Question 1

For which of the following hypotheses is a one-tailed test of significance appropriate?

Accepted Answer

A one-tailed test of significance is appropriate when the hypothesis predicts a direction of the effect, such as expecting one group to score higher or lower than another. Option D predicts that children receiving a dietary supplement will show greater achievement gains than those receiving a placebo, indicating a specific direction and thus making a one-tailed test appropriate. Options A, B, and C suggest comparisons without specifying a direction of difference or are testing for any significant difference, which would require a two-tailed test.

Question 2

Use of a one-tailed versus a two-tailed t test to test the significance of the difference between two sample means depends on whether

Accepted Answer

A one-tailed t-test is used when the difference is expected to be in one direction only, allowing for testing a specific hypothesis about the direction of the difference between two sample means.

Question 3

If any of the assumptions underlying the t test are violated to a modest extent,

Accepted Answer

The t test is robust to modest violations of its assumptions, meaning it can still provide accurate estimates of statistical significance even if the assumptions are not perfectly met. This robustness is particularly true for violations of normality when sample sizes are large enough.

Question 4

The t test for correlated means should be used when

Accepted Answer

The t-test for correlated means is appropriate when the two groups being compared are matched or paired on some variable, ensuring that the comparison between the groups takes into account the matching variable, which is meant to control for its effects.

Question 5

In comparing the mean performance of 25 delinquents and 25 matched nondelinquents, one should use the

Accepted Answer

The answer of In comparing the mean performance of 25...

Question 6

Match each condition below with the test most appropriate under that condition To determine whether:
-the sample mean differs significantly from a specified population mean.

Accepted Answer

The t test for a single mean is specifically designed to compare the mean of a single sample to a known population mean to determine if there is a significant difference.

Question 7

Match each condition below with the test most appropriate under that condition To determine whether:
-the mean achievement of a random sample of delinquents differs significantly from that of a randomly selected control group.

Accepted Answer

The t test for independent means is used when comparing the means of two independent groups to see if there is a significant difference between them. In this scenario, the groups are delinquents and a control group, which are independent of each other.

Question 8

Match each condition below with the test most appropriate under that condition To determine whether:
-the mean anxiety scores of high, middle, and low achievers are significantly different.

Accepted Answer

The analysis of variance (ANOVA) is the appropriate test when comparing the means of more than two groups to determine if there is a significant difference among them. In this case, comparing the mean anxiety scores of high, middle, and low achievers involves three groups, making ANOVA the correct choice.

Question 9

Match each condition below with the test most appropriate under that condition To determine whether:
-high, middle, and low achievers have different high school dropout rates.

Accepted Answer

The chi-square test is appropriate for comparing categorical data, such as dropout rates, across different groups (high, middle, and low achievers).

Question 10

Match each condition below with the test most appropriate under that condition To determine whether:
-the mean achievement of two groups of students matched on aptitude differs significantly.

Accepted Answer

The t test for correlated means is appropriate for comparing the means of two related groups, such as groups of students who are matched on a variable like aptitude. This test accounts for the fact that the groups are not independent of each other.

Question 11

Use of the t test for a single mean requires

Accepted Answer

The answer of Use of the t test for a...

Question 12

If a researcher wishes to determine whether a sample mean differs from the population mean, the appropriate statistic is the

Accepted Answer

The t test for a single mean is specifically designed to compare a sample mean to a known population mean to determine if there is a significant difference between them. This test assesses whether the observed sample mean is statistically significantly different from the hypothesized population mean, based on the sample's standard deviation and size.

Question 13

The F ratio is computed to determine

Accepted Answer

The F ratio is used in analysis of variance (ANOVA) to determine the statistical significance of the difference between the mean scores of two or more groups. It compares the variance between groups to the variance within groups to assess if the group means differ more than would be expected by chance.

Question 14

Analysis of variance focuses on the

Accepted Answer

Analysis of variance (ANOVA) primarily focuses on the ratio of between-groups variance to within-groups variance. This ratio helps in determining whether there are any statistically significant differences between the means of three or more independent (unrelated) groups.

Question 15

The purpose of the t test for multiple comparisons is to

Accepted Answer

The t test for multiple comparisons is designed to adjust for statistically significant differences that might occur by chance when multiple groups are compared across various variables. This adjustment helps to ensure that observed differences are more likely to reflect true differences rather than random variation.

Question 16

Analysis of covariance is the preferred test rather than analysis of variance when

Accepted Answer

Analysis of covariance (ANCOVA) is used over analysis of variance (ANOVA) when there are pre-existing differences between the groups on a covariate that is related to the dependent variable. ANCOVA can adjust for these differences, making the groups more comparable.

Question 17

In conducting a MANOVA on a cluster of five related variables, a researcher obtains an F value that is significant at the .01 level. What is the next step that should be taken in analyzing the data?

Accepted Answer

When a MANOVA (Multivariate Analysis of Variance) yields a significant F value, indicating that there are overall differences among the groups on the combined dependent variables, the next step is often to conduct separate ANOVAs (Analysis of Variance) on each dependent variable. This helps to identify which specific variables are contributing to the significant multivariate effect observed in the MANOVA.

Question 18

The test for homogeneity of independent variances, the test for homogeneity of related variances, and theF maximum test for homogeneity of variance are all forms of

Accepted Answer

These tests are all related to the analysis of variance (ANOVA), which is used to determine if there are any statistically significant differences between the means of three or more independent (unrelated) groups.

Question 19

Compared to parametric statistics, nonparametric statistics

Accepted Answer

Nonparametric statistics typically have less statistical power compared to parametric statistics because they do not assume a specific distribution for the data, which often leads to less precise estimates.

Question 20

Chi-square should be used when data are in the form of

Accepted Answer

Chi-square tests are used for data in the form of category frequencies, where the observations are categorized into a finite number of categories and the analysis is based on the counts or frequencies within those categories.

Quiz 10: Nonexperimental Research Descriptive and Causal-Comparative Designs