Question 1

To determine if the correlations among a set of variables can be accounted for by a one or more underlying factors,a _____ should be used.

Accepted Answer

Factor analysis is specifically designed to uncover latent factors that may explain the correlations among observed variables. Log-linear analysis is used to analyze categorical data, multiple regression is used to explain the relationship between a dependent variable and one or more independent variables, and Spearman correlation is used to measure the strength and direction of the association between two variables. None of these techniques are designed to uncover underlying factors.

Question 2

The joint influence of two within-subjects qualitative independent variables can be studied using:

Accepted Answer

The best choice for studying the joint influence of two within-subjects qualitative independent variables is a two-way repeated measures analysis of variance. This type of analysis allows for the examination of main effects and interaction effects between the independent variables. The other options listed are not appropriate for this type of analysis.

Question 3

An index of the strength of the relationship between the criterion variable and the set of predictor variables is provided by the _____,symbolized by _____.

Accepted Answer

The squared multiple correlation coefficient (symbolized by R) provides an index of the strength of the relationship between the criterion variable and the set of predictor variables. It represents the proportion of variance in the criterion variable that can be explained by the predictor variables. The squared multiple correlation coefficient is preferred over the regular multiple correlation coefficient because it gives a more interpretable measure of effect size (the proportion of shared variability) and is bounded between 0 and 1.

Question 4

Statistical techniques for analyzing the relationship between three or more variables are referred to as:

Accepted Answer

Multivariate statistics is the branch of statistics that deals with the analysis of relationships between three or more variables. This includes techniques such as multiple regression, factor analysis, and cluster analysis. Nonparametric statistics refer to techniques that do not make assumptions about the underlying distribution of the data, while trivariate statistics and multiple correlations are more specific terms that do not encompass the full range of multivariate techniques.

Question 5

Alternatives to the "null hypothesis testing approach" include:

Accepted Answer

Estimating effect sizes and Bayesian statistics offer alternatives to the null hypothesis testing approach. Estimating effect sizes emphasizes the magnitude and practical significance of the observed effect, rather than just determining statistical significance. Bayesian statistics, on the other hand, allows for the incorporation of prior knowledge and beliefs into the analysis, rather than relying on a fixed significance level. Combining both approaches (a and b) can provide a more comprehensive understanding of the data, allowing for a more nuanced interpretation of the results.

Question 6

The strength of the relationship is usually indexed by the 95% confidence interval.

Accepted Answer

The strength of the relationship is usually indexed by the correlation coefficient, not the 95% confidence interval. The confidence interval provides information about the precision of the estimate, but not the strength of the relationship itself.

Question 7

When applied to a single independent variable having only two levels,multivariate analysis of variance is referred to as:

Accepted Answer

The Hotelling T² test is used in multivariate statistics to compare the means of two groups, similar to a t-test but for multiple dependent variables.

Question 8

A _____ is often used to test whether the groups have different population means on the dependent variables considered jointly.

Accepted Answer

Multivariate analysis of variance (MANOVA) is specifically designed to test for differences in multiple dependent variables between groups. It is often used in research where multiple variables are measured for the same group of participants and the researcher wants to know if there are significant differences between groups on these variables taken as a whole. Multiple regression (B) is used to predict a dependent variable based on one or more independent variables, while Hotelling's T-squared test (C) is used to test for differences between two populations' mean vectors. Factor analysis (D) is used to identify underlying factors that explain the correlations between multiple observed variables.

Question 9

_____ will usually be applied to research questions requiring that three or more qualitative variables be simultaneously examined.

Accepted Answer

Log-linear analysis is used to examine the relationships between three or more categorical (qualitative) variables simultaneously.

Question 10

If the dependent variable is measured on an ordinal level that seriously departs from interval characteristics,then a _____ test is typically used.

Accepted Answer

Nonparametric tests are appropriate for variables measured on an ordinal level, as they do not assume that the data follows a specific distribution or that the scale of measurement is interval. These tests include the Wilcoxon rank-sum test and the Kruskal-Wallis test. Parametric tests, on the other hand, assume that the data is normally distributed and measured on an interval scale, which may not be the case with ordinal data.

Question 11

______ is the statistic used to indicate the strength of relationship between a criterion variable and several predictors in the context of a linear model

Accepted Answer

R² is the statistic used to indicate the strength of relationship between a criterion variable and several predictors in the context of a linear model. It represents the proportion of variance in the criterion variable that is explained by the predictors.

Question 12

Statistical analyses that are designed to analyze the relationship between three or more variables simultaneously are called _____ tests.

Accepted Answer

Multivariate tests are designed to analyze the relationship between three or more variables simultaneously. Interaction comparison and simple main effects are specific types of analyses that can be conducted within a multivariate test, but they do not encompass the entire scope of a multivariate analysis. Correlational tests are designed to analyze the relationship between two variables, not three or more variables simultaneously.

Question 13

Given two between-subjects variables that are multi-valued and measured on a level that at least approximates interval characteristics,the most common method of analysis is:

Accepted Answer

When dealing with multi-valued between-subjects variables that are measured on an interval scale, the most common method of analysis is Pearson correlation. This would allow us to determine if there is a linear relationship between the two variables. Spearman rank-order correlation, point-biserial correlation, and nonparametric correlation may be more appropriate for other types of data or variable measurement scales.

Question 14

Inference of a relationship between two variables depends on the comparison of means.

Accepted Answer

Inference of a relationship between two variables can depend on a variety of factors, including correlation coefficients, regression analyses, and hypothesis testing. While comparing means can be one method of analyzing relationships between variables, it is not the only or definitive approach.

Question 15

The appropriate means of analysis for research designs involving one between-subjects qualitative independent variable and one within-subjects qualitative independent variable would be a:

Accepted Answer

A two-way between-within analysis of variance (ANOVA) would be the appropriate means of analysis for research designs involving one between-subjects qualitative independent variable and one within-subjects qualitative independent variable. This type of ANOVA allows for the examination of the main effects and interaction effects of two independent variables. It also takes into account both the between-subjects and within-subjects factors, which is important in controlling for individual differences and potential order effects.

Question 16

Under the correct circumstances a nonparametric tests can be as powerful as a parametric test.

Accepted Answer

Nonparametric tests can be as powerful as parametric tests when the assumptions of normality and equal variance are not met, or when the sample size is small. In such cases, nonparametric tests may have the advantage of not making strict assumptions about the shape of the distribution, and may be more robust to outliers. Therefore, it is not accurate to say that parametric tests are always more powerful than nonparametric tests.

Question 17

Some psychologists have argued that the question "is there a relationship between two variables" is meaningless,in part because:

Accepted Answer

The null hypothesis, which states that there is no relationship between the two variables, is almost always false in psychological research. However, this does not mean that the alternative hypothesis (which states that there is a relationship between the two variables) is always true. Therefore, the question of whether there is a relationship between two variables is not meaningless, but rather requires careful empirical investigation and statistical analysis. Option A is incorrect as it is not relevant to the argument. Option B is incorrect because the alternative hypothesis can be true in some cases. Option D is also incorrect because empirical relationships are not rare in psychological research.

Question 18

The goal of _____ is to determine if the correlations among a set of variables can be accounted for by one or more underlying dimensions,or _____.

Accepted Answer

The description matches the process of factor analysis, which seeks to identify underlying factors that can explain the correlations among observed variables. Regression analysis is a different method that focuses on predicting one variable based on others. Log-linear analysis is a statistical technique used in categorical data analysis to model the relationship between two or more categorical variables.

Question 19

Multiple regression analysis involves the prediction of a _____ variable from two or more _____ variables.

Accepted Answer

In multiple regression analysis, the criterion variable (the variable being predicted) is typically labeled as the dependent variable and is predicted from one or more predictor variables, also known as independent variables. Therefore, the correct answer is D, with "criterion" referring to the dependent variable and "predictor" referring to the independent variables.

Question 20

In multiple regression analysis,each predictor has a "slope" (â)that is called a:

Accepted Answer

Each predictor in multiple regression has a regression coefficient (slope) which represents the change in the dependent variable associated with a one-unit change in that predictor, holding all other predictors constant. Therefore, the best choice is C. Factors, squared multiple correlation coefficient, and multiple r are not equivalent to the regression coefficient.

Quiz 17: Overview and Extension: Statistical Tests for More Complex Designs