Q.3
Agricultural Statistics- ICAR JRF/SRF 2024 (Q.38)
MCQ (Single Correct) +4 −1
In a Chi-square test, the contingency table has 5 rows and 5 columns. What is the number of degrees of freedom?
EXPLANATION Hypothesis Testing: Neyman-Pearson Fundamental Lemma, UMP Tests, Likelihood Ratio Tests (LRT) & Non-Parametric Tests
  • Degrees of Freedom in Contingency Tables:
  • For an $r \times c$ two-way contingency table with $r$ rows and $c$ columns testing for independence of attributes using the Chi-square statistic:
$$df = (r - 1) \times (c - 1)$$
  • Given $r = 5$ and $c = 5$:
$$df = (5 - 1) \times (5 - 1) = 4 \times 4 = 16$$
  • Conclusion: The number of degrees of freedom is 16 (Option 3).

Correct option: (3) 16

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Agricultural Statistics विषय एवं अध्याय

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खंड अ: सामान्य कृषि

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Statistical Methods I

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Statistical Methods II

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Multivariate Analysis (Wishart, Hotelling T2, MANOVA, PCA, Factor & Cluster Analysis) & Linear Programming Optimization Hypothesis Testing: Neyman-Pearson Fundamental Lemma, UMP Tests, Likelihood Ratio Tests (LRT) & Non-Parametric Tests सक्रिय Correlation, Multiple/Partial Regression, Collinearity Diagnostics & Econometric Residual Analysis
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