Question 1

The t-test has some stringent assumptions, if the data reasonably depart from those assumptions

Accepted Answer

If the data reasonably depart from the assumptions of the t-test, such as violations of normality or homogeneity of variances, the t-test results can still be used. However, the validity of the results may be compromised and alternative methods may be more appropriate if the violations are severe. It is always important to assess the extent of the violations and the potential impact on the conclusions before deciding on the next step.

Question 2

The Levene's test is used for which purpose below?

Accepted Answer

Levene's test is used to assess the equality of variances for a variable calculated for two or more groups. It helps determine which t-test to use by checking the assumption of equal variances, which is a prerequisite for the standard independent t-test. If variances are equal, you can use the standard t-test; if not, you might use a version of the t-test that does not assume equal variances.

Question 3

Assuming all assumptions are met, which version below is the most powerful (accurate) t-test?

Accepted Answer

The equal variance t-test, also known as the pooled variance t-test, is generally considered the most powerful (accurate) version of the t-test when the assumption of equal variances between the two groups being compared is met. This is because it effectively pools the variance estimates from both groups, leading to a more precise estimate of the population variance and, consequently, a more accurate test statistic.

Question 4

The t-distribution for smaller sample sizes is slightly different from a normal distribution because:

Accepted Answer

The t-distribution for smaller sample sizes has fatter tails compared to a normal distribution. This means that it has more data in the tails of the curve.

Question 5

A t-test can compare as many as four groups at a time without losing power.

Accepted Answer

A t-test can only compare two groups at a time. To compare more than two groups, an ANOVA (analysis of variance) or a non-parametric alternative such as Kruskal-Wallis test should be used.

Question 6

If a variable is measured in an experiment at time 1 (pretest) and again at time 2 (posttest), the most appropriate t-test would be

Accepted Answer

The related samples t-test, also known as the paired samples t-test or dependent samples t-test, is appropriate for comparing the means of two related groups, such as pretest and posttest scores. This test takes into account the fact that the two sets of data are from the same individuals and are therefore correlated.

Question 7

If you propose a one-tailed hypothesis, you must examine the group means before proceeding.

Accepted Answer

The answer of If you propose a one-tailed hypothesis, you...

Question 8

If the F-ratio test (Levene's test) produces a significant result, which of the choices below would be correct?

Accepted Answer

If the F-ratio test (Levene's test) produces a significant result, it indicates that the assumption of equal variances between groups has been violated. Therefore, option A is the correct choice as it uses the unequal variance t-test (also called Welch's t-test) which is appropriate when the assumption of equal variances is not met.

Question 9

If you have two groups with equal variances, which of the t-tests below would you use?

Accepted Answer

When the variances of two groups are equal, the appropriate t-test to use is the equal variance t-test.

Question 10

An equal-variance t-test is best used when the groups have essentially the same amount of dispersion.

Accepted Answer

An equal-variance t-test assumes that the variances of the two groups being compared are approximately equal. This means that the amount of dispersion or variability within each group should be similar. If the groups have different variances, using an equal variance t-test can lead to inaccurate results. In such cases, a Welch's t-test or a non-parametric test may be more appropriate.

Question 11

There are two forms of variation that a t-test can measure. The type of variation used to test your hypothesis is called

Accepted Answer

The answer of There are two forms of variation that...

Question 12

The t-test is designed to examine the number of cases in two groups to determine which one is the group with the most cases.

Accepted Answer

The t-test is a statistical test used to determine if there is a significant difference between the means of two groups. It does not determine which group has the most cases.

Question 13

If the probability associated with a t-test is larger than your alpha level, what do you do?

Accepted Answer

If the probability (p-value) associated with a t-test is larger than your alpha level, it means there is not enough evidence to reject the null hypothesis. Therefore, you fail to reject the null hypothesis and do not accept your research hypothesis.

Question 14

The t-test is properly used with which level of measurement below?

Accepted Answer

The t-test is most appropriate for use with interval level measurements. It is designed to compare the means of two groups, and interval level measurements provide a continuous scale with equal intervals between values. It is not appropriate for nominal or ordinal level measurements, which lack the necessary numerical properties.

Question 15

When used with small samples, the t-test produces a conservative estimate of differences.

Accepted Answer

When used with small samples, the t-test tends to produce a more cautious or conservative estimate of differences, meaning that it is less likely to find a significant result when one does not truly exist in the population. This is because small sample sizes increase the likelihood of random variation or error influencing the results, and the t-test takes this into account when calculating the significance level.

Question 16

The best alternative to a independent-samples t-test if assumptions are violated is the Mann-Whitney U-test.

Accepted Answer

The Mann-Whitney U-test is a nonparametric equivalent of the independent-samples t-test and can be used when assumptions of normality and equal variances are violated. It does not require the data to be normally distributed and can handle unequal variances. Therefore, it is the best alternative in such situations.

Question 17

Which of these assumptions below apply to the t-test?

Accepted Answer

The t-test assumes that the dependent variable is normally distributed and there are two groups.

Question 18

Typical data used with the t-test are those from survey and secondary datasets.

Accepted Answer

The t-test can be used with any type of data as long as the assumptions of normality and equal variances are met. However, it is commonly used with survey and secondary datasets in social sciences research.

Question 19

The t-test is a

Accepted Answer

The t-test is a parametric statistic that is used to compare the means of two groups. It assumes that the data is normally distributed and has equal variances.

Question 20

A two-tailed hypothesis is the most appropriate for a t-test because of the difficulty of determining direction in the variances.

Accepted Answer

A two-tailed hypothesis is used when the researcher does not predict the direction of the difference or relationship, not because of difficulty in determining direction in variances. A t-test can be one-tailed or two-tailed depending on the hypothesis being tested.

Quiz 12: Testing for Significance in Two Groups: The T-Test