Question 1

If the sample size is less than 15,the correlated groups t test may show inflated Type I errors for data that are markedly skewed.

Accepted Answer

This is true. The correlated groups t test assumes that the data is normally distributed and if the sample size is less than 15, the t test may not accurately reflect the distribution of the data, leading to inflated Type I errors if the data is highly skewed. In such cases, non-parametric tests may be more appropriate.

Question 2

One procedure for venly distributing carry-over effects across conditions is called counterbalancing.

Accepted Answer

Counterbalancing is a technique used to evenly distribute carry-over effects across conditions in an experiment. This can involve alternating the order of conditions for different participants or using a Latin square design to ensure that each condition is presented an equal number of times in each sequence.

Question 3

The formula for computing eta-squared from t and its degrees of freedom for the correlated groups t test is the same as that for the independent groups t test.

Accepted Answer

The formula for computing eta-squared from t and its degrees of freedom is the same for both the correlated groups t test and the independent groups t test. This is because eta-squared is a measure of effect size that is independent of the type of t test that is used.

Question 4

In the correlated groups t test,eta-squared represents the proportion of variability in the dependent variable that is associated with the independent variable after variability due to individual differences has been included.

Accepted Answer

Eta-squared represents the proportion of variability in the dependent variable that is associated with the independent variable, excluding variability due to individual differences.

Question 5

One of the underlying assumptions of the correlated groups t test is that the population of mean scores is normally distributed.

Accepted Answer

The assumption is that the distribution of difference scores (not mean scores) is normally distributed.

Question 6

If we were to compute the average nullified score for each research participant,we would find that every person would have the same average score.

Accepted Answer

Since the nullified score is calculated by subtracting the individual score from the group's average score, the average nullified score for each participant will be zero. Therefore, every person will have the same average nullified score of zero.

Question 7

Since variability due to individual differences is extracted from the dependent variable as part of the correlated groups t test procedure,a correlated groups t test will usually be more powerful than a corresponding independent groups t test.

Accepted Answer

This is because the correlated groups design controls for individual differences, which can reduce error variance and increase the sensitivity of the test to detect differences between the conditions being compared. In contrast, the independent groups design does not control for individual differences and may include more error variance, lowering the power of the test.

Question 8

Because the correlated groups t test involves the analysis of nullified scores,the question of the nature of the relationship is not meaningful.

Accepted Answer

The question of the nature of the relationship is indeed meaningful in the correlated groups t test, as the analysis involves comparing the mean differences between two related groups.

Question 9

A correlated groups t-test provides a more sensitive test of the relationship between the independent and dependent variables.

Accepted Answer

A correlated groups t-test, also known as a paired samples t-test or dependent samples t-test, compares the means of two related groups on a single continuous variable. Because the groups are related, this test is more sensitive to detecting differences between the groups. The difference between the paired observations within each group is used to calculate the t-statistic, which is a measure of how different the means are relative to the within-group variability. Therefore, a correlated groups t-test is more sensitive than an independent groups t-test when the groups are related.

Question 10

Unlike the independent groups t test,larger sample sizes will not increase the power of the correlated groups t test.

Accepted Answer

Larger sample sizes can increase the power of the correlated groups t test by reducing the variability in the data and increasing the precision of the estimated mean difference.

Question 11

A correlated groups t test is analogous to an independent groups t test with the effects of individual differences added to the dependent variable.

Accepted Answer

A correlated groups t-test, also known as a paired samples t-test, is used when the same subjects are measured under two conditions, thus controlling for individual differences, not adding them.

Question 12

With smaller sample sizes,larger population effect sizes are necessary to obtain adequate statistical power.

Accepted Answer

The answer of With smaller sample sizes,larger population effect sizes...

Question 13

There is less variability in a set of nullified scores because the effects of individual differences in background have been removed.

Accepted Answer

Nullifying scores means removing the effects of individual differences in background variables, such as age, gender, or socio-economic status. As a result, the variability in the scores is reduced, as individual differences are no longer contributing to it. Therefore, there is less variability in a set of nullified scores.

Question 14

The correlated groups t test has N - 2 degrees of freedom associated with it.

Accepted Answer

The correlated groups t-test, also known as the paired samples t-test, has N - 1 degrees of freedom, where N is the number of paired observations.

Question 15

It is possible to obtain a large value of eta-squared without obtaining a statistically significant t value.

Accepted Answer

Eta-squared is a measure of effect size, whereas t value is a measure of statistical significance. It is possible for a variable to have a large effect size indicated by a high eta-squared value, but not reach statistical significance indicated by a low t value.

Question 16

The analysis of the nature of the relationship for the correlated groups t test involves examination of the mean scores for the two conditions.

Accepted Answer

The analysis of the nature of the relationship for the correlated groups t test involves examining the mean scores for the two conditions. This comparison helps to determine the strength and direction of the relationship between the variables being studied.

Question 17

The assumption of independent,random sampling is not an important one for the correlated groups t test.

Accepted Answer

The assumption of independent, random sampling is important for the correlated groups t test. The correlated groups t test requires that the pairs of observations are independent of each other and that the sample is randomly selected from the population. Failure to meet these assumptions can lead to biased results and incorrect conclusions. Therefore, option B is the correct answer.

Question 18

For sample sizes of 40 or more,the correlated groups t test is quite robust to violations of the normality assumption,even for distributions exhibiting considerable skewness.

Accepted Answer

For sample sizes of 40 or more, the central limit theorem applies and the distributions of sample means become approximately normal, even for non-normal population distributions. Therefore, the correlated groups t test can still be considered valid and robust in these cases.

Question 19

It is typically the case that the estimated standard error for the correlated groups t test is larger than the estimated standard error for the independent groups t test.

Accepted Answer

The estimated standard error for the correlated groups t-test is typically smaller because it accounts for the correlation between paired observations, reducing variability.

Question 20

The interpretation of eta-squared for the correlated groups t test is the same as that for the independent groups t test.

Accepted Answer

The answer of The interpretation of eta-squared for the correlated...

Quiz 11: Correlated Groups T-Test