State hypothesis for 2k factorial design

AI Thread Summary
In a 2k factorial design involving two factors, the null hypothesis states that the effects of each factor (A and B) and their interaction are not significant. The alternative hypothesis posits that at least one of these effects is significant. The discussion seeks a more formal notation for expressing these hypotheses, suggesting that the null hypothesis could be represented as Ho: τ1 = τ2 = 0, while the alternative could be Ha: at least one τi ≠ 0. Participants are looking for clarity on how to articulate these hypotheses effectively. Overall, the conversation emphasizes the need for precise statistical notation in hypothesis formulation.
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How to state null and alternative hypothesis for 2k factorial design of two factors?

The Attempt at a Solution



All i can think of right now is

null hypothesis - Factor A effects not significant.
alternative hypothesis - Factor A effects significant

null hypothesis - Factor B effects not significant.
alternative hypothesis - Factor B effects significant

null hypothesis - interaction effects not significant.
alternative hypothesis - interaction effects significant

i think it is abit too simplistic, so i want to find out if there are other ways to express this or different notation.
 
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any help?
 
i need some way to express it in terms like
Ho : τ1 = τ2 = τ3 ... τa =0
Ha : at least one τi ≠ 0
however i need equation that is suitable for this specific purpose

is it just Ho : τ1 = τ2=0
Ha : at least one τi ≠ 0
 
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