Stat 502 Concepts and Vocabulary:
induction
experimental units
observational units
Replication
Randomization
Blocking
completely randomized design (CRD)
randomized blocks design (RBD)
randomized complete block design (RCBD)
p-value
randomization distribution
empirical distribution
sampling distribution
null distribution
type I error
type II error
level- test
power
sampling model
t-statistic/t-distribution
chi-squared distribution
F-distribution
two-sided test
confidence interval
acceptance region
rejection region
coverage probability
noncentrality
qq-plot (normal probability plot)
paired design
paired comparisons
pairwise error rate
experimental error rate
multiple comparisons
treatment means model
treatment effects model
various sums of squares and mean squares
expected mean square
orthogonal decompositions in the anova
balanced/unbalanced designs
standard error
contrast
orthogonal contrasts
multiple comparisons
Bonferroni
Fisher’s LSD
Scheffe
Tukey
residuals
heteroscedasticity
mean-variance relationship
Levene’s test
Bartlett’s test
variance stabilizing transformations
power transformations
interpretation of models on transformed scales, especially for log transform
Box-Cox transformation
factorial design
additive and multiplicative models
interaction effects
balanced vs unbalanced designs
Review Questions: Answer each with a few sentences
(a) What are the benefits of randomization?
(b) What is a test statistic?
(c) What is a null distribution?
(d) What are two ways of deriving a null distribution?
(e) What is a p-value? What does it measure?
(f) What is a hypothesis test?
(g) What is a confidence interval? What is it useful for?
(h) What is an ANOVA table describing?
(i) Discuss the connection between the t-statistic and the t-distribution.
(j) For comparing two groups, what is the difference between a paired sample design and a
CRD? What are the standard test procedures you perform in each case?
(k) Describe how the following are used together to make a statistical decision: Null and
alternative hypotheses, a test statistic, a null distribution, and a p-value. (You may
need more than a few sentences for this one, maybe make a flowchart).
Midterm exam, Nov 6:
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understand all the above concepts and vocabulary
you will be presented with computer output and be asked to interpret it.
Simple calculations may be required; you may bring a hand calculator, but it is
not necessary as approximate hand computations of products and ratios will
suffice.
you might be asked to demonstrate that you understand a certain result or
calculation (probability of a type I error in a particular circumstance, noncentrality
for a simple test, orthogonality, randomization procedure for a particular design).
This is a “closed-book” exam; no notes.
“Part II”
marginal means vs least squares means for unbalanced anova
interaction plot
sequential sums of squares and F-tests
Analysis of covariance
test of equal slopes
design issues: blocking vs analysis of covariance
factor effects in 2k factorial designs
QQ (Daniel) plots for factorial designs
blocked and fractional factorial designs
aliasing/confounding of higher order interactions
generators and defining relation for blocked factorial design
nested design
split-plot design
repeated measures design
random effects model or mixed effects model
variance component