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Summary Review of the course advanced statistics. $7.05   Add to cart

Summary

Summary Review of the course advanced statistics.

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This is the summary of the content needed for the course advanced statistics.

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  • July 28, 2022
  • 15
  • 2021/2022
  • Summary
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Advanced statistics




1. Inference : Drawing conclusion about a population based on a limited set of
observation
- interested in the mean response of the population : μ = μy
- interested in the mean ≠ in the pop (paired obs) d=x-y

, - interested in the mean ≠ of the response (2 independent samples) μ1 - μ2
Point estimator :
- estimator (estimate is the outcome of the estimator in the sample) : estimate±
tdf(α/2)* se
- se : measure of how certain we can be about the estimate




*P-value : 2 sided (LPV = 2sided/2; RPV = 1-LPV = 1-2sided/2) : see table 2 (t-test)
CI : if 0 in the interval the hypothesis Ho x=0 might be valid (should not be rejected)

2. Finding Required sample size
P(Type I error) < a (typically 0.05) (rejecting Ho when it is true)
P(type II error β ) depends on (not rejecting Ho when it is false) :
- α , σ , true parameter value, sample size n, Δ (≠ between the true mean and the
Ho is)

a. One sample situation


CI : find the min n using E Find min n using ≠ between ȳ and μy
*Error margin ≤ E Testing Ho : μ = Vo at size α
*W = 2E ⇒ Want to reject Ho with proba π=1−β (the
Δ = V1 – V0 (≠ between μ and μo) power) when in reality μ=V 1




b. Paired obs


CI Testing Ho : μd = Vo at size α
Δ = V1 – V0 (≠ between μ and Vo) ⇒ Want to reject Ho with proba
π=1−β (the power) when in reality μ d=V 1




c. 2 independent samples

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