Question 1

Two sample t tests are designed to learn if there is support for a relationship between variables when:

Accepted Answer

Two-sample t tests are appropriate when the dependent variable is interval or ratio level and the independent variable is nominal level and dichotomous (only two groups). This test cannot be performed when both variables are nominal level, and other statistical tests would need to be used.

Question 2

The degrees of freedom for the one sample t test are:

Accepted Answer

The degrees of freedom for the one sample t test is the sample size minus one.

Question 3

Simple ANOVA is described as "an omnibus test." What does this mean?

Accepted Answer

ANOVA (Analysis of Variance) is considered an omnibus test because it tests the overall difference among three or more groups to see if there is a relationship between variables. However, if significant, it does not specify which groups are significantly different from each other; further post-hoc tests are needed for those specifics.

Question 4

The two sample dependent t test should be used when two samples consist of the same people or objects measured "before" and "after" some event occurs, or when two samples consist of

Accepted Answer

The two sample dependent t test is specifically designed to compare two samples consisting of the same individuals or objects measured before and after some event occurs. Thus, option A is incorrect as it refers to independent samples, and option B is incorrect as it refers to naturally different groups. Option C is the correct answer as it describes matching of individuals or objects to make them comparable in relation to certain variables, which is necessary for the two sample dependent t test.

Question 5

Which statistical test is sometimes used to determine if a research sample is sufficiently representative in relation to some potentially confounding variable?

Accepted Answer

The one sample t-test is used to determine if the sample mean is significantly different from a known or hypothesized population mean, which can help assess if the sample is representative concerning a specific variable.

Question 6

Using a measurement scale believed to produce interval level measurement, an instructor wishes to learn if the variable "attitude toward statistics" will show improvement over the course of a semester in her class. She administers the scale the first and last days of the class and compares the pairs of scores for every student. What test should she use to learn if there is statistical support for her hypothesis that students will show improved attitudes following her course?

Accepted Answer

The instructor is comparing the scores of the same group of students at two different times (before and after the course), so she should use a paired or dependent t-test, which is designed for this type of analysis. The other options (one sample t, two sample independent t, and simple ANOVA) are not appropriate for comparing the pre- and post-course scores of the same group of students.

Question 7

When do researchers use t distributions and the family of t tests to seek support for a relationship between variables rather than simply computing confidence intervals based on the normal distribution (as described in Chapter 5)?

Accepted Answer

Researchers use t distributions and the family of t tests when the standard deviation of the dependent variable within the population is not known. This is because the t distribution adjusts for the additional uncertainty introduced by estimating the population standard deviation from the sample.

Question 8

Multifactor ANOVA is appropriate for use when there are:

Accepted Answer

The answer of Multifactor ANOVA is appropriate for use when...

Question 9

The non-parametric test that requires at least ordinal level data and that examines the entire distribution of a variable within two samples (and identifies the point at which the two samples differ the most) is:

Accepted Answer

The Kolmogorov-Smirnov test is a non-parametric test that requires at least ordinal level data and examines the entire distribution of a variable within two samples. It identifies the point at which the two samples differ the most, making it a useful test for determining if two samples come from different populations. The Mann-Whitney U test is also a non-parametric test that can be used to compare two samples, but it only examines the rank order of the data, not the entire distribution. The Kruskal-Wallis test is used for comparing three or more groups and requires at least ordinal level data. The Wilcoxon signed-rank test is used to compare two related samples, rather than two independent samples.

Question 10

A social worker wishes to examine the effectiveness of an innovative method for the treatment of people with a diagnosis of pedophilia. She suspects that it may improve symptoms among some clients, but may make them worse among others. However, she would like to learn if the intervention makes a statistically significant difference in client behaviors. What statistical test should she use?

Accepted Answer

The Moses Test of Extreme Reactions is designed to detect differences in the variability or dispersion of scores between groups, rather than differences in central tendency (mean or median). This makes it suitable for the scenario described, where the intervention is suspected to have varying effects on different individuals, potentially improving symptoms for some while worsening them for others. This test specifically looks for significant differences in the extremities of reactions (improvements or deteriorations), which aligns with the social worker's interest in understanding the diverse impacts of the innovative treatment method on clients with a diagnosis of pedophilia.

Question 11

A non-parametric alternative to the one sample t test is:

Accepted Answer

The answer of A non-parametric alternative to the one sample...

Question 12

The independent t test is often well-suited for comparing the effectiveness of two methods of treatment intervention for addressing some problem such as substance abuse because:

Accepted Answer

The independent t-test is suitable for comparing two treatment interventions because it allows for a nominal and dichotomous independent variable (e.g., treatment type), can handle dependent variables at the interval or ratio level (e.g., level of substance abuse), and accommodates subsamples of different sizes.

Question 13

The parametric test designed to examine the relationship among one dichotomous independent variable and a set of interval or ratio level dependent variables is:

Accepted Answer

Hotelling's T² test is used to examine the relationship between a dichotomous independent variable and multiple dependent variables that are interval or ratio level.

Question 14

If the instructor in the previous question had wished to learn instead whether there was a statistically significant difference in attitudes toward statisics among the three sections of the course that she teaches following completion of it, what statistical test should she use?

Accepted Answer

A simple ANOVA would be the best choice for comparing the mean attitudes toward statistics among three different sections of the same course. The ANOVA can determine whether there is a statistically significant difference in attitudes between any of the three groups, without assuming any particular pairings or relationships between the groups.

Question 15

If the problem being addressed (the dependent variable) in the previous question can be measured at only the ordinal level, what would be an appropriate statistical test to use?

Accepted Answer

The answer of If the problem being addressed (the dependent...

Quiz 7: T Tests and Analysis of Variance