Topics or Units of Study
1.
Exploring Data: Observing patterns and
departures from patterns
A.
Interpreting graphical displays of distributions of univariate
data (dot plot, stemplot, histogram, cumulative frequency plot)
(1) Center and spread
(2) Clusters and gaps
(3) Outliers and other unusual features
(4) Shape
B.
Summarizing distributions of univariate data
(1) Measuring center: median, mean
(2) Measuring spread: range, interquartile range, standard
deviation
(3) Measuring position: quartiles, percentiles, standardized scores
(z-scores)
(4) Using boxplots
(5) The effect of changing units
on summary measures
C. Comparing distributions of univariate data (dotplots, back-to-back stemplots, parallel boxplots)
(1) Comparing center and spread: within group, between group variation
(2) Comparing clusters and gaps
(3) Comparing outliers and other
unusual features
(4) Comparing shapes
D.
Exploring bivariate data
(1) Analyzing patterns in
scatterplots
(2) Correlation and linearity
(3) Least-squares regression line
(4) Residual plots, outliers, and
influential points
(5) Transformations to achieve
linearity: logarithmic and power transformations
E.
Exploring categorical data: frequency tables
(1) Marginal and joint
frequencies for two-way tables
(2) Conditional relative
frequencies and association
2.
Planning a Study: Deciding what and how
to measure
A.
Overview of methods of data collection
(1) Census
(2) Sample survey
(3) Experiment
(4) Observational study
B.
Planning and conducting surveys
(1) Characteristics
of a well-designed and well-conducted survey
(2)
Populations, samples, and random selection
(3) Sources of bias in surveys
(4) Simple random sampling
(5) Stratified random sampling
C.
Planning and conducting experiments
(1) Characteristics of a
well-designed and well-conducted experiment
(2) Treatments, control groups, experimental
units, random assignments, and
replication
(3) Sources of bias and
confounding, including placebo effect and blinding
(4) Completely randomized design
(5) Randomized block design, including matched pairs design
D.
Generalizability of results from observational studies, experimental studies,
and surveys
3.
Anticipating Patterns: Producing models
using probability theory and simulation
A.
Probability as relative frequency
(1) "Law of large
numbers" concept
(2) Addition rule, multiplication
rule, conditional probability, and independence
(3) Discrete random variables and
their probability distributions, including binomial
(4) Simulation of probability
distributions, including binomial and geometric
(5) Mean (expected value) and
standard deviation of a random variable, and linear transformation of a random
variable
B.
Combining independent random variables
(1) Notion of independence versus
dependence
(2) Mean and standard deviation
of sums and differences of independent random variables
C. The
normal distribution
(1) Properties of the normal
distribution
(2) Using tables of the normal
distribution
(3) The normal distribution as a
model for measurements
D.
Sampling distributions
(1) Sampling distribution of a
sample proportion
(2) Sampling distribution of a
sample mean
(3) Central Limit Theorem
(4) Sampling distribution of a difference
between two independent sample proportion
(5) Sampling distribution of a difference
between two independent sample means
(6) Simulation of sampling
distributions
4.
Statistical Inference: Confirming
models
A.
Confidence intervals
(1) The meaning of a confidence
interval
(2) Large sample confidence
interval for a proportion
(3) Large sample confidence
interval for a mean
(4) Large sample confidence
interval for a difference between two proportions
(5)
Large sample confidence interval for a difference between two means (unpaired
and paired)
B.
Tests of significance
(1) Logic of significance tests,
null and alternative hypotheses; p-values; one-
and two-sided tests; concepts of Type I and Type II errors;
concept of power
(2) Large sample test for a
proportion
(3) Large sample test for a mean
(4) Large sample test for a
difference between two proportions
(5) Large sample test for a
difference between two means (unpaired and paired)
(6) Chi-square test for goodness
of fit, homogeneity of proportions, and
independence (one- and two-way tables)
C.
Special case of normally distributed data
(1) t-distribution
(2) Single sample t procedures
(3) Two sample (independent and
matched pairs) t procedures
(4) Inference for the slope of
least-squares regression line