Deck 11: The T Test for Two Related Samples

Question 1

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.What 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.

Answer 1

​Reject the null hypothesis with a one-tailed test but fail to reject with two tails.

Question 2

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)​independent-measures design
B)​repeated-measures design
C)​matched-subjects design
D)​between-measures design

Answer 2

​repeated-measures design

Question 3

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

Answer 3

​a significant effect does not necessarily mean that the effect size will be large

Question 4

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

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

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

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

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

Question 8

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 9

The null hypothesis for a repeated-measures test states that ____.​

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 μD = 0
D)​the individuals have different means

Question 10

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 11

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 12

For the repeated-measures t statistic,where n1 and n2 are the number of scores before and after treatment,and n = n₁= n₂,df = ____.​

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

Question 13

If other factors are held constant,which set 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 14

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 15

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 16

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

A)​3
B)​3.5
C)​4
D)​2

Question 17

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 18

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)​Change α to α = .10.

Question 19

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 20

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 21

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 22

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 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 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 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.What 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

Which possible outcome is of 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)​You lose too many degrees of freedom.

Question 27

A repeated-measures design has the maximum advantage over an independent-measures design when ____.​

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

Question 28

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 29

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 30

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 referred to as ____.​

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

Question 31

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 32

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 33

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

Question 34

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 35

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 36

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)​a very large variance in 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

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 to ____.​

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 39

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)​This cannot be determined without knowing the sample size.

Question 40

Assuming that other factors are held constant,which approach 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)​Decrease the sample mean difference.

Question 41

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

Question 42

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 43

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 44

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

Question 45

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 46

?For the following data from a repeated-measures study,the sample mean difference is M_D = 4. $$\begin{array} { l r r } \text { Participant } & X _ { 1 } & X _ { 2 } \\\hline \text { A } & 1 & 7 \\\text { B } & 4 & 8 \\\text { C } & 5 & 3 \\\hline\end{array}$$

Question 47

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 48

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 49

In a repeated-measures design,or a within-subjects design,one group of participants is measured in two different treatment conditions so there are two separate scores for each individual in the sample.

Question 50

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 51

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 52

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 53

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

Question 54

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

Question 55

A related-sample design consists of scores in one set that are directly related,one-to-one,with the scores in the second set.

Question 56

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

Question 57

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

Question 58

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

Question 59

A Wilcoxon test can be used if there is reason to suspect that one of the assumptions for the repeated-measures t test has been violated.

Question 60

A matched-subjects design involves two separate samples,but each individual in one sample is matched one-to-one with an individual in the other sample.

Question 61

Individual differences are characteristics such as age,IQ,gender,and personality that vary from one individual to another.

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

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

Question 66

Calculate the difference scores and find M_D for the following data from a repeated-measures study.Subject Treatment 1 Treatment 2

Question 67

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

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

Question 70

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

Question 71

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

Question 72

A researcher would like to examine how the chemical tryptophan,contained in foods such as turkey,can affect mental alertness.A sample of n = 9 college students is obtained and each student's performance on a familiar video game is measured before and after eating a traditional Thanksgiving dinner including roast turkey.The average score dropped by M = 14 points after the meal with SS = 1152 for the difference scores.
a. Is there is significant difference in performance before eating versus after eating? Use a two-tailed test with α = .05.
b. Compute r2 to measure the size of the effect.
c. Write a sentence demonstrating how the outcome of the test and the measure of effect size would appear in a research report.

Question 73

One of the major advantages of a repeated-measures design is that it removes individual differences from the variance and,therefore,reduces the standard error.The following two sets of data demonstrate this fact.The first set of data represents the original results from a repeated-measures study.To create the second set of data we started with the original scores but increased the individual differences by adding 10 points to each score for subject B,adding 20 points to each score for subject C,and adding 30 points to each score for subject D.Note that this change produces a huge increase in the differences from one subject to another and a huge increase in the variability of the scores within each treatment condition.​​ ​
a. Find the difference scores for each set of data and compute the mean and variance for each sample of difference scores.
b. You should find that both sets of data produce the same mean difference and the same variance for the difference scores. Explain what happened to the huge individual differences that were added to the second set of data.

Question 74

A teacher gives a third grade class of n = 16 a reading skills test at the beginning of the school year.To evaluate the changes that occur during the year,students are tested again at the end of the year.Their test scores revealed an average improvement of MD = 4.7 points.
a. If the variance for the difference scores is s2 = 144, are the results sufficient to conclude that there is significant improvement? Use a one-tailed test with α = .05.
b. If the variance for the difference scores is reduced to s2 = 64, are the results sufficient to conclude that there is significant improvement? Use a one-tailed test with α = .05.
c. Describe the effect on reducing the variance of the difference scores.

Question 75

A researcher would like to determine if relaxation training will affect the number of headaches for chronic headache sufferers.For a week prior to training,each participant records the number of headaches suffered.Participants then receive relaxation training and for the week following training the number of headaches is again measured.The data are as follows:
a. Compute the mean and variance for the sample of difference scores.
b. Do the results indicate a significant difference? Use a two-tailed test with α = .05.
c. Compute Cohen's d to measure the size of the effect.

Question 76

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.