Discriminant Analysis: Classifying Observations in Psychology

Question 1

What is the primary purpose of the discriminant function in discriminant analysis?

Accepted Answer

To predict the group membership of an observation.

Answer

To maximize the variance between the groups.

Answer

To minimize the variance within the groups.

Answer

To determine the relative importance of the independent variables.

Question 2

When is discriminant analysis most appropriate to use?

Accepted Answer

When the dependent variable is categorical and the independent variables are continuous.

Answer

When the dependent variable is continuous and the independent variables are categorical.

Answer

When the relationship between the independent variables and the dependent variable is non-linear.

Answer

When the sample size is small.

Question 3

In which scenario is discriminant analysis an appropriate statistical method to employ?

Accepted Answer

Predicting the likelihood of a patient having a specific disease based on observed symptoms.

Answer

Identifying the factors that influence job satisfaction levels.

Answer

Creating a scatterplot to visualize the distribution of data points.

Answer

Testing the statistical significance of a difference between two group means.

Question 4

Which assumption is essential for discriminant analysis?

Accepted Answer

Groups are mutually exclusive and collectively exhaustive.

Answer

Predictor variables are normally distributed.

Answer

Predictor variables are independent.

Answer

Sample size is 20 times the number of predictor variables.

Question 5

In quadratic discriminant analysis, the assumption of equal covariance matrices is:

Accepted Answer

Relaxed

Answer

Strict

Answer

Optional

Answer

Invalid

Question 6

In discriminant analysis, the discriminant function represents:

Accepted Answer

The linear combination of predictor variables used to classify observations

Answer

The probability of belonging to a particular group

Answer

The distance between observations and the group centroids

Answer

The optimal cutoff value for group membership

Question 7

Which of the following is NOT a step in the process of conducting discriminant analysis?

Accepted Answer

Analysis of variance

Answer

Data collection and preparation

Answer

Model building

Answer

Model evaluation

Question 8

What distinguishes linear from quadratic discriminant analysis?

Accepted Answer

Linear discriminant analysis assumes linearity, while quadratic discriminant analysis allows for non-linear relationships

Answer

Linear discriminant analysis uses a single discriminant function, while quadratic discriminant analysis uses multiple discriminant functions

Answer

Linear discriminant analysis is more susceptible to outliers, while quadratic discriminant analysis is more robust

Answer

Linear discriminant analysis is computationally more intensive than quadratic discriminant analysis

Question 9

Which measure assesses the overall accuracy of a discriminant analysis model?

Accepted Answer

Classification rate

Answer

R-squared

Answer

F-statistic

Answer

Eigenvalue

Question 10

How does a canonical discriminant function differ from a discriminant function?

Accepted Answer

A canonical discriminant function maximizes the correlation between discriminant scores and the group membership variable

Answer

A discriminant function maximizes the separation between groups

Answer

A canonical discriminant function utilizes all predictor variables, while a discriminant function uses only a subset

Answer

There is no difference between a canonical discriminant function and a discriminant function

Question 11

Which of the following is the primary objective of discriminant analysis?

Accepted Answer

Classifying observations into distinct groups

Answer

Identifying patterns within data

Answer

Predicting future events

Answer

Reducing the complexity of data

Question 12

What is the main purpose of a discriminant function?

Accepted Answer

Predicting group membership

Answer

Determining the probability of group membership

Answer

Identifying crucial predictor variables

Answer

Simplifying data

Question 13

What is the key difference between canonical and stepwise discriminant analysis?

Accepted Answer

Canonical considers all variables simultaneously, while stepwise selects sequentially

Answer

Stepwise considers all variables simultaneously, while canonical selects sequentially

Answer

Canonical uses a linear model, while stepwise uses a quadratic model

Answer

Stepwise uses a linear model, while canonical uses a quadratic model

Question 14

What is the recommended minimum sample size for discriminant analysis?

Accepted Answer

At least 20 observations per predictor variable

Answer

At least 50 observations per group

Answer

At least 100 observations total

Answer

No minimum sample size requirement

Question 15

How can outliers affect the precision and reliability of discriminant analysis models?

Accepted Answer

Outliers can diminish model precision and reliability.

Answer

Outliers can improve model precision and reliability.

Answer

Outliers typically have no significant impact on discriminant analysis models.

Answer

Outliers only impact linear discriminant analysis models, not quadratic discriminant analysis models.

Question 16

In discriminant analysis, the discriminant function is a linear combination of which of the following?

Accepted Answer

Independent variables.

Answer

Dependent variables.

Answer

Categorical variables.

Answer

Continuous variables.

Question 17

The Wilks' lambda statistic in discriminant analysis indicates:

Accepted Answer

The ratio of within-group variance to between-group variance.

Answer

The proportion of variance explained by the discriminant function.

Answer

The distance between group centroids.

Answer

The significance of the discriminant function.

Question 18

The cutoff score in discriminant analysis maximizes which of the following?

Accepted Answer

Probability of correct classification.

Answer

Probability of misclassification.

Answer

Difference between group means.

Answer

Variance within groups.

Question 19

Which of the following measures the overall accuracy of a discriminant analysis model?

Accepted Answer

Classification matrix.

Answer

Wilks' lambda.

Answer

Receiver operating characteristic curve.

Answer

AIC.

Question 20

How do prior probabilities affect the classification of observations in discriminant analysis?

Accepted Answer

Prior probabilities determine the likelihood of an observation belonging to each group, influencing classification.

Answer

Prior probabilities have no role in the classification process.

Answer

Prior probabilities are only used to calculate group averages.

Answer

Prior probabilities are only relevant in quadratic discriminant analysis.

Question 21

Which of the following is NOT a measure of classification accuracy in discriminant analysis?

Accepted Answer

R-squared

Answer

Hit rate

Answer

False positive rate

Answer

Sensitivity

Question 22

What is the purpose of a canonical discriminant function?

Accepted Answer

To maximize the variance between the groups on a linear combination of predictor variables.

Answer

To identify the most important predictor variables.

Answer

To determine the cutoff point for classification.

Answer

To estimate the probability of an observation belonging to each group.

Question 23

What is the meaning of the Wilks' lambda statistic in discriminant analysis?

Accepted Answer

It tests the hypothesis that the groups have equal means on the linear combination of predictor variables.

Answer

It measures the proportion of variance in the dependent variable that is explained by the discriminant function.

Answer

It is used to calculate the cutoff point for classification.

Answer

It estimates the prior probability of an observation belonging to each group.

Question 24

What is the importance of cross-validation in discriminant analysis?

Accepted Answer

It helps to prevent overfitting and provides a more accurate estimate of the model's performance.

Answer

It can be used to select the optimal number of predictor variables.

Answer

It allows for the identification of outliers.

Answer

It is a necessary step before using discriminant analysis on a new dataset.

Question 25

Which of the following is a key assumption of discriminant analysis?

Accepted Answer

The groups have equal variance-covariance matrices and the predictors follow a multivariate normal distribution.

Answer

The observations are independent and normally distributed.

Answer

The predictor variables are correlated.

Answer

The groups have a linear relationship.

Question 26

What is the primary purpose of the discriminant function?

Accepted Answer

To predict the group membership of an observation.

Answer

To identify the most important predictor variables.

Answer

To test the significance of the differences between groups.

Answer

To create a graphical representation of the data.

Question 27

Which type of discriminant analysis employs a quadratic equation to classify observations?

Accepted Answer

Quadratic discriminant analysis

Answer

Linear discriminant analysis

Question 28

What is a significant limitation of discriminant analysis?

Accepted Answer

It is sensitive to outliers.

Answer

It can only be used to classify observations into two groups.

Answer

It requires a large sample size.

Answer

It is difficult to interpret.

Question 29

What is the primary purpose of cross-validation in discriminant analysis?

Accepted Answer

To evaluate the accuracy of the classification model.

Answer

To select the most important predictor variables.

Answer

To reduce the effects of overfitting.

Answer

To improve the interpretability of the discriminant function.

Question 30

What is the Wilks' lambda statistic primarily used for in discriminant analysis?

Accepted Answer

To test the overall significance of the discriminant function.

Answer

To compare the classification accuracy of different discriminant models.

Answer

To determine the relative importance of the predictor variables.

Answer

To estimate the probability of group membership.

Question 31

What is the primary purpose of using cross-validation in discriminant analysis?

Accepted Answer

To estimate the generalization accuracy of the discriminant model.

Answer

To identify overfitting.

Answer

To select the optimal number of predictor variables.

Answer

To test the significance of the discriminant function.

Question 32

What is the key difference between linear and quadratic discriminant analysis?

Accepted Answer

Linear discriminant analysis assumes that the groups are linearly separable, while quadratic discriminant analysis does not.

Answer

Quadratic discriminant analysis assumes that the groups are normally distributed, while linear discriminant analysis does not.

Answer

Linear discriminant analysis is more interpretable than quadratic discriminant analysis.

Answer

Quadratic discriminant analysis is more accurate than linear discriminant analysis.

Question 33

Which of the following is a fundamental assumption of linear discriminant analysis?

Accepted Answer

The covariance matrices of the distinct groups are identical.

Answer

The predictor variables exhibit a normal distribution.

Answer

The sample sizes of the groups are equivalent.

Answer

The discriminant function is linear.

Question 34

In discriminant analysis, the canonical discriminant function:

Accepted Answer

Is a linear combination of predictors that maximizes group separation.

Answer

Is a non-linear combination of predictors that minimizes classification error.

Answer

Establishes rules for assigning observations to specific groups.

Answer

Provides a graphical representation of predictor-group relationships.

Question 35

In discriminant analysis, what is the purpose of prior probabilities?

Accepted Answer

To address unequal group sizes.

Answer

To enhance classification accuracy.

Answer

To correct for sample bias.

Answer

To ensure equal representation of groups in the analysis.

Question 36

In discriminant analysis, the predictor variables that contribute most to group differentiation are identified by the:

Accepted Answer

Discriminant function coefficients.

Answer

Canonical discriminant function.

Answer

Classification matrix.

Answer

Prior probabilities.

Question 37

Which of the following is a prerequisite for using discriminant analysis?

Accepted Answer

The dependent variable must be categorical.

Answer

The independent variables must be continuous.

Answer

The groups must be normally distributed.

Answer

The covariance matrices of the groups must be equal.

Question 38

What is the intended purpose of the canonical discriminant function?

Accepted Answer

Creating a new variable that optimally separates the groups.

Answer

Identifying the variables most influential in group discrimination.

Answer

Estimating the probability of an observation belonging to a specific group.

Answer

Determining the number of discriminant functions required for observation classification.