Lecture 16 (Week 8, Wednesday)

Analyzing ScienceData: A practical application of sampling distributions

Which distribution did b₁ come from? Could it have come from a DGP with a β₁ = 0?

Four Ways of Creating Sampling Distributionos

simulation
randomization
bootstrapping
mathematical models

Let's use simulation to answer this question.

to simulate: N = 80, 40 in each group
assume sample come from normal DGP, mean = Grand Mean; SD = b₀, β₁ = 0

Distribution of Games: Assume Normal?

M = 3.83, SD = 1.52

Simulate a Single Random Sample

if I make a histogram of Games.sim, will it be a sampling distribution?
- no
- sampling statistic: b₁
- we only have one b₁, one sample
- we would need 1,000 b₁s to have a sampling distribution

Simulate sampling distribution of b₁

what will be the shape of this sampling distribution? what will be the center? what will be the spread?
- shape: normal
- center: 0
- spread: you don't know - this is why we're making the sampling distribution
we make sampling distributions because we don't knoow the spread and want to know the probability
will the mean of this sampling distribution tell us the mean of the DGP?
- yes, it should be centered at the mean of the DGP
- no, it won't necessarily be centered at the mean of the DGP