I . Exploring Data: Describing patterns and departures from patterns . . .. . . . . . . . . . . . . . .  . . . . . . . . . . . . . (20%–30%)
    Exploratory analysis of data makes use of graphical and numerical techniques to study patterns and

    departures from patterns. Emphasis should be placed on interpreting information from graphical and

    numerical displays & summaries.
    A . Constructing and interpreting graphical displays of distributions of univariate data (dotplot,

           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

            1 . Frequency tables and bar charts

            2 . Marginal and joint frequencies for two-way tables

            3 . Conditional relative frequencies and association

            4 . Comparing distributions using bar charts

 

II . Sampling and Experimentation: Planning and conducting a study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (10%–15%)

       Data must be collected according to a well-developed plan if valid information on a conjecture

       is to be obtained. This plan includes clarifying the question and deciding upon a method of data

       collection and analysis.

     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 sampling and surveys

            4 . Sampling methods, including simple random sampling, stratified random sampling and

                      cluster 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 and types of conclusions that can be drawn from observational

                studies, experiments and surveys

 

III . Anticipating Patterns: Exploring random phenomena using probability and simulation . . . . . . . . . . . . . (20%–30%)

        Probability is the tool used for anticipating what the distribution of data should look like under

        a given model.
     A . Probability
            1 . Interpreting probability, including long-run relative frequency interpretation
            2 . “Law of Large Numbers” concept
            3 . Addition rule, multiplication rule, conditional probability and independence
            4 . Discrete random variables and their probability distributions, including binomial and

                      geometric 
            5 . Simulation of random behavior and probability distributions
            6 . 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 for 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 proportions
            5 . Sampling distribution of a difference between two independent sample means
            6 . Simulation of sampling distributions
            7 . t-distribution
            8 . Chi-square distribution

 

IV . Statistical Inference: Estimating population parameters and testing hypotheses . . . . . . . . . . . . . . . . . . (30%–40%)
        Statistical inference guides the selection of appropriate models.
     A . Estimation (point estimators and confidence intervals)
            1 . Estimating population parameters and margins of error
            2 . Properties of point estimators, including unbiasedness and variability
            3 . Logic of confidence intervals, meaning of confidence level and confidence 

                  intervals, and properties of confidence intervals
            4 . Large sample confidence interval for a proportion
            5 . Large sample confidence interval for a difference between two proportions

            6 . Confidence interval for a mean
            7 . Confidence interval for a difference between two means (unpaired and paired)
            8 . Confidence interval for the slope of a least-squares regression line
     B . Tests of significance
            1 . Logic of significance testing, 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 difference between two proportions
            4 . Test for a mean
            5 . 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)
           7 . Test for the slope of a least-squares regression line