Statistic 1
A repeated-measures experiment and a matched-subjects experiment each produce a t statistic with df = 10. How many individuals participated in each study?
11 for repeated and 22 for matched
In general, what characteristics of the difference scores are most likely to produce a significant t statistic for the repeated-measures hypothesis test?
A large number of scores and a small variance
Which of the following is a fundamental difference between the t statistic and a z-score?
The t statistic uses the sample variance in place of the population variance.
Which of the following is not needed to compute a t statistic?
The value of the population variance or standard deviation
If other factors are held constant, how does sample size influence the likelihood of rejecting the null hypothesis and measures of effect size such as r2 and Cohen's d?
A larger sample increases the likelihood but has little influence on measures of effect size.
A hypothesis test produces a t statistic of t = 2.20. If the researcher is using a two-tailed test with α = .05, how large does the sample have to be in order to reject the null hypothesis?
At least n = 13
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?
MD = 3 with s2 = 20 for the difference scores
Two samples, each with n = 8, produce an independent-measures t statistic of t = -2.15. Which of the following decisions is justified for a two-tailed test?
Reject H0 with α = .05 but fail to reject with α = .01
For the independent-measures t statistic, what is the effect of increasing the sample variances?
Decrease the likelihood of rejecting H0 and decrease measures of effect size
Which of the following confidence intervals also indicates a significant difference between treatments with α = .05?
Estimate that μ1 - μ2 is in an interval between 2 and 10 with 95% confidence
Under what circumstances can a very small treatment effect be statistically significant?
If the sample size big and the sample variance is small
For an independent-measures t statistic, what is the effect of increasing the number of scores in the samples?
Increase the likelihood of rejecting H0 and have little or no effect on measures of effect size
A researcher selects a sample from a population with = 30 and uses the sample to evaluate the effect of a treatment. After treatment, the sample has a mean of M = 32 and a variance of s2 = 6. If Cohen's d is used to measure the size of the treatment effect, which of the following would have no effect on the value of Cohen's d?
Increase the number of individuals in the sample
Which of the following would have no effect on the width of a confidence interval?
Increase the sample mean
Which combination of factors would definitely increase the width of a confidence interval?
Increase the sample mean and increase the percentage of confidence
When n is small (less than 30), how does the shape of the t distribution compare to the normal distribution?
It is flatter and more spread out than the normal distribution.
A sample has a mean of M = 39.5 and a standard deviation of s = 4.3, and produces a t statistic of t = 2.14. For a two-tailed hypothesis test with α = .05, what is the correct statistical decision for this sample?
It is impossible to make a decision about H0 without more information.
Which of the following describes what a confidence interval does?
It uses a sample mean to estimate the corresponding population mean.
One sample has n = 10 scores and a variance of s2 = 20, and a second sample has n = 15 scores and a variance of s2 = 30. What can you conclude about the pooled variance for these two samples?
It will be closer to 30 than to 20
Which combination of factors is most likely to produce a significant value for an independent-measures t statistic?
Large samples and small variance
If other factors are held constant, how does sample variance influence the likelihood of rejecting the null hypothesis and measures of effect size such as r2 and Cohen's d?
Larger sample variance increases both the likelihood and measures of effect size.
How does sample variance influence the estimated standard error and measures of effect size such as r2 and Cohen's d?
Larger variance increases the standard error but decreases measures of effect size
If other factors are held constant, which set of sample characteristics is most likely to reject a null hypothesis stating that = 80?
M = 90 and small sample variance, n =100
For a repeated-measures study, if the null hypothesis is true, then what value should be obtained for the sample mean
MD near 0
Which of the following describes the effect of an increase in the variance of the difference scores?
Measures of effect size and the likelihood of rejecting the null hypothesis both decrease.
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. What is this problem is called?
Order effects
Why are t statistics more variable than z-scores?
The extra variability is caused by variations in the sample variance.
What value is estimated with a confidence interval using the repeated-measures t statistic?
The mean for a population of difference scores
Which of the following possibilities is a serious concern with a repeated-measures study?
The results will be influenced by order effects.
Two samples from the same population both have n = 10 scores with M = 45. If the t statistic is computed for each sample, then what is the relationship between the two t values?
The sample with the smaller variance will produce the larger t statistic.
If a researcher is using a t statistic to test a null hypothesis about a population, what information is needed from the population to calculate the t statistic?
The t statistic does not require any information about the population.
What is assumed by the homogeneity of variance assumption?
The two populations have equal variances
Which of the following sets of data would produce the largest value for an independent-measures t statistic?
The two sample means are 10 and 20, with variances of 20 and 25.
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, what should the researcher find?
The variance of the difference scores is near zero.
Which of the following describes the effect of increasing sample size?
There is little or no effect on measures of effect size, but the likelihood of rejecting the null hypothesis increases.
The narrower the confidence interval, the more precise it is. With this in mind, which combination of factors will produce the most precise estimate of the difference between two population means?
Two samples of n = 50 and 80% confidence
For which of the following situations would a repeated-measures design have the maximum advantage over an independent-measures design?
When very few subjects are available and individual differences are large
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 small variance for the difference scores and a small standard error
One sample of n = 8 scores has a variance of s2 = 6 and a second sample of n = 8 scores has s2 = 10. If the pooled variance is computed for these two samples, then the value obtained will be ______.
exactly halfway between 6 and 10
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 ______.
individual differences
Which of the following sets of data would produce the largest value for Cohen's d?
n = 20 for both samples, a pooled variance of 15, and a mean difference of 5 points
Two separate samples are being used to estimate the population mean difference between two treatment conditions. Which of the following would produce the widest confidence interval?
n1 = n2 = 10 with a pooled variance of 100
Which set of sample characteristics is most likely to produce a significant value for the independent-measures t statistic and a large measure of effect size?
A large mean difference and small sample variances
A research study produces a t statistic with df = 14. For this study, which of the following designs would require a total of 30 participants?
A matched-subjects design
If other factors are held constant, which of the following sets of data is most likely to produce a significant mean difference?
A sample mean difference of 10 points with n = 10 for both samples
If a repeated-measures study shows a significant difference between two treatments with α = .01, then what can you conclude about measures of effect size?
A significant effect does not necessarily mean that the effect size will be large.
What is indicated by a large variance for a sample of difference scores?
An inconsistent treatment effect and a low likelihood of a significant difference
If two samples are selected from the same population, under what circumstances will the two samples have exactly the same t statistic?
If the samples are the same size and have the same mean and the same variance
A researcher selects a sample from a population with = 30 and uses the sample to evaluate the effect of a treatment. After treatment, the sample has a mean of M = 32 and a variance of s2 = 6. Which of the following would definitely increase the likelihood of rejecting the null hypothesis?
Increase the number of individuals in the sample Increase the sample mean Decrease the sample variance All of the other options will increase the likelihood of rejecting the null hypothesis.
Assuming that other factors are held constant, which of the following would tend to increase the likelihood of rejecting the null hypothesis?
Increase the sample mean difference
Which of the following will not increase the width of a confidence interval?
Increase the sample mean from MD = 2 to MD = 4
Two samples from the same population both have M = 84 and s2 = 20, but one sample has n = 10 and the other has n = 20 scores. Both samples are used to evaluate a hypothesis stating that μ = 80 and to compute Cohen's d. How will the outcomes for the two samples compare?
The larger sample is more likely to reject the hypothesis, but the two samples will have the same value for Cohen's d.
If other factors are held constant, which of the following sets of data is most likely to satisfy the homogeneity of variance assumption?
The other 3 options are equally likely to satisfy the assumption.
If other factors are held constant, which of the following sets of data would produce the largest value for an independent-measures t statistic?
The two samples both have n = 30, with sample variances of 20 and 25.
What value is estimated with a confidence interval using the t statistic?
The value for an unknown population mean
