PSY201: Chapter 11 - Repeated Measures

Question 1

Repeated-Measures Designs

Answer 1

related-samples hypothesis test allows researchers to evaluate mean diff betw 2 treatment conditions using data from single sample
single group of individuals obtained + each indiv is measured in both of treatment conditions being compared.

Question 2

Repeated-Measures Designs

Answer 2

data consist of 2 scores for each indiv

Question 3

Hypothesis Tests with the Repeated- Measures t

Answer 3

repeated-measure ststatistic allows researchers to test hypothesis about pop mean diff betw 2 treatment conditions using sample data

Question 4

Hypothesis Tests with the Repeated- Measures t

Answer 4

possible to compute difference score for each indiv:
difference score = D = X2 – X1
X1 - first treatment + X2 score in second treatment
always subtract in same direction (2nd - 1st) even if result is negative value

Question 5

Hypothesis Tests with the Repeated- Measures t

Answer 5

n The related-samples t test can also be used for a similar design, called a matched-subjects design, in which each individual in one treatment is matched one-to-one with a corresponding individual in the second treatment.
can be better than the independent depending on subject, but less valid

Question 6

Hypothesis Tests with the Repeated- Measures t

Answer 6

n The matching is accomplished by selecting pairs of participants so that the two subjects in each pair have identical (or nearly identical) scores on the variable that is being used for matching., e.g., match on IQ scores

Question 7

Hypothesis Tests with the Repeated- Measures t

Answer 7

n Thus, the data consist of pairs of scores with each pair corresponding to a matched set of two “identical” subjects.
n For a matched-subjects design, a difference score is computed for each matched pair of individuals.

Question 8

Hypothesis Tests with the Repeated- Measures t

Answer 8

n However, because the matching process can never be perfect, matched-subjects designs are relatively rare.
n As a result, repeated-measures designs (using the same individuals in both treatments) make up the vast majority of related-samples studies.

Question 9

Hypothesis Tests with the Repeated- Measures t

Answer 9

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Question 10

Hypothesis Tests with the Repeated- Measures t

Answer 10

The sample of difference scores is used to test hypotheses about the population of difference scores. The null hypothesis states that the population of difference scores has a mean of zero,
H0: μD = 0

Question 11

Hypothesis Tests with the Repeated- Measures t

Answer 11

n In words, the null hypothesis says that there is no consistent or systematic difference between the two treatment conditions.
n Note that the null hypothesis does not say that each individual will have a difference score equal to zero.

Question 12

Hypothesis Tests with the Repeated- Measures t

Answer 12

n Some individuals will show a positive change from one treatment to the other, and some will show a negative change.
no consistent systematic effect/difference between scores

Question 13

Hypothesis Tests with the Repeated- Measures t

Answer 13

n On average, the entire population will show a mean difference of zero.
n Thus, according to the null hypothesis, the sample mean difference should be near to zero.

Question 14

Hypothesis Tests with the Repeated- Measures t

Answer 14

Remember, the concept of sampling error states that samples are not perfect and we should always expect small differences between a sample mean and the population mean.

Question 15

Hypothesis Tests with the Repeated- Measures t

Answer 15

Thealternativehypothesisstatesthatthereisa systematic difference between treatments that causes the difference scores to be consistently positive (or negative) and produces a non-zero mean difference between the treatments:
H1: μD≠0

Question 16

Hypothesis Tests with the Repeated- Measures t

Answer 16

Accordingtothealternativehypothesis,thesample mean difference obtained in the research study is a reflection of the true mean difference that exists in the population.

Question 17

Hypothesis Tests with the Repeated- Measures t

Answer 17

n The repeated-measures t statistic forms a ratio with exactly the same structure as the single-sample t statistic presented in Chapter 9.
n The numerator of the t statistic measures the difference between the sample mean and the hypothesized population mean.

Question 18

Hypothesis Tests with the Repeated- Measures t

Answer 18

n For the repeated-measures t statistic, all calculations are done with the sample of difference scores.
n The mean for the sample appears in the numerator of the t statistic and the variance of the difference scores is used to compute the standard error in the denominator.

Question 19

Hypothesis Tests with the Repeated- Measures t

Answer 19

Similar to before, the standard error is computed by

sMD = s2/n or sMD = s/√n

Question 20

Measuring Effect Size for the Independent-Measures t

Answer 20

n Effectsizefortheindependent-measurestismeasured in the same way that we measured effect size for the single-sample t and the independent-measures t.

Question 21

Measuring Effect Size for the Independent-Measures t

Answer 21

n Specifically,youcancomputeanestimateofCohen’sd to obtain a standardized measure of the mean difference, or you can compute r2 to obtain a measure of the percentage of variance accounted for by the treatment effect.

Question 22

Comparing Repeated-Measures and Independent-Measures Designs

Answer 22

n Becausearepeated-measuresdesignusesthesame individuals in both treatment conditions, this type of design usually requires fewer participants than would be needed for an independent-measures design.

Question 23

Comparing Repeated-Measures and Independent-Measures Designs

Answer 23

n Inaddition,therepeated-measuresdesignisparticularly well suited for examining changes that occur over time, such as learning or development.

Question 24

Comparing Repeated-Measures and Independent-Measures Designs

Answer 24

n The primary advantage of a repeated-measures design, however, is that it reduces variance and error by removing individual differences.
n The first step in the calculation of the repeated- measures t statistic is to find the difference score for each subject.

Question 25

Comparing Repeated-Measures and Independent-Measures Designs

Answer 25

This simple process has two very important consequences:
1. First, the D score for each subject provides an indication of how much difference there is between the two treatments. If all of the subjects show roughly the same D scores, then you can conclude that there appears to be a consistent, systematic difference between the two treatments. You should also note that when all the D scores are similar, the variance of the D scores will be small, which means that the standard error will be small and the t statistic is more likely to be significant.

Question 26

Comparing Repeated-Measures and Independent-Measures Designs

Answer 26

2. Also, note that the process of subtracting to obtain the D scores removes the individual differences from the data. That is, the initial differences in performance from one subject to another are eliminated. Removing individual differences also tends to reduce the variance, which creates a smaller standard error and increases the likelihood of a significant t statistic.

Question 27

Comparing Repeated-Measures and Independent-Measures Designs

Answer 27

n First, all show an increase of roughly 5 points when they move from treatment 1 to treatment 2.
n Becausethetreatmentdifferenceisveryconsistent,the D scores are all clustered close together will produce a very small value for s2.

Question 28

Comparing Repeated-Measures and Independent-Measures Designs

Answer 28

n This means that the standard error in the bottom of the t statistic will be very small.

Question 29

Comparing Repeated-Measures and Independent-Measures Designs

Answer 29

n Second, the original data show big differences from one subject to another. For example, subject B has scores in the 20’s and subject E has scores in the 70’s.
n These big individual differences are eliminated when the difference scores are calculated.

Question 30

Comparing Repeated-Measures and Independent-Measures Designs

Answer 30

n Because the individual differences are removed, the D scores are usually much less variable than the original scores.
n Again, a smaller variance will produce a smaller standard error, which will increase the likelihood of a significant t statistic.

Question 31

Comparing Repeated-Measures and Independent-Measures Designs

Answer 31

n Finally, you should realize that there are potential disadvantages to using a repeated-measures design instead of independent-measures.

Question 32

Comparing Repeated-Measures and Independent-Measures Designs

Answer 32

n Becausetherepeated-measuresdesignrequiresthat each individual participate in more than one treatment, there is always the risk that exposure to the first treatment will cause a change in the participants that influences their scores in the second treatment.

Question 33

Comparing Repeated-Measures and Independent-Measures Designs

Answer 33

practice in first treatment may cause improved performance in the 2nd treatment
scores in 2nd treatment may show diff, but diff is not caused by the second treatment

Question 34

Comparing Repeated-Measures and Independent-Measures Designs

Answer 34

When participation in 1 treatment influences scores in another treatment, results may be distorted by order effects - can be serious problem
Reducing order effects by counterbalancing

Question 35

Comparing Repeated-Measures and Independent-Measures Designs

Answer 35

could pick up strategies on first test to use on second test, so it may not be treatment (practice effects, one test is easier) - counterbalance
half ppl do one word list first time + opposite in second treatment
time can introduce confounds