Lecture 1 highlights

Introduction: Discussion of syllabus, course website, hypothetical data examples

Chapter 0

Scales of measurement (nominal, ordinal, interval)

Random variable (r.v.): a variable whose value is a numerical outcome of a random phenomenon

Discrete random variable: a random variable that only assumes a finite (or countably infinite) number of values

Probability distribution: the set of values that a r.v. can assume, along with the associated probabilities

Cumulative distribution function (CDF): FX(x) = P(X <= x)

Binomial distribution: applicable for a process where a) only 2 outcomes, b) constant success prob., c) independent trials

Continuous random variable: a random variable that can assume a continuous range of values

Probability density function; cumulative distribution function

Normal distribution, standard normal distribution, zp percentile values

Central limit theorem: Asymptotically, the sampling distribution of the sample mean is normal with mean mu and std dev sigma/sqrt(n)

location-scale distributions: f(x) = 1/b h( (x-a)/b )

Other continuous distributions: Uniform, exponential, double exponential (Laplace), Cauchy (note book misprint)

Characteristics of a distribution: skewness, tail weight (kurtosis)

Population; sample; parameter; statistic; point estimate

Interval estimate: Example for normal data

Interpretation of an interval estimate

Hypothesis tests; null hypothesis; alternative hypothesis; test statistic;

Significance level = P(reject H0 when it is true); Power( ) = P(reject H0 when it is false)

Example for normal data

Parametric vs. nonparametric methods

Classes of nonparametric methods:

i) Binomial

ii) Permutation methods: Under H0, all permutations of the observations between groups are equally likely.  Generally used along with ranks or scores.

iii) Bootstrap methods: Mimic sampling from the population by taking samples with replication from the data.

iv) Smoothing methods: Using local averaging, for example.

v) Non-least squares methods: L1 estimation, M estimation, etc.