Deck 10: Testing Means: Truehe Related-Samples T Test

Question 1

Which of the following is the denominator of the test statistic for the related-samples t test?

A) standard error
B) estimated standard error
C) estimated standard error for the difference
D) estimated standard error for difference scores

Answer 1

estimated standard error for difference scores

Question 2

A researcher matched 30 participants on intelligence (hence 15 pairs of participants)and then compared differences in emotional responsiveness to two experimental stimuli between each pair.For this test,what are the critical values,assuming a two-tailed test at a .05 level of significance?

A) ±2.042
B) ±2.045
C) ±2.131
D) ±2.145

Answer 2

±2.145

Question 3

All other things being equal,as the sample size increases,what happens to the critical value for a related-samples t test (or for any t test,for that matter)?

A) The critical value increases.
B) The critical value decreases.
C) The critical value does not change.
D) It depends on the value of the test statistic.

Answer 3

The critical value decreases.

Question 4

Each of the following is an estimate of error for a t test,except

A) standard error.
B) estimated standard error.
C) estimated standard error for the difference.
D) estimated standard error for difference scores.

Question 5

Which of the following is the numerator of the test statistic for the related-samples t test?

A) the sum of the difference scores for each participant
B) the value of the test statistic plus the degrees of freedom
C) the mean difference observed minus the mean difference stated in a null hypothesis
D) estimated standard error for difference scores

Question 6

Which of the following is a type of related-samples design in which different participants are observed in each group,but treated statistically as if they are the same persons in each group?

A) repeated-measures design
B) matched-samples design
C) pre-post design
D) within-subjects design

Question 7

How does the test statistic differ for a t test using the repeated measures versus the matched-samples design?

A) Using the matched-samples design, we analyze raw scores, whereas using the repeated measures, we analyze difference scores before computing the test statistic for the related-samples t test.
B) Using the repeated-measures design, we analyze raw scores, whereas using the matched-samples design, we analyze difference scores before computing the test statistic for the related-samples t test.
C) Using the repeated-measures design, we treat each pair of scores as related; we do not treat each pair of scores as related using the matched-samples design.
D) The test statistic for the repeated measures and the matched-samples design does not differ; the test statistic is computed the same.

Question 8

A researcher records the time (in seconds)it takes participants to respond (by pressing a key)to a familiar and an unfamiliar word flashed onto a computer screen.In this study,the difference in response time for each participant is compared.The type of design described here is called a

A) repeated-measures design.
B) matched-samples design.
C) repeated-measures design and matched-samples design.

Question 9

A researcher compares the difference in the amount of texting by students in class during the first week and last week of classes.The type of design described here is called a

A) repeated-measures design.
B) matched-samples design.
C) repeated-measures design and matched-samples design.

Question 10

A researcher measures deviant behavior in a sample of 12 children from abusive homes (Sample A).Another researcher measures the same behavior in a sample of 18 children from abusive homes (Sample B).Which sample is associated with larger degrees of freedom?

A) Sample A
B) Sample B
C) Each sample has the same degrees of freedom.
D) There is not enough information to answer this question.

Question 11

Each of the following is an advantage for using the related-samples design,except

A) it can be more practical.
B) it minimizes standard error.
C) it increases the power of a research design.
D) it increases the variability measured in a study.

Question 12

The test statistic for a related-samples t test makes tests concerning a single sample of

A) raw scores.
B) difference scores.
C) participant scores.
D) original data.

Question 13

A type of related-samples design in which participants are observed more than once is called a

A) repeated-measures design.
B) matched-pairs design.
C) matched-samples design.
D) all of these.

Question 14

The denominator of the test statistic for a related-samples t test

A) compares mean differences observed to the mean differences stated in a null hypothesis.
B) is the sum of the difference scores for each participant.
C) provides an estimate of the error associated with the original scores.
D) provides an estimate of the error associated with the difference scores.

Question 15

A researcher records the strength of a conditioned response among 12 rats in the presence and absence of conditioned cues.If he computes a related-samples t test at a .05 level of significance (two-tailed test),then what are the critical values for this test?

A) ±2.201
B) ±2.179
C) ±1.796
D) ±1.782

Question 16

For the related-samples t test,assuming that all other values remain constant,then as samples size increases,

A) the value of the test statistic increases.
B) the power to detect an effect increases.
C) the estimate for standard error decreases.
D) all of these.

Question 17

A researcher asks a sample of brothers and sisters to rate how positive their family environment was during childhood.In this study,the differences in ratings between each brother and sister pair were compared.The type of design described here is called a

A) repeated-measures design.
B) matched-samples design.
C) repeated-measures design and matched-samples design.

Question 18

A researcher records the level of attention among 18 students during an interactive and lecture portion of a single class.If she computes a related-samples t test at a .05 level of significance (two-tailed test),then what are the critical values for this test?

A) ±1.734
B) ±1.740
C) ±2.110
D) ±2.101

Question 19

What are the degrees of freedom for the related-samples t test?

A) (n_D - 1)
B) (n - 1) (n - 1)
C) (n - 1) + (n - 1)
D) (n - 1) - (n - 1)

Question 20

One difference between a repeated-measures design and a matched-samples design is that

A) only one design is a type of related-samples design.
B) only one design increases the power to observe an effect.
C) only one design involves observing the same participants in each group.
D) only one design eliminates between-persons variability.

Question 21

A researcher conducts a study in which the same participants are observed across each level of the independent variable.If there are only two levels of the independent variable,then what type of t test is appropriate for this study?

A) one-sample t test
B) two-independent-sample t test
C) related-samples t test
D) there is not enough information to answer this question

Question 22

A researcher selects a sample of 36 dog owners and measures their responsiveness to pictures depicting the humane and inhumane treatment of dogs.The researcher finds that responsiveness significantly differed,t = 3.243.Use $\eta$ ² to compute the proportion of variance for this result.

A) $\eta$ ² = .21
B) $\eta$ ² = .23
C) $\eta$ ² = .25
D) there is not enough information to answer this question

Question 23

A researcher conducts a study in which different participants are independently observed within groups,and the same participants are observed between groups.If there are only two groups,then what type of t test is appropriate for this study?

A) one-sample t test
B) two-independent-sample t test
C) related-samples t test
D) There is not enough information to answer this question.

Question 24

Each of the following is needed to compute the estimated Cohen's d,except

A) the mean difference.
B) the standard error.
C) the standard deviation of difference scores.

Question 25

A professor compares scores on a competency exam among students at two times during a single semester.What type of t test is most appropriate for this study?

A) one-sample t test
B) two-independent-sample t test
C) related-samples t test
D) there is not enough information to answer this question

Question 26

A researcher tests how well participants know their spouse while under hypnosis,and again without hypnosis.It was hypothesized that participant responses would be more accurate (greater number of correct responses)when under hypnosis.The mean number of correct responses was M = 5.30 under hypnosis and M = 3.40 without hypnosis in a sample of 30 participants.If the estimated standard error for difference scores was 2.52,then what is the decision at a .05 level of significance (two-tailed test)?

A) Retain the null hypothesis; responses were more accurate under hypnosis.
B) Retain the null hypothesis; responses were not more accurate under hypnosis.
C) Reject the null hypothesis; responses were more accurate under hypnosis.
D) Reject the null hypothesis; responses were not more accurate under hypnosis.

Question 27

All other things being equal,as the degrees of freedom increase,what happens to the critical value for a related-samples t test (or for any t test,for that matter)?

A) The critical value increases.
B) The critical value decreases.
C) The critical value does not change.
D) It depends on the value of the test statistic.

Question 28

To increase the value of estimated Cohen's d,a researcher increases the sample size.Will this change the value of d?

A) Yes; as sample size increases, effect size increases.
B) No; as sample size increases, effect size decreases.
C) No; the sample size is not used to compute effect size.
D) Yes; as sample size increases, effect size decreases.

Question 29

A researcher selected a sample of 24 participants and observed their behavior at two times.The result of a related-samples t test at a .05 level of significance was t = 2.68.Which of the following correctly describes the result of this test?

A) A related-samples t test is the correct test for this study; the result of the test is not significant.
B) A related-samples t test is the correct test for this study; the result of the test is significant.
C) The result of the test cannot be appropriately interpreted because the related-samples t test was not the correct test for this study; the researcher should have computed a two-independent-sample t test.
D) The result of the test cannot be appropriately interpreted because the related-samples t test was not the correct test for this study; the researcher should have computed a one-sample t test.

Question 30

To compute a related-samples t test,a researcher has to know many values.Which of the following is NOT a value that the researcher must know to compute this test?

A) the estimated standard error for difference scores
B) the population variance of difference scores
C) the sample size or number of pairs of scores
D) the sample variance of difference scores

Question 31

A researcher conducts a study in which the population variance of difference scores between two groups is unknown.What type of t test is most appropriate for this study?

A) one-sample t test
B) two-independent-sample t test
C) related-samples t test
D) there is not enough information to answer this question

Question 32

A professor computes the mean difference in exam scores before and after a lecture as 9.0 ± 14.5 (M_D ± S_D),and this difference was significant.What is the effect size for this result using estimated Cohen's d?

A) d = 0.62 (medium effect)
B) d = 1.61 (medium effect)
C) d = 0.62 (large effect)
D) d = 1.61 (large effect)

Question 33

A researcher placed male rodents in the presence and absence of a conspecific male.Cortisol (a stress hormone)levels were compared at both times.What type of t test is most appropriate for this study?

A) one-sample t test
B) two-independent-sample t test
C) related-samples t test
D) There is not enough information to answer this question.

Question 34

A researcher sampled 25 participants and measured their alcohol consumption (in ounces)in both a home and a bar setting.If the mean difference in satisfaction ratings for this sample was 11.4 ± 2.5 (M_D ± S_MD),then what is the decision at a .05 level of significance?

A) Alcohol consumption significantly differed, t(23) = 4.56.
B) Alcohol consumption significantly differed, t(24) = 4.56.
C) Alcohol consumption significantly differed, t(23) = 22.80.
D) Alcohol consumption significantly differed, t(24) = 22.80.

Question 35

A researcher sampled 16 couples and measured the mean difference in their marital satisfaction.Each couple was paired and the differences in their ratings (on a 7-point scale)were taken.If the mean difference in satisfaction ratings for this sample was 1.8 ± 2.0 (M_D ± S_D),then what is the decision at a .05 level of significance?

A) Satisfaction ratings do not significantly differ, t(14) = 0.90.
B) Satisfaction ratings do not significantly differ, t(15) = 0.90.
C) Satisfaction ratings significantly differ, t(14) = 3.60.
D) Satisfaction ratings significantly differ, t(15) = 3.60.

Question 36

All other things being equal,reducing the level of significance from .05 to .01 will ______ the value of the test statistic for a related-samples t test.

A) increase
B) decrease
C) have no effect on

Question 37

A researcher computes the mean difference in locomotion in a sample of 12 rats before and 30 min after an injection of amphetamine.Rats were placed in a box with infrared beams.The number of times rats crossed the beams was used as a measure of locomotion.The mean difference in locomotion was 6.2 ± 8.4 (M_D ± S_D)and this difference was significant.What is the effect size for this result using estimated Cohen's d?

A) d = 0.74 (medium effect)
B) d = 1.36 (medium effect)
C) d = 0.74 (large effect)
D) d = 1.36 (large effect)

Question 38

A researcher conditions rats to fear a tone that was sounded just prior to a brief shock.To measure fear following this conditioning,she records the number of lever presses by each rat in the presence and in the absence of the tone.It was hypothesized that reduced lever pressing in the presence of the tone was evidence for a conditioned fear response in rats.If the researcher tested this hypothesis at a .05 level of significance (two-tailed test),then what is her decision if she computes t = -2.842 in a sample of eight rats.

A) Retain the null hypothesis; there is evidence for a conditioned fear response.
B) Retain the null hypothesis; there is no evidence for a conditioned fear response.
C) Reject the null hypothesis; there is evidence for a conditioned fear response.
D) Reject the null hypothesis; there is no evidence for a conditioned fear response.

Question 39

All other things being equal,increasing the sample size will ______ the value of the test statistic for a related-samples t test.

A) increase
B) decrease
C) have no effect on

Question 40

Which of the following is an assumption for computing the related-samples t test?

A) The population being sampled from is normally distributed.
B) The population variance of difference scores is unknown.
C) Samples are related or matched between groups, but not within groups.
D) All of these.

Question 41

Compared to the two-independent-sample t test,the related-samples design decreases

A) power.
B) effect size.
C) standard error.
D) significance.

Question 42

The degrees of freedom for the related-samples t test are the number of difference scores minus one.

Question 43

A study in which 26 participants are observed two times is associated with 26 degrees of freedom for a related-samples t test.

Question 44

"Elementary school children spent significantly more time reading the presence of a teacher than when the teacher was absent,t(7)= 2.804,p < .05 ( $\omega$ ² = .46)." In this related-samples t test,how many participants were observed?

A) 5
B) 6
C) 7
D) 8

Question 45

Participants can be matched through experimental manipulation or through natural occurrences to use the matched-pairs design.

Question 46

Two researchers analyze the same data set.Researcher A uses a two-independent-sample t test and decides to retain the null hypothesis.Researcher B uses a related-samples t test and decides to reject the null hypothesis.Which of the following is a likely explanation for the disparity in the decisions made?

A) The two-independent-sample t test had greater power to detect the effect.
B) The two-independent-sample t test was associated with fewer degrees of freedom.
C) The related-samples t test had greater power to detect the effect.
D) The related-samples t test was associated with more degrees of freedom.

Question 47

When reporting data in a results section,it is ______ necessary to identify the type of t test computed.

A) always
B) not
C) usually
D) significantly

Question 48

A researcher selects a sample of 24 college students and has them rate their liking for two advertisements aimed at improving the image of the college.The researcher finds that liking ratings significantly differed,t = 2.900.Use $\omega$ ² to compute the proportion of variance for this result.

A) $\omega$ ² = .30
B) $\omega$ ² = .24
C) $\omega$ ² = .21
D) there is not enough information to answer this question

Question 49

The estimated standard error for difference scores is in the denominator of the test statistic for the related-samples t test.

Question 50

The repeated-measures design,but not the matched-pairs design,is associated with greater power to detect an effect compared with the independent-samples design.

Question 51

The degrees of freedom for the related-samples t test are the number of pairs of participants minus one and not always the total number of participants minus one.

Question 52

The related-samples design can ______.

A) eliminate within-groups error
B) have no effect on power
C) increase standard error
D) be more practical

Question 53

The test statistic for the related-samples t test is equivalent to the test statistic for the two-independent-sample t test.

Question 54

Which of the following is an advantage for selecting related samples compared to selecting independent samples in behavioral research?

A) Selecting related samples can be more practical.
B) Selecting related samples minimizes standard error.
C) Selecting related samples increases power.
D) All of these.

Question 55

Using APA format,which value is typically given in parentheses when reporting the results for a t test?

A) The degrees of freedom
B) The estimate for standard error
C) The value of the test statistic
D) The level of significance

Question 56

The related-samples t test is associated with no degrees of freedom.

Question 57

The related-samples t test makes tests concerning the difference between pairs of measured scores.

Question 58

Which of the following identifies a large effect size for a t test?

A) $\eta$ ²= .25
B) d = .76
C) $\omega$ ² = .20
D) t = 2.32

Question 59

The related-samples design can ______ the power to detect an effect by making the standard error ______.

A) increase; smaller
B) increase; larger
C) decrease; smaller
D) decrease; minimal

Question 60

An example of matching by experimental manipulation would be if we matched participants based on their gender (male,female).

Question 61

Using the same data,a related-samples t test has greater power than a two-independent-sample t test to detect an effect.

Question 62

Selecting related samples minimizes standard error and increases power.

Question 63

A researcher computes a related-samples t test with t(20)= 2.096.In this example,the decision is to reject the null hypothesis for a one-tailed test,but not for a two-tailed test.

Question 64

A researcher computes d = 0.12,which is a small effect size.

Question 65

Selecting related samples increases standard error and reduces power.

Question 66

The decision is to reject the null hypothesis for the following related-samples t test: t(23)= 2.25,p < .05 (d = 0.18).

Question 67

The estimate for standard error is placed in the numerator of the test statistic for a related-samples t test.

Question 68

The estimated Cohen's d for the related-samples t test uses the sample standard deviation for difference scores as an estimate of the standard deviation of difference scores in the population.

Question 69

Original pairs of scores are first reduced to difference scores before computing the test statistic for the related-samples t test.

Question 70

Selecting related samples can be more practical.

Question 71

As the value of the test statistic for a related-samples t test increases,the likelihood of deciding to retain the null hypothesis also increases.

Question 72

A researcher computes d = 0.26.Hence,it is appropriate to conclude that 26% of the variability in the dependent variable can be accounted for by the presence of the independent variable.

Question 73

The estimated standard error for difference scores is the denominator of the test statistic for a related-samples t test.

Question 74

Both estimates of proportion of variance, $\eta$ ² and $\omega$ ²,are computed the same for two-independent and related-samples t tests.

Question 75

The assumptions for a related-samples t test apply to both the repeated-measures and matched-pairs designs.

Question 76

If a related-samples t test is significant,then it will also be associated with a large effect size.

Question 77

To compute the related-samples t test,we assume independence within groups.

Question 78

The type of t test that was used is typically reported in a data analysis section that precedes the results section in an APA-style paper.

Question 79

To summarize a related-samples t test,we report the test statistic,critical values,and p value.

Question 80

The assumptions for a related-samples t test are the same as those for the two-independent-sample t test.