### Variance, Measures, Repeated Measures T Test, Rejecting the Null Hypothesis – Statistics

The key terms in these Statistics chapters include Sample, Variance Measures, Repeated Measures T Test, The Null Hypothesis, Rejecting the Null Hypothesis And Stats Quiz.

For measures study, if other factors are held constant, then an increase in the size of the sample will increase the likelihood of finding a significant treatment effect.

**True**

In the repeated-measures t statistic, the value for the estimated standard error in the denominator is computed entirely from the sample data.

**True**

One advantage of a repeated-measures design is that it typically requires fewer participants than an independent-measures design.

**True**

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**

If a set of n = 9 difference scores has a mean of MD = 3.5 and a variance of s2 = 36, then the sample will produce a repeated-measures t statistic of t = 3.5/2.

**True**

The following data were obtained from a repeated-measures research study. What is the value of MD for these data?

Subject 1st 2nd

#1 10 15

#2 4 8

#3 7 5

#4 6 11

**3**

One advantage of a repeated-measures design is that it typically requires fewer participants than an independent-measures design.

**True**

For measures study, if other factors are held constant, then an increase in the size of the sample will increase the likelihood of finding a significant treatment effect.

**True**

In the repeated-measures t statistic, the value for the estimated standard error in the denominator is computed entirely from the sample data.

**True**

One advantage of a repeated-measures design is that it typically requires fewer participants than an independent-measures design.

**True**

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**

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**

A sample of difference scores has a mean of MD = 5 with a variance of s2 = 100. If effect size is measured using Cohen’s d, what is the value of d?

**d = 5/10**

If a set of n = 9 difference scores has a mean of MD = 3.5 and a variance of s2 = 36, then the standard error for the sample mean difference is 4 points.

**False**

If all of the participants in a repeated-measures study show roughly the same 10-point difference between treatments, then the data are likely to produce a significant value for the t statistic.

**True**

A repeated-measures study with a sample of n = 16 participants produces a repeated-measures t = 2.00. If effect size is measured using r2, then r2 = 4/20.

**False**

For a repeated-measures study, as the sample mean difference increases, the likelihood of rejecting the null hypothesis also increases.

**True**

For a repeated-measures design, the sample mean difference is always located exactly in the center of the confidence interval estimate for the population mean difference.

**True**

In general, if the variance of the difference scores increases, what will happen to the value of the t statistic?

**It will decrease (move toward 0 at the center of the distribution).**

If all of the participants in a repeated-measures study show roughly the same 10-point difference between treatments, then the data are likely to produce a significant value for the t statistic.

**True**

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 study comparing two treatments with a sample of n = 15 participants, the researcher measures two scores for each individual to obtain a total of 30 scores and the repeated-measures t statistic has df = 29.

**False**

Repeated-measures designs are particularly well-suited to research studies examining learning or other changes that occur over time.

**True**

One concern for a repeated-measures study is that a participant’s score in one treatment may be influenced by practice or experience gained in a previous treatment.

**True**

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 called?

**Order effects**

Which of the following possibilities is a serious concern with a repeated-measures study?

**The results are influenced by order effects.**

For a repeated-measures study, if other factors are held constant, then an increase in the size of the sample will increase the likelihood of finding a significant treatment effect.

**True**

For a repeated-measures study, a small variance for the difference scores indicates that the treatment effect is consistent across participants.

**True**

For a repeated-measures study, if other factors are held constant, then an increase in the size of the sample will increase measures of effect size.

**False**

For a repeated-measures study comparing two treatment conditions, a researcher obtains a sample of n = 9 difference scores with a mean of MD = 4 and a variance of s2 = 36. What is the value for the repeated-measures t statistic for these data?

**4/2**

A repeated-measures research study uses a total of 20 participants to compare two treatment conditions. If the results are used to construct a 90% confidence interval for the population mean difference, then the t values will be ±1.729.

**True**

A repeated-measures study and matched-subjects study both produce t statistics with df = 20. The repeated-measures study used more participants.

**False**

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**

A repeated-measures study and an independent-measures study both produce a t statistic with df = 20. The repeated-measures study used more subjects than the independent-measures study.

**False**

For a repeated-measures study, a small variance for the difference scores indicates that the treatment has little or no effect.

**False**

For a repeated-measures study, if the null hypothesis is true, then what value should be obtained for the sample mean.

**MD near 0**

For measures study, if other factors are held constant, then an increase in the size of the sample will increase the likelihood of finding a significant treatment effect.

**True**

In the repeated-measures t statistic, the value for the estimated standard error in the denominator is computed entirely from the sample data.

**True**

**True**

**A small variance for the difference scores and a small standard error**

A researcher conducts a repeated-measures study to evaluate a treatment with a sample of n = 16 participants and obtains a t statistic of t = 1.94. The treatment is expected to increase scores and the sample mean shows an increase. Which of the following is the correct decision for a hypothesis test using α = .05.

**Reject the null hypothesis with a one-tailed test but fail to reject with two tails**

For which of the following situations would a repeated-measures research design be appropriate?

**Comparing pain tolerance with and without acupuncture needles**

For the following data from a repeated-measures study, the sample mean difference is MD = 1Participant X1 X2

A 1 5

B 4 6

C 5 2

**True**

In a repeated measures study, the null hypothesis says that the mean for the sample of difference scores is equal to zero.

**False**

Which of the following is the correct null hypothesis for a repeated-measures t test?

**µD = 0**

If the null hypothesis is true, what value is expected on average for the repeated-measures t statistic?

**0**

The null hypothesis for a repeated-measures test states:

**The entire population will have a mean difference of μD = 0.**

A researcher would like to compare two treatment conditions with a set of 30 scores in each treatment. If a repeated-measures design is used, the study will require n = 60 participants.

**False**

The estimated standard error in the denominator of the repeated-measures t statistic measures the average mean difference that is expected for a sample selected from a population with a zero mean difference.

**True**

For which of the following situations would a repeated-measures research design be appropriate?

**Comparing pain tolerance with and without acupuncture needles**

Which of the following is the correct null hypothesis for a repeated-measures t test?

**mD = 0**

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**

Although a repeated-measures study measures two scores for each participant, the sample mean and variance are computed using only one score for each participant.

**True**

A researcher reports df = 18 for a repeated-measures t statistic. This research study used a total of n = 19 participants.

**True**

For a repeated-measures study, as the variance of the difference scores increases, the likelihood of finding a significant difference also increases.

**False**

A repeated-measures research study comparing two treatments with a set of 10 scores in each treatment will produce a t statistic with df = 18.

**False**

In general, what is the effect of an increase in the variance for the sample of difference scores?

**An increase in the standard error and a decrease in the value of t**

A research report describing the results from a repeated-measures study states that the data show no significant difference between the two treatments, t(10) = 1.65, p > .05. Based on this report, how many individuals participated in the research study?

**11**

A repeated-measures study using a sample of n = 20 participants would produce a t statistic with df = ____.

**19**

A repeated-measures study comparing two treatments with a sample of n = 4 participants produces MD = 3 with SS = 48 for the set of difference scores. What is the repeated-measures t statistic for these data?

**3/2 = 1.50**

A set of n = 16 difference scores has a mean of MD = 4 and a variance of s2 = 36. Cohen’s d for this sample is d = 4/6.

**True**

For a repeated-measures study comparing two treatment conditions, a researcher obtains Cohen’s d = 0.50 for a sample of n = 4 scores with a variance of s2 = 16. What is the value of the sample mean?

**MD= 2**

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.**