In analysis of variance (ANOVA), what does a... | Fish Biotechnology

ICAR JRF Fish Biotechnology 29 Jun 2024Shift 1

MCQ (Single Correct) +4 −1

In analysis of variance (ANOVA), what does a high F-statistic value indicate?

There is a strong linear relationship between the variables. There is a significant difference between group means. Correct There is no significant difference between group means. The variance explained by the independent variable is low.

ANOVA and the $F$-Statistic:
In Analysis of Variance (ANOVA), the $F$-statistic tests the null hypothesis that multiple group population means are equal:

$$F = \frac{\text{Mean Square Between Groups (Treatment)}}{\text{Mean Square Within Groups (Error)}} = \frac{\text{MS}_{\text{between}}}{\text{MS}_{\text{within}}}$$

high $F$-statistic indicates that the variation between group means is substantially greater than random within-group variation, rejecting the null hypothesis and proving statistically significant differences between group means.
Correct Option: Option 2 (There is a significant difference between group means).

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