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
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
