State hypothesis for 2k factorial design

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SUMMARY

The discussion focuses on formulating null and alternative hypotheses for a 2k factorial design involving two factors, A and B. The proposed null hypotheses state that the effects of Factor A and Factor B, as well as their interaction effects, are not significant. The alternative hypotheses assert that these effects are significant. The user seeks more sophisticated notation for expressing these hypotheses, specifically in terms of τ (tau) parameters, indicating that at least one effect is non-zero.

PREREQUISITES
  • Understanding of factorial design principles
  • Knowledge of hypothesis testing terminology
  • Familiarity with statistical notation for effects
  • Basic proficiency in statistical software for analysis
NEXT STEPS
  • Research how to formulate hypotheses in ANOVA for factorial designs
  • Learn about the implications of interaction effects in 2k factorial designs
  • Study statistical software options for conducting factorial analysis, such as R or SAS
  • Explore advanced statistical notation and its applications in hypothesis testing
USEFUL FOR

Statisticians, researchers in experimental design, and students studying hypothesis testing in factorial experiments.

Deathfish
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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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