10-400-13 Lecture Notes - Lecture 6: Confounding, Lincoln Near-Earth Asteroid Research, Analysis Of Variance
Statistics Summary
THEME 3:
- Variable: Any quantity or characteristic that is subject to change from one individual
to another OR from one sample to another.
- Probability law: Binomial, Poisson, Normal (continuous), Student (continuous)
a) Normal Law:
- Area = Probability
- We typically use:
1) P(-1.645 < z < 1.645) = 90%
2) P(-1.96 < z < 1.96) = 95%
3) P(-2.576 < z < 2.576 = 99%
b) General Normal Law:
find more resources at oneclass.com
find more resources at oneclass.com
Why is a normal law so useful?
Central Limit Theorem
Suppose variables X1, X2, X3, … Xn are identical and independent, then the sum of X1 +
X2 + X3 + … + Xn is a variable that converges to a normal law
Bigger samples lead to less variations from
c) Building a confidence interval (survival guide)
1- Conduct a survey / sample
2- Point estimate: find ‘x bar’
Hope ‘x bar’ is equal to
3- Find a margin of error
E = q (quantile obtained from
confidence level) * s/n
4- Confidence interval
(‘x bar’ – E , ‘x bar’ + E)
d) Proportions
Parameter: proportion of population
with a specific characteristic
Symbol: p
P hat is called the sample proportion
and will be used to estimate p.
1- Conduct a survey
2- Point estimator : “p hat”
Hope “p hat” is equal to p
3- Find margin of error:
find more resources at oneclass.com
find more resources at oneclass.com
4- Confidence Interval: “p hat” +/- E
** If we wish for more precision, we can find a bigger sample or reduce confidence level.
*** Level of significance is equal to 1%, 5% or 10%
THEME 4:
a) Hypothesis Testing
Test on one average, test on comparisons of 2 averages (independent population ->
distinct populations) or (paired test -> no real differences between populations), test on
one proportion, test on difference of 2 proportions
A hypothesis test always confronts 2 hypotheses (Complementary, exclusive)
1- Null Hypothesis = H0 -> “status quo”, “benefit of doubt”, “only rejected if proven
false”
H0 is assumed TRUE until evidence proves otherwise.
=, ≥, ≤
2- Alternative Hypothesis = H1 -> Is accepted only if H0 is rejected.
,, ,
So, if p-value is small enough, reject H0.
b) What does the p-value means?
Risk that rejecting H0 is a wrong decision!
c) Mechanics of hypothesis testing
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
Variable: any quantity or characteristic that is subject to change from one individual to another or from one sample to another. Probability law: binomial, poisson, normal (continuous), student (continuous: normal law: We typically use: p(-1. 645 < z < 1. 645) = 90, p(-1. 96 < z < 1. 96) = 95, p(-2. 576 < z < 2. 576 = 99, general normal law: Suppose variables x1, x2, x3, xn are identical and independent, then the sum of x1 + X2 + x3 + + xn is a variable that converges to a normal law. Bigger samples lead to less variations from : building a confidence interval (survival guide) E = q (quantile obtained from confidence level) * s/ n. 4- confidence interval ( x bar" e , x bar" + e: proportions. Parameter: proportion of population with a specific characteristic. P hat is called the sample proportion and will be used to estimate p.
