Question 1

If the F value indicates that the between-groups variance estimate is significantly greater than the within-groups variance estimate in an ANOVA, we can conclude that
A) there is random error.
B) the group means are from the same population.
C) the null hypothesis that the differences between the groups are due only to chance can be rejected.
D) there was an error in the calculation.

Accepted Answer

The F value in an ANOVA test is used to compare the variance between groups to the variance within groups. A significantly greater between-groups variance suggests that the groups are not all from the same population, meaning their means differ more than would be expected by chance alone. This leads to the rejection of the null hypothesis, which posits that any observed differences are due to random variation.

Question 2

Within-group variance in an ANOVA is considered to indicate
A) systematic error.
B) differences among the group means.
C) that the group means are from the same population.
D) random error.

Accepted Answer

Within-group variance in an ANOVA is considered to indicate random error, as it measures the variability of observations within each group, which is not explained by the treatment or condition being tested.

Question 3

Which of the following is NOT a bivariate statistic?
A) Pearson correlation coefficient
B) Chi-square
C) One-way ANOVA
D) Multiple regression

Accepted Answer

D

Question 4

Researcher Jones is interested in assessing the relationship between sex of participant and helping behavior (whether the person helped or did not help). Which of the following statistics should be used?
A) Chi-square statistic
B) Kappa
C) Bivariate regression
D) Pearson's r

Accepted Answer

The Chi-square statistic is appropriate for assessing the relationship between two categorical variables, such as sex (male/female) and helping behavior (helped/did not help).

Question 5

A psychologist wanted to determine whether attitudes toward capital punishment were affected by religious commitment. He chose a sample of sixty people, thirty of whom were "very religious" and thirty of whom were "not religious." He then assessed the person's attitude toward capital punishment. Thirteen of the "very religious" people were opposed to capital punishment, whereas only eight of the "not religious" people were opposed. What would be the most appropriate statistical analysis for this experimental data?
A) Bivariate regression
B) One-way analysis of variance
C) Correlation coefficient
D) Chi-square test for independence

Accepted Answer

The most appropriate statistical analysis for this experimental data is the Chi-square test for independence. This test is used to determine if there is a significant association between two categorical variables, in this case, the level of religious commitment and attitudes toward capital punishment.

Question 6

A negative correlation coefficient indicates that
A) there is no relationship between the variables.
B) high scores on one variable are associated with low scores on the other variable.
C) high scores on one variable are associated with high scores on the other variable.
D) it was not calculated accurately.

Accepted Answer

A negative correlation coefficient indicates that as one variable increases, the other decreases, and vice versa, which means high scores on one variable are associated with low scores on the other variable.

Question 7

As the value of r increases, the proportion of variability statistic
A) increases.
B) decreases.
C) does not change.
D) may increase or decrease.

Accepted Answer

As the value of r (correlation coefficient) increases, it indicates a stronger linear relationship between the two variables, which means the proportion of variability explained by the linear model (statistic) increases.

Question 8

A researcher is interested in whether students' grade point averages differed in between those enrolled in lab science, social science, humanities, and mathematics courses. She compared students from a chemistry, an economics, an art, and a calculus class. What would be the most appropriate statistical analysis for these data?
A) Bivariate regression
B) One-way analysis of variance
C) Correlation coefficient
D) Chi-square test for independence

Accepted Answer

The most appropriate statistical analysis for comparing means across more than two groups (in this case, different types of courses) is the One-way Analysis of Variance (ANOVA). ANOVA is used to determine if there are any statistically significant differences between the means of three or more independent (unrelated) groups.

Question 9

Statistical methods used to measure the relationships between two variables are referred to as
A) inferential statistics.
B) correlational statistics.
C) bivariate statistics.
D) multivariate statistics.

Accepted Answer

The answer of Statistical methods used to measure the relationships...

Question 10

For a 2 x 2 contingency table, the appropriate effect size statistic is
A) r.
B) Cohen's kappa.
C) Phi.
D) Cramer's statistic.

Accepted Answer

Phi is specifically designed for measuring effect size in 2 x 2 contingency tables, providing a measure of the strength of association between two binary variables.

Question 11

A researcher calculates a regression equation in order to
A) predict a score on a second variable from a known score on a first variable.
B) determine the strength of the relationship between two nominal variables.
C) predict the differences between scores on one variable from the scores on a second variable
D) determine the causal relationship between two variables.

Accepted Answer

A regression equation is primarily used to predict the value of a dependent variable based on the value of at least one independent variable, making option A the correct choice.

Question 12

Which of the following Pearson correlation coefficients indicates the strongest relationship between two variables?
A) .56
B) -.81
C) -.05
D) .34

Accepted Answer

The Pearson correlation coefficient ranges from -1 to 1, where -1 indicates a perfect negative linear relationship, 1 indicates a perfect positive linear relationship, and 0 indicates no linear relationship. The strength of the relationship is determined by the absolute value of the coefficient, regardless of the sign. Therefore, -.81 indicates the strongest relationship among the options because its absolute value is the highest.

Question 13

If the F value indicates that the between-groups variance is not significantly greater than the within-groups variance in an ANOVA, we can conclude that
A) there is random error.
B) the group means are from the same population.
C) the null hypothesis that the differences between the groups are due only to chance can be rejected.
D) there was an error in the calculation.

Accepted Answer

When the F value in an ANOVA indicates that the between-groups variance is not significantly greater than the within-groups variance, it suggests that the differences in group means could be due to random chance, implying that the groups do not significantly differ from each other and could be from the same population.

Question 14

A researcher wanted to know if aggressive behavior was related to watching violent programs on TV. He selected some students and measured how many violent programs they watched per week (from 0 to 25) and how aggressive their behavior was (as rated on a 1 to 7 scale). What would be the most appropriate statistical analysis for these data?
A) Bivariate regression
B) One-way analysis of variance
C) Multiple regression
D) Chi-square test for independence

Accepted Answer

Bivariate regression is the most appropriate statistical analysis for these data because it allows the researcher to examine the relationship between two continuous variables: the number of violent programs watched per week and the level of aggression in behavior.

Question 15

A correlation coefficient specifies the __________ and __________ of the linear association between two variables.
A) direction; magnitude
B) strength; shape
C) direction; distribution
D) shape; distribution

Accepted Answer

The correlation coefficient measures the direction (positive or negative) and magnitude (strength) of the linear relationship between two variables.

Question 16

The proportion of variance measure for the Pearson correlation coefficient is
A) r.
B) the effect size.
C) the coefficient of determination.
D) the contingency table.

Accepted Answer

The coefficient of determination, denoted as $r^2$, represents the proportion of variance in the dependent variable that is predictable from the independent variable and is a measure related to the Pearson correlation coefficient ($r$).

Question 17

__________ is used to compare the means on a dependent variable between two or more groups of participants who differ on a single independent variable.
A) One-way analysis of variance
B) Regression
C) A contingency table
D) Kappa

Accepted Answer

One-way analysis of variance (ANOVA) is specifically designed to compare the means of a dependent variable across two or more groups that differ based on one independent variable, making it the correct choice for this purpose.

Question 18

If a correlation is positive, this indicates that __________ scores on one variable are associated with __________ scores on another variable.
A) low; high
B) high; low
C) high; high
D) high; medium

Accepted Answer

A positive correlation means that as scores on one variable increase, scores on another variable also increase.

Question 19

What statistic is used to assess the degree of association between two nominal variables?
A) The chi-square statistic
B) Bivariate regression
C) ANOVA
D) Pearson's r

Accepted Answer

The chi-square statistic is used to assess the degree of association between two nominal variables by testing the independence of the variables in a contingency table.

Question 20

The coefficient of determination is to the Pearson correlation coefficient as which of the following is to chi-square?
A) R
B) F
C) The p-value
D) Phi

Accepted Answer

The coefficient of determination (R^2) is the square of the Pearson correlation coefficient (r), indicating the proportion of the variance in the dependent variable that is predictable from the independent variable. Similarly, Phi (Φ) is a measure of association for two binary variables and can be derived from the chi-square statistic, making it analogous to how R^2 relates to r.

Quiz 17: Bivariate Statistics

If the F value indicates that the between-groups variance estimate is significantly greater than the within-groups variance estimate in an ANOVA, we can conclude that

Within-group variance in an ANOVA is considered to indicate

Which of the following is NOT a bivariate statistic?

Researcher Jones is interested in assessing the relationship between sex of participant and helping behavior (whether the person helped or did not help) . Which of the following statistics should be used?

A negative correlation coefficient indicates that

As the value of r increases, the proportion of variability statistic

Statistical methods used to measure the relationships between two variables are referred to as

For a 2 x 2 contingency table, the appropriate effect size statistic is

A researcher calculates a regression equation in order to

Which of the following Pearson correlation coefficients indicates the strongest relationship between two variables?

If the F value indicates that the between-groups variance is not significantly greater than the within-groups variance in an ANOVA, we can conclude that

A correlation coefficient specifies the and of the linear association between two variables.

The proportion of variance measure for the Pearson correlation coefficient is

__________ is used to compare the means on a dependent variable between two or more groups of participants who differ on a single independent variable.

If a correlation is positive, this indicates that scores on one variable are associated with scores on another variable.

What statistic is used to assess the degree of association between two nominal variables?

The coefficient of determination is to the Pearson correlation coefficient as which of the following is to chi-square?