Question:
The procedure of decomposing the overall variation in the observed responses in an experiment into different components attributable to various sources of variation is known as
The procedure of decomposing the overall variation in the observed responses in an experiment into different components attributable to various sources of variation is known as
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ANOVA is essentially a method of partitioning the total variance into assignable causes (treatments) and unassignable causes (chance/error).
Updated On: Aug 24, 2026
- analysis of decomposition
- analysis of variation
- analysis of covariance
- analysis of variance
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The Correct Option is D
Solution and Explanation
Step 1: Understanding the Concept:
Experimental data exhibits total variation, which is caused by both controlled experimental factors and uncontrolled random error.
Step 2: Detailed Explanation:
The statistical technique used to isolate and compare these different sources of variation is called Analysis of Variance (ANOVA).
Developed by Sir Ronald A. Fisher, ANOVA partition the Total Sum of Squares ($SS_{\text{Total}}$) into:
- Sum of Squares due to Treatments ($SS_{\text{Treatment}}$), representing the variation caused by controlled factors.
- Sum of Squares due to Error ($SS_{\text{Error}}$), representing the variation caused by random fluctuations.
This decomposition enables the computation of $F$-ratios to test whether treatment means are significantly different.
Therefore, this procedure is known as the analysis of variance.
Step 3: Final Answer
The correct option is (D).
Experimental data exhibits total variation, which is caused by both controlled experimental factors and uncontrolled random error.
Step 2: Detailed Explanation:
The statistical technique used to isolate and compare these different sources of variation is called Analysis of Variance (ANOVA).
Developed by Sir Ronald A. Fisher, ANOVA partition the Total Sum of Squares ($SS_{\text{Total}}$) into:
- Sum of Squares due to Treatments ($SS_{\text{Treatment}}$), representing the variation caused by controlled factors.
- Sum of Squares due to Error ($SS_{\text{Error}}$), representing the variation caused by random fluctuations.
This decomposition enables the computation of $F$-ratios to test whether treatment means are significantly different.
Therefore, this procedure is known as the analysis of variance.
Step 3: Final Answer
The correct option is (D).
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