Estimation of the Variance of a Distribution
Suppose we assume that X1, , Xn ~ N (mu, sigma^2). Then, S^2 ~ sigma^2 Chi-sq (n-1) / (n-1).
Estimation for the Binomial Distribution
X is Binomial RV with parameters n and p. An UE of p is given by the sample

Treatment of Outliers
Extreme Studentized Deviate (ESD statistic)= max i=1,n |xi-x-bar|/s.
ESD Single-Outlier Procedure: Suppose we have a sample x1, xn ~ N (,^2), but feel that
there may be some outliers present. To test the hypothesis, Ho: that no outli

ROC curve
In some instances, a test provides several categories of response rather than simply test positive or test
negative. In other instances, the results of the test are reported as a continuous variable. In either case,
designation of a cutoff point

Regression and Correlation Methods
Residual or residual component, yi - yi-hat
Regression component, yi-hat - y-bar
Yi y-bar = residual component + regression component
Generally speaking, a good-fitting regression line will have regression components lar

Hypothesis Testing: Categorical Data
Two-Sample Test for Binomial Proportions (Normal-Theory Test): To test the hypothesis Ho:
p1=p2, H1: p1p2, where the proportions are obtained from two independent samples, use the
following procedure:
Z= [|p1^hat p2^h

Nonparametric Method
So far, we have assumed the data come from some underlying distribution, such as the normal
or binomial distribution, whose general form was assumed know. Methods of estimation and
hypothesis testing have been based on these assumptio

Hypothesis Testing:
Type I error: the probability of rejecting the null hypothesis when Ho is true.
Type II error: the probability of accepting the null hypothesis when H1 is true.
The probability of a type I error is usually denoted by and is commonly re

Multisample Inference
ANOVA (One-Way Analysis of Variance) - Fixed-Effects Model
yij = + i + eij, where eij is normally distributed with mean 0 and variance 2
Interpretation:
represents the underlying mean of all groups taken together
i represents the

Normal Approximation to the Binomial Distribution
If X is a binomial random variable with parameters n and p, then Pr(a X b) is approximated by the
area under an N(np, npq) curve from (a-1/2) to (b+1/2). This rule implies that for the special case a=b,
th

Randomized Clinical Trials
A randomized clinical trial (RCT) is a type of research design for comparing different treatments, in
which the assignment of treatments to patients is by some random mechanism. The process of assigning
treatments to patients is