7

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

Question 8

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 9

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 10

A repeated-measures study comparing two treatments with n = 4 participants produces M_D = 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 11

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 12

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

Question 13

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 14

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 15

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 16

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 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

A repeated-measures study comparing two treatments with a sample of n = 4 participants produces M_D = 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 19

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 20

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

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

Question 21

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 22

In general,if the variance of the difference scores increases,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 23

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 24

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 25

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 26

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 27

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 28

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 29

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 30

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 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 31

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 32

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 33

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,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 34

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 35

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 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

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

Question 38

Which of the following describes the effect of an increase in the variance of the difference scores?

A)Measures of effect size and the likelihood of rejecting the null hypothesis both decrease.
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 39

Which of the following describes the effect of increasing sample size?

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 40

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 41

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 42

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 43

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 44

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

Question 45

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

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 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 48

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 49

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 50

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

Question 51

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

Question 52

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

Question 53

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 M_D = 2 to M_D = 4
D)All of the other options will increase the width of a confidence interval.

Question 54

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 55

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 56

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 57

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 58

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

Question 59

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

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

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

Question 62

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

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

Briefly explain the advantages and disadvantages of using a repeated-measures design as opposed to an independent-measures design.

Question 65

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

Question 66

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 67

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 68

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 69

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

Question 70

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 71

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

Question 72

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

Question 73

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.

Question 74

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 75

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

Question 76

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.