How do you formulate null and alternative hypotheses?

easy

Answer

$({\mu}_{A}\; = \;{\mu}_{B}, \;{\beta}\; = \;0, \;\mathrm{treatment}\;\mathrm{has}\;\mathrm{no}\;\mathrm{impact})$
$({\mu}_{A}\; \ne \;{\mu}_{B}\;\mathrm{two} - \mathrm{sided}, \;\mathrm{or}\;{\mu}_{A}\; > \;{\mu}_{B}\;\mathrm{one} - \mathrm{sided})$
$One-sided tests are more powerful but only appropriate when you commit ex ante to the direction.$
$Rule: define H0 / H1 before seeing the data.$
$Post-hoc directional testing inflates type I error.$

Check yourself — multiple choice

H0 = what we suspect
H0: no-effect; H1: suspected direction (two-sided or one-sided committed ex ante); post-hoc direction inflates type I
H1 = mean = 0
Same thing

H0: no-effect; H1: alternative; commit direction before data.

#hypothesis-testing

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