N758PE Advanced Statistics
Bundled exam with correct
answers and rationale graded A+
new!!
1. A researcher wants to compare the mean blood pressure of three different
treatment groups. The data are normally distributed, and the variances are
approximately equal. Which statistical test is most appropriate?
a) Paired t-test
b) Independent samples t-test
c) One-way ANOVA
d) Chi-square test
Rationale: One-way ANOVA is used to compare the means of three or more
independent groups when the dependent variable is continuous and normally
distributed.
2. Which of the following is NOT an assumption of the one-way ANOVA?
a) Independence of observations
b) Normality of the dependent variable within groups
c) Homogeneity of variances
d) The dependent variable must be categorical.
Rationale: ANOVA requires a continuous dependent variable. A categorical
dependent variable would be analyzed using a different test, such as chi-square.
3. A post-hoc test is conducted after a significant ANOVA. What is the primary
purpose of this test?
a) To determine the effect size
b) To check for normality
c) To identify which specific group means differ from each other
d) To test for homogeneity of variance
Rationale: While ANOVA tells you that at least one group mean is different, post-
hoc tests (like Tukey's HSD) are used to make pairwise comparisons to find where
those differences lie.
4. In a study examining the relationship between a continuous independent
variable (X) and a continuous dependent variable (Y), a Pearson correlation
,coefficient (r) is calculated as -0.85. What does this indicate?
a) A weak positive relationship
b) A strong positive relationship
c) A strong negative relationship
d) No relationship
Rationale: The value -0.85 indicates a strong relationship (close to -1), and the
negative sign indicates that as X increases, Y tends to decrease.
5. What is the primary difference between simple linear regression and Pearson
correlation?
a) Correlation assesses the strength of a relationship, while regression predicts the
value of one variable from another.
b) Correlation assesses the strength of a relationship, while regression predicts
the value of one variable from another.
c) Regression is used for categorical variables, while correlation is for continuous
variables.
d) There is no difference; they are the same test.
Rationale: Correlation measures the strength and direction of an association.
Regression goes a step further by creating a model to predict the dependent variable
based on the independent variable.
6. A researcher wants to predict the likelihood of a patient developing a disease
(yes/no) based on age and BMI. Which statistical method is most appropriate?
a) Multiple linear regression
b) Logistic regression
c) One-way ANOVA
d) Pearson correlation
Rationale: Logistic regression is used when the dependent variable is binary (e.g.,
yes/no, disease/no disease).
7. In a multiple linear regression model, what does the coefficient of
determination (R²) represent?
a) The p-value of the overall model
b) The strength of the correlation between the first predictor and the outcome
c) The proportion of variance in the dependent variable explained by the
independent variables
d) The standard error of the estimate
Rationale: R² is a measure of goodness-of-fit. It quantifies how much of the
variability in the outcome is predictable from the predictors.
8. What is multicollinearity in multiple regression?
a) When the dependent variable is highly correlated with an independent variable
b) When two or more independent variables are highly correlated with each
other
, c) When the residuals are not normally distributed
d) When the relationship between variables is non-linear
Rationale: Multicollinearity can make it difficult to determine the individual effect of
each predictor on the outcome and can lead to unstable coefficient estimates.
9. Which of the following is a non-parametric alternative to the independent
samples t-test?
a) Wilcoxon signed-rank test
b) Mann-Whitney U test
c) Kruskal-Wallis H test
d) Friedman test
Rationale: The Mann-Whitney U test is used to compare two independent groups
when the assumption of normality is violated. The Wilcoxon signed-rank test is for
paired data.
10. A researcher collects data on a Likert scale (e.g., 1=Strongly Disagree to
5=Strongly Agree) and wants to compare two independent groups. The data
are not normally distributed. Which test is most appropriate?
a) Independent samples t-test
b) Mann-Whitney U test
c) Paired t-test
d) Chi-square test
Rationale: Likert scale data are ordinal. When the normality assumption is violated
for comparing two independent groups, the non-parametric Mann-Whitney U test is
the correct choice.
11. What is the purpose of a chi-square test of independence?
a) To compare means of two groups
b) To assess the correlation between two continuous variables
c) To determine if there is an association between two categorical variables
d) To predict a continuous outcome from a categorical predictor
Rationale: The chi-square test of independence is used to analyze the relationship
between two categorical variables (e.g., gender and smoking status).
12. In a 2x2 contingency table for a chi-square test, the expected frequency for
a cell is 3. What is the most appropriate action?
a) Proceed with the standard chi-square test.
b) Use Fisher's Exact Test.
c) Combine categories to increase the expected frequency.
d) Use a t-test instead.
Rationale: A common rule of thumb for the chi-square test is that all expected
frequencies should be 5 or greater. If an expected frequency is less than 5 (especially
in a 2x2 table), Fisher's Exact Test is more appropriate.
Bundled exam with correct
answers and rationale graded A+
new!!
1. A researcher wants to compare the mean blood pressure of three different
treatment groups. The data are normally distributed, and the variances are
approximately equal. Which statistical test is most appropriate?
a) Paired t-test
b) Independent samples t-test
c) One-way ANOVA
d) Chi-square test
Rationale: One-way ANOVA is used to compare the means of three or more
independent groups when the dependent variable is continuous and normally
distributed.
2. Which of the following is NOT an assumption of the one-way ANOVA?
a) Independence of observations
b) Normality of the dependent variable within groups
c) Homogeneity of variances
d) The dependent variable must be categorical.
Rationale: ANOVA requires a continuous dependent variable. A categorical
dependent variable would be analyzed using a different test, such as chi-square.
3. A post-hoc test is conducted after a significant ANOVA. What is the primary
purpose of this test?
a) To determine the effect size
b) To check for normality
c) To identify which specific group means differ from each other
d) To test for homogeneity of variance
Rationale: While ANOVA tells you that at least one group mean is different, post-
hoc tests (like Tukey's HSD) are used to make pairwise comparisons to find where
those differences lie.
4. In a study examining the relationship between a continuous independent
variable (X) and a continuous dependent variable (Y), a Pearson correlation
,coefficient (r) is calculated as -0.85. What does this indicate?
a) A weak positive relationship
b) A strong positive relationship
c) A strong negative relationship
d) No relationship
Rationale: The value -0.85 indicates a strong relationship (close to -1), and the
negative sign indicates that as X increases, Y tends to decrease.
5. What is the primary difference between simple linear regression and Pearson
correlation?
a) Correlation assesses the strength of a relationship, while regression predicts the
value of one variable from another.
b) Correlation assesses the strength of a relationship, while regression predicts
the value of one variable from another.
c) Regression is used for categorical variables, while correlation is for continuous
variables.
d) There is no difference; they are the same test.
Rationale: Correlation measures the strength and direction of an association.
Regression goes a step further by creating a model to predict the dependent variable
based on the independent variable.
6. A researcher wants to predict the likelihood of a patient developing a disease
(yes/no) based on age and BMI. Which statistical method is most appropriate?
a) Multiple linear regression
b) Logistic regression
c) One-way ANOVA
d) Pearson correlation
Rationale: Logistic regression is used when the dependent variable is binary (e.g.,
yes/no, disease/no disease).
7. In a multiple linear regression model, what does the coefficient of
determination (R²) represent?
a) The p-value of the overall model
b) The strength of the correlation between the first predictor and the outcome
c) The proportion of variance in the dependent variable explained by the
independent variables
d) The standard error of the estimate
Rationale: R² is a measure of goodness-of-fit. It quantifies how much of the
variability in the outcome is predictable from the predictors.
8. What is multicollinearity in multiple regression?
a) When the dependent variable is highly correlated with an independent variable
b) When two or more independent variables are highly correlated with each
other
, c) When the residuals are not normally distributed
d) When the relationship between variables is non-linear
Rationale: Multicollinearity can make it difficult to determine the individual effect of
each predictor on the outcome and can lead to unstable coefficient estimates.
9. Which of the following is a non-parametric alternative to the independent
samples t-test?
a) Wilcoxon signed-rank test
b) Mann-Whitney U test
c) Kruskal-Wallis H test
d) Friedman test
Rationale: The Mann-Whitney U test is used to compare two independent groups
when the assumption of normality is violated. The Wilcoxon signed-rank test is for
paired data.
10. A researcher collects data on a Likert scale (e.g., 1=Strongly Disagree to
5=Strongly Agree) and wants to compare two independent groups. The data
are not normally distributed. Which test is most appropriate?
a) Independent samples t-test
b) Mann-Whitney U test
c) Paired t-test
d) Chi-square test
Rationale: Likert scale data are ordinal. When the normality assumption is violated
for comparing two independent groups, the non-parametric Mann-Whitney U test is
the correct choice.
11. What is the purpose of a chi-square test of independence?
a) To compare means of two groups
b) To assess the correlation between two continuous variables
c) To determine if there is an association between two categorical variables
d) To predict a continuous outcome from a categorical predictor
Rationale: The chi-square test of independence is used to analyze the relationship
between two categorical variables (e.g., gender and smoking status).
12. In a 2x2 contingency table for a chi-square test, the expected frequency for
a cell is 3. What is the most appropriate action?
a) Proceed with the standard chi-square test.
b) Use Fisher's Exact Test.
c) Combine categories to increase the expected frequency.
d) Use a t-test instead.
Rationale: A common rule of thumb for the chi-square test is that all expected
frequencies should be 5 or greater. If an expected frequency is less than 5 (especially
in a 2x2 table), Fisher's Exact Test is more appropriate.
