In a two-way classified data with usual notations, the null hypothesis for blocks or varieties is:

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This question was previously asked in

SSC CGL Tier-II (JSO) 2022 Official Paper (Held On: 4 March 2023)

Answer 1

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Key Points

In a two-way classified data, we often analyze the effects of two categorical factors or variables, typically referred to as "rows" and "columns." The null hypothesis for the "blocks" or "varieties" (which is one of the factors) can be stated as follows:
H0: The mean effect of the "j-th" block or variety is equal to zero, where j takes values from 1 to h.
In this context, "Bj" represents the mean effect of the j-th block or variety. The null hypothesis assumes that there is no significant difference between the various blocks or varieties in terms of their effects.
To test this null hypothesis, statistical methods such as analysis of variance (ANOVA) or appropriate regression models can be used to examine the significance of the block or variety effects. If the null hypothesis is rejected based on the observed data and appropriate statistical tests, it implies that there are significant differences between the blocks or varieties.
It's important to note that the specific hypothesis formulation may vary depending on the context and research question at hand.

The notation H0: Bj = 0 is a general representation of the null hypothesis for block or variety effects in a two-way classified data analysis.