Question

Match the following Statistical tools with their suitable explanation

List-I (Statistical tool)	List-II (suitable explanation)
(A) Correlation	(I) It establishes the nature of the relationship between variables to study the cause and effect relationship
(B) Student t-distribution	(II) It should not be used when N is less than 50
(C) ANOVA	(III) It helps in determining the degree of relationship between two or more variables
(D) $\chi^2$ test	(IV) This is specifically used to test whether the means of more than two quantitative populations are equal
(E) Regression	(V) It is used when sample size is 30 or less

Choose the correct answer from the options given below

• (A) - (I), (B) - (II), (C) - (IV), (D) - (V), (E) - (III)
• (A) - (III), (B) - (V), (C) - (IV), (D) - (II), (E) - (I)
• (A) - (V), (B) - (III), (C) - (I), (D) - (II), (E) - (IV)
• (A) - (II), (B) - (IV), (C) - (V), (D) - (I), (E) - (III)

Hint:

To remember key test differences:
t-test = Comparing means of exactly 2 groups (or small sample \( \le 30 \)).
ANOVA = Comparing means of 3 or more groups.
Correlation = Measuring the degree of relationship.
Regression = Modeling cause-and-effect.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Biostatistics uses various analytical tools and hypothesis tests to analyze biological data.
These tools are used to measure relationships, test differences between group means, or evaluate goodness-of-fit for categorical data.

Step 2: Detailed Explanation:
Let us analyze and match each statistical tool:
1.Correlation (A): Correlation analysis measures the strength and direction of the linear association between variables.
It helps determine the *degree* of relationship between two or more variables.
Thus, (A) matches with (III).
2.Student's t-test (B): This is a parametric hypothesis test used to compare the means of two small groups.
It is specifically designed for small sample sizes, typically when \( n \le 30 \).
Thus, (B) matches with (V).
3.ANOVA (Analysis of Variance) (C): ANOVA is a parametric test used to determine if there are any statistically significant differences between the means of *three or more* independent groups.
Thus, (C) matches with (IV).
4.Chi-square (\( \chi^2 \)) test (D): This is a non-parametric test used to analyze categorical data and determine goodness-of-fit or independence.
For the test to be valid, the total sample size (\( N \)) should be sufficiently large, with a common guideline stating it should not be used if \( N < 50 \) or if expected cell frequencies are too small.
Thus, (D) matches with (II).
5.Regression (E): Regression analysis models the mathematical relationship between a dependent variable and one or more independent variables.
It helps establish the nature of the relationship to study cause-and-effect.
Thus, (E) matches with (I).
Combining these matches:
\[ \text{(A)-(III), (B)-(V), (C)-(IV), (D)-(II), (E)-(I)} \]

Step 3: Final Answer:
The correct matching sequence is (A) - (III), (B) - (V), (C) - (IV), (D) - (II), (E) - (I).