Lecture 18 (Week 10, Monday)

Sampling Distributions

how extreme of an observed b₁ would cause us to reject the null model?
arrange the sampling distribution of b₁ for SE=4 to represent the empty model
what observed b₁s would lead you to reject the empty model
- empty model: centered at zero (β₁=0)
changing the sampling distribution of b₁ to SE=3 and 1 to represent the empty model
- if in a study you observe b₁ = -6, what would you conclude?
- how would changing SE affect this?
- changing the SE changes the cutoff points
if we reject the null model with a larger standard error, do we also reject it if the standard error were smaller?
- yes
- if SE gets smaller, assuming same b₁, the peak gets lower
if we fail to reject the null model with a larger standard error, would we also fail to reject it if the standard error were smaller?
which of these would affect the width of a confidence interval?
- level of confidence, sample size, standard error (width of sampling distribution), standard deviation of the DGP

The null model can always be rejected if the sample size is large enough.

unless your b₁ is exactly zero, as your sample size gets bigger, you can always reject the null hypothesis
why do we even do research then?
just because you get p<.05 doesn't mean you've found something significant
how big of a difference do you want to detect?