A New View of Statistics

© 2001 Will G Hopkins

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Summarizing Data
    Simple Statistics & Effect Statistics



Data and Variables · Frequency Distributions · Probability · Statistics

        Simple Statistics


The Middle · The Spread
Standard Deviation
Root Mean Square Error (RMSE)
Standard Error of the Estimate (SEE)
Percentile Ranges

        Effect Statistics


Difference in Means
Correlation Coefficient
Relative Frequency
A Scale of Magnitudes

    Dimension Reduction
Principal Components · Factor Analysis · Cluster Analysis
    Precision of Measurement
        Measures of Reliability


Shift in the Mean · Within-Subject Variation ·  Retest Correlation · Kappa Coefficient · Alpha Reliability

        Applications of Reliability


Sample Size for an Experiment · Individual Responses · Assessing an Individual · Spreadsheet for Assessing an Individual · Comparing Reliability of Measures · Sample Sizes for Reliability Studies

        Reliability: Calculations


Introduction ·  Two Trials ·  Three or More Trials · Non-Uniform Error · Modeling Variances for Reliability · Biased Estimated of Reliability · Spreadsheet for Calculating Reliability

        Measures of Validity


Introduction · Estimation Equation · Typical Error of Estimate · Correlation · Nominal Variables · Spreadsheet for Calculating Validity

        Applications of Validity


Sample Size for a Cross-sectional Study · Assessing an Individual · Comparing Validity of Measures · Validity for Monitoring Changes · Sample Size for Validity Studies

       How Many Digits?
Mean ± SD or Mean ± SEM?
Generalizing to a Population
    Confidence Limits

        Generalizing via Confidence Limits


Introduction · An Example · Effect of Sample Size on Confidence Interval · Confidence Interval and Statistical Significance · A Spreadsheet for Confidence Intervals · Bootstrapping · Meta-Analysis · Bayesian Analysis

        P Values and Statistical Significance


What is a P Value? · Test Statistics · P Values and Confidence Intervals · Confidence Limits from a P Value · One Tail or Two? · Why 0.05? · Hypothesis Testing · Using P Values

        Getting It Wrong


Type I Error · Type II Error · Bias · Slideshow

    Statistical Models
What is a Model?
Simple Models and Tests


Linear Regression
T Test and One-Way ANOVA
Contingency Table
Categorical Modeling

        Models: Important Details


How a Stats Program Fits a Model · Parameters · Residuals · Goodness of Fit · Calculation of Confidence Limits · Independence of Observations · Normality of Sampling Distribution · Uniformity of Residuals · Uniformity of Residuals in Complex Models
Log Transformation for Better Fits · Percent Effects · More Examples
Non-Parametric Models: Rank Transformation
Ordinal Dependent Variables
Counts and Proportions as Dependent Variables · Binomial and Poisson Regression · Square-root and Arcsine-root Transformation
Linear and Non-Linear Models

        Complex Models


More Than One Independent Variable · Controlling for Something · Interactions
Analysis of Covariance (ANCOVA)
Multiple Linear Regression · Stepwise Regression
Polynomial Regression
More Than One Dependent Variable · Variables of Uncertain Status

        Repeated-Measures ANOVA


Paired T Test: Two trials and no between-subjects effect
Two trials plus a between-subjects effect · Simple crossovers
Three or more trials and no between-subjects effect
Three or more trials plus a between-subjects effect · Multiple crossovers
Other Repeated-Measures Models
Proc Mixed for Repeated Measures
Regression to the Mean

    Estimating Sample Size
The Right Number of Subjects
What Determines Sample Size
Sample Size Based on Confidence Limits
Sample Size "On The Fly"
On the Fly for Correlations
On the Fly for Differences Between Means
On the Fly for Differences Between Frequencies
        On the Fly: Miscellaneous


Other Designs · On the Fly for the Ethical Committee · Do NOT Fly with Statistical Significance · Spreadsheet

        Simulation for Sample Size


Steps in the Process · Cross-Sectional Study · Longitudinal Study

Summary: The Most Important Points
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Last updated 14 June 00