Chapter 11-Repeated Measures t-Test

Question 1

Repeated Measures Design Usage

Answer 1

-Evaluates the mean difference between two measurements taken from a single sample… we test a hypothesis about the population mean difference between two measurements using a single sample
-Used when we have no standard deviation, cannot estimate the mean, and are examining one sample

aka the within-subject, related-samples, or dependent-samples design

Question 2

Difference score

Answer 2

D=X2-X1
* X1 is the person’s score at first measurement
* X2 is the person’s score at the second measurement

We must compute a difference score for each individual difference score

Question 3

Advantages to repeated-measures designs

Answer 3

• Repeated measures designs require fewer participants than needed for an independent-measures design
• Repeated-measures designs are particularly well suited for examining changes that occur over time (for example, learning or development)

Question 4

Why do repeated measures designs require fewer participants than needed for an independent-measures design?

Answer 4

• Individual differences in performance to another are eliminated
• This reduces the variance between subjects, reduces the estimated standard error, and increases power

Question 5

Disadvantages to the repeated-measures designs

Answer 5

• Testing effects
• Floor and ceiling effects

Question 6

What are testing effects?

Answer 6

• Expposure to the first condition may influence scores in the second condition
• For example, practice on an IQ test in the first condition may cause improved performance in the second condition

Question 7

What are floor and ceiling effects?

Answer 7

• Floor effects: occur when an individual’s score is so low in condition 1 that they have nowhere to go but up in condition 2
• Ceiling effects: occur when an individual has such a high score in condition 1 that there is nowhere to go but down in condition 2

Question 8

What is used for hypothesis testing w repeated-measures t-stat?

Answer 8

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 9

Null hypothesis for repeated-measures t-statistic:

Answer 9

-There is no consistent or systematic difference between the two conditions. Some participants may show a positive or negative difference, but on average, μD = zero.

Question 10

Alternative hypothesis (two-tailed)

Answer 10

• There is a systematic difference between conditions that produces a non-zero mean difference: H1: μD ≠ 0
• The alternative hypothesis is that the sample mean difference represents a true mean difference in the population

Question 11

What are calculations done with for the repeated-measures t-test?

Answer 11

The sample of difference scores

Question 12

What is the numerator of the repeated-measures t-test?

Answer 12

• The theoretical numerator of the repeated-measures t-test is: MD - μD
• MD=observed mean difference score
• uD= hypothesized population difference
• So, since the null hypothesis is that uD=0, practically speaking, numerator=MD

Question 13

Estimated Standard Error for the MD

Answer 13

• is calculated essentially the same way we calculated the estimated standard error of the M (for a one-sample t-test)
• But in this case, the numerator (SD) is the standard deviation of the difference scores

SMD= SD / Square root of n

Question 14

Steps to hypothesis testing with the repeated-measures t-statistic

Answer 14

1. State the hypotheses and select the alpha level (for a non-directional repeated-measures test, H0 states there is no difference between conditions)
2. Locate the critical region (degrees of freedom=n-1)
3. Compute the test statistic (has the same general structure as the one-sample t-test)
4. Make a decision (compare t-value to critical value)