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Behavioral Objectives
Probability
Counting rules:
1.
The student will be able to use appropriate rules for determining number
of outcomes including number of permutations and combinations.
2.
The student will be able to relate the binomial expansion to the binomial
probability function.
Definitions:
3.
The student will be able to define and identify the following:
Sample space
Point in the sample space
Event
Probability of the event
Probability function
Joint event
Conditional probability
Independent events
Independent experiments
and Mutually independent experiments
Random Variables:
4.
The student will be able to define and identify random variables and
probability distribution functions of random variables including joint functions,
conditional functions, and the special cases of the discrete, uniform, binomial,
and hypergeometric functions.
Properties of Random Variables:
5.
The student will be able to state and use properties of random variables
from both definitions and theorems such as the expected value, variance,
covariance, expected value of a joint function, and covariance of independent
random variables.
6.
The student will be able to sum consecutive integers and squares of
integers.
Continuous Random Variables:
7.
The student will able to define and distinguish between discrete and
continuous random variables.
8.
The student will be able to define and compute normal and chi-squared
probabilities in appropriate situations.
9.
The student will be able to state and use the Central Limit Theorem.
Approaches to Probability:
10.
The student will be able to discuss relative merits of different approaches
to probability assignments.
Statistical Inference Objectives
Populations, Samples and Statistics:
11.
The student will be able to distinguish between Conover's two definitions
of random samples.
12.
The student will be able to ascertain measurement scales. i.e. nominal,
ordinal, interval and ratio.
13.
The student will be able to define and identify the following:
Statistics
Order statistics of rank k
Estimation:
Empirical distribution function
pth sample quantile
sample mean, variance and estimation.
Hypothesis testing:
Simple and composite hypothesis
Test statistics
Critical region
Type I and type II error
Power
Critical level
Properties of hypothesis tests:
Unbiasedness
Consistency
Efficiency
Relative efficiency
Nonparametric statistical methods
Binomial Objectives
14.
To review the binomial distribution.
15.
To discuss the binomial as a sampling distribution for the number of
successes or the proportion of successes in the sample.
16.
To present inferences (tests of hypothesis and confidence interval
estimates) about p, the parameter of the binomial random variable or
alternatively the population proportion of successes.
17.
To use the binomial distribution to make inferences about quantiles.
18.
To determine sample sizes required for tolerance limits.
19.
To present the sign test as a special application of the binomial test when
p = 0.5.
20.
To define the McNemar test for significance of change, the Cox and
Stuart test for trend and the test of correlation as variations of the sign
test.
Contingency Table Objectives
21.
To review Chi square tests for equal probabilities (or equivalently
independence) with 2 x 2 and r x c tables.
22.
To present the median test for the hypothesis of identical medians for c
populations.
23.
To present the extension of the median test to analysis of a randomized
block design.
24.
To define measures of dependence available in NCSS Crosstabs and/or
SAS PROC FREQ.
25.
To discuss implementation and advantages of the Chi square goodness
of fit test.
26.
To present Cochran's test for identical distributions with a randomized
block design and a dichotomous response variable.
27.
To introduce log linear models for three way and larger contingency
tables.
Rank Transform Objectives
28.
The student will be able to test hypotheses of identical distribution or
equal means with data from two or more independent samples using the
Mann-Whitney and the Kruskal-Wallis test.
29.
The student will be able to construct confidence intervals for the
difference in means between two random variables from the sampling
distributions.
30.
The student will know and be able to interpret the asymptotic relative
efficiency (ARE) of the Mann-Whitney test relative to the t test and the
median test.
31.
The student will know and be able to interpret the ARE of the KruskalWallis test relative to the F test for one way analysis of variance.
32.
The student will be able to test hypotheses of equal variance with the
squared ranked test.
33.
The student will be able to construct, interpret and compare Spearman's
Rho, Kendal's Tau and Kendal's partial correlation co-efficient as
measures of correlation.
34.
The student will be able to test hypotheses and construct confidence
intervals for the slope parameter in linear regression.
35.
The student will be able to estimate ranks using nonparametric monotone
regression.
36.
The student will be able to test hypotheses of identical distributions, equal
medians or equal means with data from paired samples using the
Wilcoxon signed ranked tests.
37.
The student will be able to construct confidence intervals for the median
difference.
38.
The student will know and be able to interpret the ARE of the Wilcoxon
test relative to the t test and the sign test.
39.
The student will be able to test appropriate hypotheses for dependent
samples using the Quade test and the Friedman test for both one and
multiple observations per experimental unit and the Durban test.
40.
The student will be able to test hypotheses of identical distributions with
independent samples using normal scores, random normal deviates or
expected normal score..
41.
The student will be able to use Fisher's randomization test for two
independent samples or for matched pairs.
42.
The student will be able to explain and support the strategy of
simultaneously using rank transform and raw data with common
"parametric" procedures.
Goodness of Fit Objectives
43.
The student will be able to test if the empirical distribution function of a
random sample agrees with a specified distribution function, using the
Kolgomorov goodness of fit test.
44.
The student will be able to construct a confidence band for the population
distribution function using the sampling distribution of the Kolgomorov test
statistic and the empirical distribution function.
45.
The student will be able to perform the goodness of fit tests for families of
distributions where parameters are estimates from data, using the Lillefors
test for the exponential distribution or the Shapiro-Wilks test for normality.
46.
The student will be able to test hypotheses of two identical distribution
functions using the Smirnov test or the Cramer-Von Mises Two Sample
test.
47.
The student will be able to perform tests on several independent samples
using the Birnbaum-Hall test, the One-Sided k-sample Smirnov test or the
Two-Sided k-sample Smirnov test.