Question 1

The estimated standard error for difference scores is the denominator of the test statistic for a related samples t test.

Accepted Answer

This statement is true. The estimated standard error for the difference scores is calculated as the standard deviation of the differences divided by the square root of the sample size, which is the denominator of the test statistic for a related samples t test.

Question 2

Selecting related samples can be more practical in that selecting related samples may provide a better way to test your hypotheses.

Accepted Answer

By selecting related samples, you may be able to control for extraneous variables and increase the homogeneity of your samples, which can make it easier to detect differences or relationships between variables. This can ultimately lead to more robust and accurate conclusions about your hypotheses.

Question 3

The estimate for standard error is placed in the numerator of the test statistic for a related samples t test.

Accepted Answer

In a related-samples t-test, the estimate for standard error is placed in the denominator of the test statistic formula, not the numerator. The formula for the test statistic is the difference between the sample mean difference and the population mean difference (often assumed to be 0), divided by the standard error of the difference scores.

Question 4

If a related samples t test is significant,then it will also be associated with a large effect size.

Accepted Answer

A significant related-samples t-test indicates that there is a statistically significant difference between the means of the two related groups, but it does not necessarily imply a large effect size. The effect size is a separate measure that indicates the magnitude of the difference, independent of sample size.

Question 5

Using the same data,a related samples t test is more likely than a two-independent sample t test to result in a decision to reject the null hypothesis.

Accepted Answer

A related samples t test (also called a paired t test) involves comparing the mean difference between two related groups (e.g. pre-test and post-test scores for the same group). This type of test typically results in a higher statistical power (i.e. ability to detect a significant difference) than a two-independent sample t test, which involves comparing the means of two separate and unrelated groups. Therefore, a related samples t test is more likely to reject the null hypothesis when a true difference exists between the groups being compared.

Question 6

Both estimates of proportion of variance,  and  ,are computed the same for independent and related samples t tests.

Accepted Answer

The statement is true. The proportion of variance estimates for independent and related samples t tests are computed the same way. They both measure the effect size and indicate the proportion of the total variance in the dependent variable that can be explained by the independent variable or group difference.

Question 7

A researcher computes a related samples t test with t(20)= 2.096.In this example,the decision is to reject the null hypothesis for a one-tailed test,but not for a two-tailed test.

Accepted Answer

The answer of A researcher computes a related samples t...

Question 8

The decision is to reject the null hypothesis for the following related samples t test: t(23)= 3.02,p < .05 (d = .18).

Accepted Answer

The decision to reject the null hypothesis (represented by A in the answer choices) is accurate based on the given t-value and alpha level. The effect size (d = .18) indicates a small effect, but this is not relevant to determining whether to reject or fail to reject the null hypothesis.

Question 9

Original pairs of scores are first reduced to difference scores before computing the test statistic for the related samples t test.

Accepted Answer

This statement is true. In a related samples t test, the paired scores are first subtracted from each other to create difference scores. The test statistic is then calculated based on these difference scores.

Question 10

The type of t test that was used is typically reported in a data analysis section that precedes the results section in an APA-style paper.

Accepted Answer

The type of t test used is typically reported in the data analysis section of an APA-style paper, which comes before the results section.

Question 11

Selecting related samples minimizes standard error and increases power.

Accepted Answer

Selecting related samples (e.g. repeated measures within subjects designs) can reduce variability between observations, thereby decreasing the standard error and increasing statistical power compared to selecting unrelated samples.

Question 12

The estimated Cohen's d for the related samples t test uses the sample standard deviation for difference scores as an estimate of the standard deviation of difference scores in the population.

Accepted Answer

This is true. Cohen's d is calculated by taking the difference between the means of the two related samples and dividing it by the sample standard deviation of the difference scores. This calculation is used to estimate the effect size of the difference between the two related samples. The sample standard deviation of the difference scores is used as an estimate of the standard deviation of the difference scores in the population.

Question 13

The assumptions for a related samples t test are the same as those for the two-independent sample t test.

Accepted Answer

The assumptions for the related-samples t test are different from those for the two-independent-sample t test. The related-samples t test assumes that the differences between the paired observations have a normal distribution, while the two-independent-sample t test assumes that the populations from which the samples were drawn have normal distributions, and have equal variances.

Question 14

A researcher computes d = .26.Hence,it is appropriate to conclude that 26% of the variability in the dependent variable can be accounted for by the presence of the independent variable.

Accepted Answer

The answer of A researcher computes d = .26.Hence,it is...

Question 15

To summarize a related samples t test,we report the test statistic,critical values,and p value.

Accepted Answer

The answer of To summarize a related samples t test,we...

Question 16

A researcher computes d = .12,which is a small effect size.

Accepted Answer

A d value of .12 is considered a small effect size, according to Cohen's guidelines.

Question 17

As the value of the test statistic for a related samples t test increases,the likelihood of deciding to retain the null hypothesis also increases.

Accepted Answer

As the value of the test statistic for a related samples t test increases, the likelihood of rejecting the null hypothesis and accepting the alternative hypothesis increases. Higher values of the test statistic suggest stronger evidence against the null hypothesis.

Question 18

Selecting related samples increases standard error and reduces power.

Accepted Answer

Selecting related samples typically decreases the standard error because related samples are more likely to be similar to each other, leading to less variability in the data. This can increase the power of a statistical test, as there is a greater chance of detecting a true effect when variability is lower.

Question 19

The assumptions for a related samples t test apply to both the repeated measures and matched-pairs designs.

Accepted Answer

Both repeated measures and matched-pairs designs involve comparing scores from two related groups, and thus share similar assumptions for conducting a related samples t test. These assumptions include normality of the differences, independence of observations, and homogeneity of variances.

Quiz 10: Testing Means: Related-Samples T Test With Confidence Intervals