A New View of Statistics

© 2001 Will G Hopkins

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CONTENTS


Items on the same line or separated by dots · are on the same page.
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About These Pages
Summarizing Data
    Simple Statistics & Effect Statistics

        Basics

              

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
Two-Way ANOVA
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
Quiz
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Last updated 14 June 00