1. Discriminant function analysis is mainly used to:

A. Predict yield from input levels
B. Classify observations into predefined groups
C. Measure genetic diversity
D. Estimate correlation among traits
Answer: B
Rationale: Discriminant analysis is a classification technique used to assign cases to known groups based on predictor variables.

2. Discriminant function analysis was developed by:

A. R.A. Fisher
B. Karl Pearson
C. Sewall Wright
D. Charles Darwin
Answer: A
Rationale: Sir Ronald A. Fisher (1936) introduced linear discriminant analysis (LDA).

3. In agricultural research, discriminant function analysis is used for:

A. Grouping genotypes based on quantitative traits
B. Estimating mean yield
C. Detecting gene frequencies
D. Determining fertilizer levels
Answer: A
Rationale: It helps to classify varieties, species, or genotypes into distinct groups using multiple traits.

4. The general purpose of discriminant function analysis is:

A. To find a linear combination of variables that best separates groups
B. To estimate variance components
C. To test hypothesis only
D. To perform random sampling
Answer: A
Rationale: LDA constructs a linear function that maximizes separation between groups.

5. The mathematical expression for a discriminant function is:

A. ( D = a + b_1X_1 + b_2X_2 + ... + b_nX_n )
B. ( Y = a + bx )
C. ( D = X^2 + Y^2 )
D. ( D = rxy )
Answer: A
Rationale: The discriminant function is a linear combination of predictor variables weighted by coefficients.

6. In Fisher’s discriminant function, the coefficients are chosen to:

A. Minimize within-group variance and maximize between-group variance
B. Maximize within-group variance
C. Minimize both variances
D. Ignore variances
Answer: A
Rationale: Optimal discrimination is achieved by maximizing the ratio of between-group to within-group variance.

7. The dependent variable in discriminant analysis is:

A. Continuous
B. Categorical (group membership)
C. Binary only
D. Nominal and continuous
Answer: B
Rationale: The dependent variable indicates the group or class (e.g., genotype category).

8. The independent variables in discriminant analysis are:

A. Quantitative (metric)
B. Qualitative
C. Categorical
D. Nominal
Answer: A
Rationale: Independent variables must be continuous and metric to calculate discriminant scores.

9. The number of discriminant functions possible equals:

A. Number of groups – 1
B. Number of variables
C. Number of observations
D. Number of parameters
Answer: A
Rationale: For k groups, only k–1 discriminant functions can be derived.

10. Which statistical test is used to check the significance of discriminant functions?

A. F-test
B. Chi-square test
C. Wilks’ Lambda
D. Kruskal-Wallis test
Answer: C
Rationale: Wilks’ Lambda tests whether discriminant functions significantly separate the groups.

11. The value of Wilks’ Lambda ranges from:

A. 0 to 1
B. –1 to +1
C. 0 to ∞
D. 1 to 100
Answer: A
Rationale: Lower values of Wilks’ Lambda indicate better group discrimination.

12. If Wilks’ Lambda is close to 0, it indicates:

A. Poor discrimination
B. High discrimination among groups
C. No relation
D. Random variation
Answer: B
Rationale: A smaller Lambda shows greater separation between groups.

13. The discriminant score of an individual is used to:

A. Predict yield
B. Classify it into one of the known groups
C. Estimate heritability
D. Determine correlation
Answer: B
Rationale: Each individual’s score helps assign it to the most probable group.

14. The ratio of between-group to within-group variance is called:

A. F-ratio
B. Discriminant ratio
C. Lambda statistic
D. Correlation ratio
Answer: A
Rationale: The F-ratio is used to measure the strength of group separation.

15. In plant breeding, discriminant function analysis helps to:

A. Differentiate genotypes based on multiple characters
B. Identify heterotic groups
C. Estimate combining ability
D. Predict disease incidence
Answer: A
Rationale: It’s used to identify genetic or phenotypic groups using morphological or physiological traits.

16. If two groups are completely separated by a discriminant function, Wilks’ Lambda becomes:

A. 0
B. 1
C. 0.5
D. Undefined
Answer: A
Rationale: Complete discrimination yields Lambda = 0, indicating no overlap.

17. In discriminant analysis, the eigenvalue represents:

A. The variance explained by each discriminant function
B. Mean difference between groups
C. Covariance matrix
D. Test statistic
Answer: A
Rationale: Each eigenvalue shows the discriminating power of a function.

18. The canonical correlation between discriminant scores and group membership indicates:

A. Strength of association
B. Test of variance
C. Regression slope
D. None of these
Answer: A
Rationale: Canonical correlation measures how well the function distinguishes between groups.

19. When independent variables are highly correlated, it leads to:

A. Multicollinearity
B. Homoscedasticity
C. Independence
D. Normality
Answer: A
Rationale: Multicollinearity affects the stability of discriminant coefficients.

20. Standardized discriminant function coefficients are used to:

A. Compare relative importance of variables
B. Compute yield
C. Test regression
D. Determine residuals
Answer: A
Rationale: They show which variables contribute most to group separation.

21. Classification matrix (confusion matrix) in discriminant analysis shows:

A. Misclassification and correct classification rates
B. Regression output
C. Variable means
D. Eigenvalues
Answer: A
Rationale: It presents how many observations were correctly or incorrectly classified.

22. A high canonical correlation value indicates:

A. Poor discrimination
B. Strong relationship between discriminant function and group
C. Weak variable selection
D. Overfitting
Answer: B
Rationale: Higher canonical correlation means greater separation power.

23. Cross-validation in discriminant analysis is used to:

A. Increase sample size
B. Check classification accuracy on independent data
C. Compute regression
D. Standardize variables
Answer: B
Rationale: It evaluates how well the discriminant model generalizes to new cases.

24. Stepwise discriminant analysis is used when:

A. All variables are equally important
B. Only significant variables are to be selected automatically
C. No variables are to be eliminated
D. Data are categorical only
Answer: B
Rationale: Stepwise method selects variables that significantly improve discrimination.

25. The major assumption of discriminant analysis is:

A. Multivariate normality and equal covariance matrices across groups
B. Data independence
C. Non-normality
D. Binary classification only
Answer: A
Rationale: Discriminant analysis assumes multivariate normal distribution and homogeneity of covariance matrices (homoscedasticity).