FInal STA

standard error of statistic

standard error of statistic

Standard deviation of sampling distribution

Big Three of Causality

1. When X changed, Y also changed. If X changes and Y doesn't change, then we cannot assert that X causes Y.

2. X happened before Y. If X happens after Y then X cannot cause Y.

3. Nothing else besides X changed systematically.

confidence intervals for comparing group proportions

prop.test((x,x)(n,n)

mean comparison of groups

t.test(response~group, data=df)

Power for tests of difference of Means

power.t.test(n=100, delta=15, sd=30, sig.level = 0.05)

Power for difference in Proportion

power.prop.test(n=200, p1=0.1, p2=0.15, sig.level = 0.05)

How does power of the test affect sample size

increase, increase

Interpret Bayesian Credible Interval

The probability that the true success rate is between qbeta(0.975, a, b) and qbeta(0.025, a, b) is .95

Two forms of randomness required to ensure valid statistical results from an experiment

random selection and random assignment

ANOVA to analyze A/B/n tests

numerical, difference of means

Chi-squared test for A/B/n

binary, proportions

Why do we need to use Tukey HSD test

it controls the type I error rate

Probability of obtaining at least one type I error

1 - (1- alpha)^(number of tests performed)

Basic Structure of a Randomized Complete Block Design

randomly assign order, every block has one replicate of the experiment (full repeat of an experiment)

latin squares design

each treatment appears exactly once in each row and each column. The rows and columns each represent a blocking factor; the treatment is represented in the square.

How does replication affect the mean square error

gives a better estimate by providing more degrees of freedom

Why is replication important

estimate for the error and perform inference

Interaction

The effect of A on the response depends on the level of factor B

Main effect

2 * coefficient

Common cause variation

natural or background or random variability

in control

only has common cause variation

assignable cause variation

Other kinds of variability that represent unacceptable level of process performance

basic framework of control chart

normal distribution; CL, UCL, LCL

DMAIC

Define Measure Analyze Improve Control

How to assess p chart for assignable cause

qcc(df$(response), df$size, type="p")

if the fraction nonconforming (defective) in a population is not in statistical control (between UCL and LCL)

How to assess Xbar chart for assignable cause

qcc(df, type="xbar")

is sample to sample variability within the control limits

How to assess R chart for assignable cause

qcc(df[,2:6], type="R")

is within subgroup variation stable