Agricultural Extension Education- ICAR JRF/SRF 2024

• Interval Level of Measurement Characteristics:
• In S.S. Stevens' typology of measurement scales (Nominal, Ordinal, Interval, Ratio):
• Interval Scale: Possesses rank order and equal unit distances (equal intervals) between successive points along the continuum (e.g., Celsius temperature scale, standardized IQ scores).
• Mathematical Operations: Permissible arithmetic operations include addition and subtraction of interval differences, calculation of means, standard deviations, and Pearson's $r$.
• No True Zero: Interval scales have an arbitrary zero point, not an absolute true zero (e.g., $0^\circ\text{C}$ does not indicate total absence of heat).
• Conclusion: Both (1) equal interval width and (3) permissible addition/subtraction are correct, making Option 4 correct.

Correct option: (4) Both (1) and (3)

• One-Tailed vs. Two-Tailed Hypothesis Testing:
• Statement 2 is incorrect: A two-tailed test is used when testing whether two population means are equal or not equal without specifying direction ($H_0: \mu_1 = \mu_2$ versus $H_1: \mu_1 \neq \mu_2$).
• one-tailed test is used only when the alternative hypothesis specifies a definite directional difference (e.g., $H_1: \mu_1 \gt \mu_2$ or $H_1: \mu_1 \lt \mu_2$).
• True Statistical Facts:
• Probability of Type I Error (rejecting true $H_0$) is level of significance $\alpha$.
• Probability of Type II Error (retaining false $H_0$) is $\beta$.

Correct option: (2) One tail-test is used when two means are equal or are not equal

• Output Metrics in Linear Regression Analysis:
• Standard outputs in ordinary least squares (OLS) regression analysis include:
• Model fit statistics: $R^2$, Adjusted $R^2$, standard error of the estimate.
• ANOVA table (testing overall regression significance via $F$-statistic).
• Regression coefficients table: unstandardized coefficients ($B$), standardized beta coefficients ($\beta$), standard errors, $t$-values, and $p$-values.
• Fisher's Exact Test: A non-parametric test used for analyzing small-sample $2 \times 2$ categorical contingency tables, NOT an output of linear regression, making Option 4 correct.

Correct option: (4) Fisher's Exact test