Population distribution of Y

Random variable Y

Population

The probability framework for statistical inference

Review of Statistical Theory

2. Estimation

3. Testing

4. Confidence Intervals

The probability framework for statistical inference

(a) Population, random variable, and distribution

(b) Moments of a distribution (mean, variance, standard deviation, covariance, correlation)

(c) Conditional distributions and conditional means

(d) Distribution of a sample of data drawn randomly from a population: Y B_1B,…, Y B _{n B}

(a) Population, random variable, and distribution

· The group or collection of all possible entities of interest (school districts)

· We will think of populations as infinitely large (¥ is an approximation to “very big”)

· Numerical summary of a random outcome (district average test score, district STR)

· The probabilities of different values of Y that occur in the population, for ex. Pr[ Y = 650] (when Y is discrete)

· or: The probabilities of sets of these values, for ex. Pr[640 £ Y £ 660] (when Y is continuous).

(b) Moments of a population distribution: mean, variance, standard deviation, covariance, correlation

mean = expected value (expectation) of Y

= E (Y)

= m B _{Y B}

= long-run average value of Y over repeated

realizations of Y

variance = E (Y – m B _{Y B})P^2P

=

= measure of the squared spread of the

distribution

standard deviation = = s B _{Y B}

Дата добавления: 2014-01-07