Chapter 11
Standard error is directly related to sample variance Larger variance leads to ____
Larger error
but each individual in one sample is matched one-to-one with an individual in the other sample (The ____ score is computed for each matched pair, similar to repeated-measures design)
difference
For independent-measures, you calculate SS or variance for the scores in each of the two separate samples For repeated-measures, the SS and variance are computed for the ____ When individual differences are eliminated (by calculating difference scores), the variance and standard error are dramatically ____ *Increases the chances of finding a significant result
difference scores reduced
A matched-subjects design involves two separate samples (similar to independent-measures), Thus, no risk of ____ or ____
order effects or carry-over effects
The results of a repeated-measures study with n = 25 participants produce a mean difference of MD = 1.2 points with SS = 96 for the difference scores and a t statistic of t = 3.00 If the percentage of variance, r^2, is used to measure effect size, then what is the value of r^2?
3*3=9 9/(9+24)=0.2727
Formula for Cohen's d with repeated-measures t
Because the population mean and standard deviation are unknown, we use the sample values instead
The 2 most commonly used measures of effect size
Cohen's d r^2, the percentage of variance accounted for
____ use the sample mean difference MD to estimate the population mean difference muD
Confidence intervals
For the repeated-measures design, the sample data are difference scores and are identified by the letter ____, rather than X
D
The sample of difference scores (D values) serves as the sample data for the hypothesis test and all calculations are done using ____
D scores
The t Statistic for a Repeated Measures Research Design is essentially the same as the single-sample t statistic Major distinction of the repeated measures t: it is based on ____ rather than raw scores
Difference scores
The primary disadvantage of a repeated-measures design is that the structure of the design allows for factors other than the treatment effect to cause a participant's score to change from one treatment to the next For example...
E.g., outside factors that change over time Health Mood Weather
Provides a measure of how much difference is reasonable to expect
Estimated standard error
As always, the null hypothesis states that for the general population, there is no effect/no change/no difference
H0 : muD = 0
The alternative hypothesis states that there is a treatment effect that causes the scores in one treatment condition to be systematically higher (or lower) than the scores in the other condition The difference scores for the individual sin the population tend to be systematically positive (or negative), indicating a ____, ____ difference between the two treatments
H1 : muD does not equal 0 consistent predictable
____ are characteristics such as age, IQ, gender, and personality that vary from one individual to another
Individual differences These individual differences can influence the scores obtained in a research study, and can affect the outcome of a hypothesis test
Are matched-subjects designs the same as a repeated-measures design?
NO !!! The matched pairs of participants in a matched-subjects design are not really the same people
Changes in scores that are caused by participation in an earlier treatment
Order effects
What is the value fro the estimated standard error for a set of n = 9 difference scores with SS = 72?
SS/df = variance 72/8 = 9 sqrt(variance/n) sqrt(9/9) = 1
Two factors that can influence the outcome of a hypothesis test:
Sample variability Sample size
Standard error is inversely related to sample size Larger sample size leads to ____
Smaller error
Which of the following is a concern with repeated-measures designs? a. Negative values for difference scores b. Carry-over effects c. Obtaining a mean difference that is due to individual differences rather than treatment differences d. All of the above
The matched pairs of participants in a matched-subjects design are not really the same people
What is n?
The number of D scores
Two basic assumptions of related samples t tests
The observations within each treatment condition must be independent The population of distribution difference scores (D values) must be normal
For a repeated-measures study with n = 12 scores in each treatment, a researcher constructs an 80% CI to describe the mean difference between treatments. What value is at the center of the interval and what t values are used to construct the interval?
The sample mean difference is at the center and t ± 1.363
A research report describing the resuslts from a repeated-measures study states, "The data showed a significant difference between treatments, t(22) = 4.71, p <.01" From this report, what can you conclude about the outcome of the hypothesis test?
The test rejected the null hypothesis
Directional prediction can be incorporated into the statement of the hypotheses E.g., academic problems will ____ when the participants have less than average sleep the previous night
increase
Matched subjects designs have the advantages of both ___ and ____ without the disadvantages of either one
independent- and repeated-measures design
The ____ design would use two separate samples (one in each treatment condition) The ____ design would use only one sample with the same individuals participating in both treatments In general, the ____ has most of the advantages
independent-measures repeated-measures repeated-measures design
The primary advantage of a repeated-measures design is that it reduces or eliminates problems caused by ____
individual differences
The normality assumption is not a cause for concern unless the sample size is relatively small With relatively ____, this assumption can be ignored
large samples (n > 30)
Occasionally, researchers try to approximate the advantages of independent-measures and repeated-measures designs by using a technique known as ____
matched subjects
A researcher conducts a repeated-measures study comparing two treatment conditions with a sample of n = 25 participants and obtains a t statistic of t = 2.21 Which of the following the correct decision for a two-tailed test? a. Reject the null hypothesis with an alpha of .05 but fail to reject with an alpha of .01 b. Reject the null hypothesis with either alpha of .05 or .01 c. Fail to reject the null hypothesis with either alpha of .05 or .01 d. Cannot determine the correct decision without more information
n = 25 df = 24 Critical region a = .05 is 2.064 a = .01 is 2.797 a. Reject the null hypothesis with an alpha of .05 but fail to reject with an alpha of .01
The picture of the sample distribution should help you understand the measure of effect size and the outcome of the hypothesis test:
n = 8, MD = 4.00 points, s = 4 points Null hypothesis is labeled Notice the scores in the sample are displaced away from zero Specifically, the data are not consistent with a population mean of 0, which is why we rejected the null Note the sample mean is located one standard deviation above 0 This distance corresponds to the effect size measured by Cohen's d = 1.00
Sample size has ____ effect on the value of Cohen's d and only a small influence on r^2
no
It's also possible that participation in the first treatment influences the individual's score in the second treatment E.g., participants may gain experience during the first treatment condition (____ effects)
practice
With a ____, one group of participants is measured in two different treatment conditions so that there are two separate scores for each individual in the sample (e.g., before and after treatment)
repeated-measures design
The same variable is being measured twice for the same set of individuals We are literally ____ measurements on the same sample
repeating
In a matched-subjects design, the ____ t test used for the repeated-measures design is used
same
The sample mean, M, is calculated from the ____ The population mean, m, is obtained from the ____ The estimated standard error, SM, is also calculated from the ____
sample data null hypothesis sample data
Use the ____ to answer questions about the general population E.g., is there any difference between two treatment conditions for the general population?
sample of difference scores
The confidence interval estimates the ____ of the treatment effect by estimating the population mean difference between the two treatment conditions
size
Larger variance produces ____ measures of effect size
smaller
Typically, the individuals are matched on one or more variables that are considered to be especially important for the study E.g., IQ Ensures the two samples are equivalent (or matched) with respect to a...
specific variable
Repeated-measures requires fewer ____
subjects
Typically, difference scores, or D values, are obtained by ____ the first score (before treatment) from the second score (after treatment) for each person Difference score = D = X2 - X1 The sign of each D score tells you the direction of change
subtracting
We are interested in whether there is a ____ difference between the scores in the first treatment condition and the scores in the second treatment condition
systematic
The repeated-measures design is especially well suited for studying learning, development, or other changes that take place over ____
time
Although variance and sample size both influence the hypothesis test, only ____ has a large influence on measures of effect size such as Cohen's d and r^2
variance
Any value greater than ____ is considered to be a large effect
.80
The hypothesis test with the repeated-measures t statistic follows the same four-step process that we have used for other test
1) State the hypothesis, and select the alpha level 2) Locate the critical region 3) Calculate t statistic 4) Make a decision
One-Tailed Test 1) State the hypothesis, and select the alpha level 2) Locate the critical region
1) State the hypothesis, and select the alpha level Hypotheses H0 : muD < 0 H1 : mu D > 0 2) Locate the critical region Two stage process Look at the sample mean difference to verify that its in the predicted direction -If not, stop the test -If it is, question if it is large enough to be significant Any t statistic beyond 1.895 positive or negative is sufficient to reject the null With an n of 8, we obtain a df of 7, and a critical value of t = 1.895 with an a of .05
E.g. study: "To study or to sleep?" The primary result from the study is that students reported more academic problems following nights with less-than-average sleep than they did after nights with more-than-average sleep, especially for the older students Recently a researcher attempted to replicate the study using a sample of n = 8 college freshman: 1) State the hypothesis, and select the alpha level 2) Locate the critical region
1) State the hypothesis, and select the alpha level Hypotheses H0 : muD = 0 H1 : muD does not equal 0 Alpha level a = .05 2) Locate the critical region n = 8 df = 8 - 1 = 7 For a = .05 and a df of 7, the critical value listed in the t distribution table is ± 2.365
For an experiment comparing two treatment conditions, an independent-measures design would obtain __ score(s) for each subject and a repeated-measures design would obtain __ score(s) for each subject
1, 2
What is the mean for the difference scores for the following data from a repeated-measures study? I . II . 5, 13 2, 10 6, 6 7, 15
13-5=8 10-2=8 6-6=0 15-7=8 8*3=24 24/4=6
A researcher conducts a research study comparing two treatment conditions and obtains 20 scores in each treatment. IF the researcher used a repeated-measures design, then how many subjects participated in the research study?
20
A matched-subjects study comparing two treatments with 10 scores in each treatment requires a total of ____ participants and measures ____ score(s) for each individual
20, 1
3) Calculate t statistic If MD = 4, SS = 112, n = 8 4) Make a decision
3) Calculate t statistic Variance ss/df = 112/7 = 16 Estimated standard error Sqrt(variance/n) Sqrt(16/8) = 1.41 t statistic t = MD-MuD/SMD t = 4-0/1.41 = 2.84 4) Make a decision t value obtained is beyond the critical value of 1.895 Reject the null Conclude that less than average sleep significantly increased academic problems the following day
How many D scores are there for each subject?
1
3) Calculate t statistic If MD = 4, SS = 112, n = 8 4) Make a decision
3) Calculate t statistic Variance ss/df = 112/7 = 16 Estimated standard error Sqrt(variance/n) Sqrt(16/8) = 1.41 t statistic t = MD-MuD/SMD t = 4-0/1.41 = 2.84 4) Make a decision t value obtained is beyond the critical value of ± 2.365 Reject the null hypothesis
Reporting results of a repeated-measures t test with r^2 to estimate effect size
"Experiencing a night of below-average sleep increased academic problems the following day by an average of M = 4.00 points with SD = 4.00. The treatment effect was statistically significant, t(7) = 2.84, p < .05, r2 = 0.526."
Reporting results of a repeated-measures t test with confidence intervals
"A night of below-average sleep compared to above-average sleep significantly increased academic problems the next ay, t(7) = 2.84, p < .05, 95% CI [0.67, 7.33]."c
For which of the following situations would an independent-measures design have the maximum advantage over a repeated-measures design? a. When individual differences are small and participating in one treatment is likely to produce a permanent change in the participant's performance b. When individual differences are small and participating in one treatment is not likely to produce a permanent change in the participant's performance c. When individual differences are large and participating in one treatment is likely to produce a permanent change in the participant's performance d. When individual differences are large and participating in one treatment is not likely to produce a permanent change in the participant's performance
a. When individual differences are small and participating in one treatment is likely to produce a permanent change in the participant's performance
A repeated-measures study finds a mean difference of MD = 5 points between two treatment conditions. Which of the following sample characteristics is most likely to produce a significant t statistic for the hypothesis test? a. A large sample size (n) and a large variance b. A large same size (n) and a small variance c. A small sample size (n) and a large variance d. A small sample size (n) and a small variance
b. A large same size (n) and a small variance
In a repeated-measures study, the same group of individuals participates in all of the treatment conditions. Which of the following situations is not an example of a repeated-measures design? a. A researcher would like to study the effect of practice on treatment b. A researcher would like to compare individuals from two different populations c. the effect of a treatment is studied in a small group of individuals with a rare disease by measuring their symptoms before and after treatment d. A developmental psychologist examines how behavior unfolds by observing the same group of children at different ages
b. A researcher would like to compare individuals from two different populations
Which of the following is the correct statement of the null hypothesis for a repeated-measures hypothesis test? a. MD =0 b. MuD = 0 c. Mu1 = Mu2 d. M1 = M2
b. MuD = 0
If he results of a repeated-measures study show that nearly all of the participants score around 5 points higher in Treatment A than in Treatment B, then which of the following accurately describes the data? a. The variance of the difference scores and the likelihood of a significant result is low b. The variance of the difference scores is small and the likelihood of a significant result is high. c. The variance of the difference scores is large and the likelihood of a significant result is low d. The variance of the difference scores is large and the likelihood of a significant result is high
b. The variance of the difference scores is small and the likelihood of a significant result is high.
A researcher is using a one-tailed hypothesis test to evaluate the significance of a mean difference between two treatments in a repeated-measures study. If the treatment is expected to increase scores, then which of the following is the correct statement of the alternative hypothesis (H1)? a. muD > 0 b. muD < 0 c. muD > 0 d. muD < 0
c. muD > 0
The size of the treatment effect also can be described with a
confidence interval estimating the population mean difference
In a repeated-measures study, the variability of the difference scores becomes a relatively concrete and easy-to-understand concept The sample variability describes the ____ of the treatment effect
consistency
E.g., if a treatment ____ adds a few points to each individual's score, then the set of difference scores will be clustered together with relatively small variability Treatment effect is likely to be significant High variability, on the other hand, means there is ____treatment effect High variability increases the size of the estimated standard error and results in small t values
consistently no consistent
One way to deal with time-related factors and order effects is to ...
counterbalance the order of presentation of treatments
Which of the following accurately describes the relationship between the repeated-measures t statistic and the single sample t statistic? a. Each uses one sample mean b. Each uses one population mean c. Each uses one sample variance to compute the standard error d. All of the above
d. All of the above
The main advantage of a repeated-measures study is that it uses exactly the same individuals in all treatment conditions Thus, there is not risk that the participants are substantially ____ from one measurement to the next
different
As always, there will be some ____ between a sample mean and the population mean, so even if H0 : muD = 0 were true, we do not expect MD to be exactly 0
error
