statistical-inference.org

Introduction to Statistical Inference

Title slide

(org-show-animate '("Quantitative Methods, Part-II" "Introduction to Statistical Inference" "Vikas Rawal" "Prachi Bansal" "" "" ""))

Sampling Distributions

Sampling Distributions

Sampling Distributions

• $Standard.error = \frac{σ}{\sqrt{n}}$

Variable	Value
Standard deviation of population ($σ$)	130
Standard errors of samples of size
5	58
20	29
50	18
200	9

Introduction to Hypothesis Testing

Transforming the Distribution to Standard Normal

Distribution of sample mean with unknown population variance

T Test for means

Testing if the mean is different from a specified value (say zero)

$H₀: μ = 0$

$H_a: μ ≠ 0$

readRDS("plfsdata/plfsacjdata.rds")->worker
worker$standardwage->worker$wage
worker->t9
t.test(t9$wage)

Testing equality of means

$H₀: μ_women = μ_men$

$H_a: μ_women ≠ μ_men$

subset(worker,sex!=3)->t9
factor(t9$sex)->t9$sex
t.test(wage~sex,data=t9)

Z Test for equality of proportions

$H₀: p_women = p_men$

$H_a: p_women ≠ p_men$

subset(worker,sex!=3)->t9
as.numeric(t9$gen_edu_level)->t9$gen_edu_level
factor(t9$sex)->t9$sex
t9[gen_edu_level>=8,.(schooled=length(fsu)),.(sex)]->a
t9[,.(all=length(fsu)),.(sex)]->b
prop.test(a$schooled,b$all)

F Test for equality of variances

$H₀: σ_women² = σ_men²$

$H_a: σ_women² ≠ σ_men²$

subset(worker,sex!=3)->t9
factor(t9$sex)->t9$sex
var.test(wage~sex,data=t9)