Statistical Methods

Outline of Elementary Statistical Methods Topics

Introduction to the Study of Statistics [How to pass a stats class]

I.  Basic Math Review

II.  Defining Statistics and Statistical Principles

• Populations and Samples

• Parameters and Statistics

• Descriptive and Inferential Methods

• Sampling and Sampling Error

• Variables and Constants

• The Correlational Method

• The Experimental Method

• Independent and Dependent Variables

• The Quasi-experimental Method

• Scales of Measurement

  • Nominal Scale

  • Ordinal Scale

  • Interval Scale

  • Ratio Scale

• Discrete and Continuous Variables

• Statistical Notation

• Order of Operations

III.  Frequency Distributions

• Defining a Frequency Distribution

• Frequency Distribution Tables [Cheat Sheet]

• Proportions and Percentages  [Cheat Sheet]

• Grouped Frequency Distribution Tables

• Frequency Distribution Graphs

  • Histograms and Bar Graphs

  • Frequency Distribution Polygons

• Relative Frequency Distributions and the "Smooth Curve"

• The Shape of Frequency Distributions

• How to Lie with Graphs

IV.  Central Tendency

• Defining Central Tendency

• The Mean  [Cheat Sheet]

  • Weighted Means

  • Characteristics of the Mean

• The Median  [Cheat Sheet]

• The Mode  [Cheat Sheet]

• Choosing the Proper Measure of Central Tendency

• Reporting Central Tendency

• Central Tendency and the Shape of Distributions

V.  Variability

• Defining Variability

• The Range [Cheat Sheet]

• Interquartile Range

• Semi-interquartile range

• Standard Deviation & Variance for Populations

• Standard Deviation and Variance for Samples [Cheat Sheet]

• Variability & Degrees of Freedom

• Bias

• Reporting Variability

VI.  z-Scores

• Overview of z-Scores

• z-Scores and Location in a Distribution

• Computing z-scores [Cheat Sheet]

• Determining a Raw Score from a z-Score [Cheat Sheet]

• Standardizing Distributions with z-Scores

• Making Comparisons with z-Scores

• Other Standard Distributions [Cheat Sheet]

VII.  Probability

• Defining Probability

• The Role of Probability in Inferential Statistics

• Random  Sampling

• Probability and the Normal Distribution

• The z-Score Table

• Probabilities, z-Scores, and Area Under the Normal Curve

  • Finding Probabilities for Specific z-Scores

  • Finding z-Score Values for Specific Proportions

  • Finding Probabilities Between Two Scores

  • Finding Scores Corresponding to Specific Probabilities

VIII.  Probability and Samples

• Samples and Sampling Error

• The Distribution of Sample Means

• The Central Limit Theorem

• The Shape of the Distribution of Sample Means

• The Mean of the Distribution of Sample Means

• The Standard Error of the Mean [Cheat Sheet]

• The Law of Large Numbers

• Population standard Deviation

• z-Scores for Sample Means [Cheat Sheet]

• Standard Error in Statistical Inference

• Reporting Standard Error

IX.  Hypothesis Testing

• Logic (the "big idea")

• Statement of the Hypothesis

• The Decision Criteria

• Computing the Sample Statistic

• Making a Statistical Decision

• What Did My Test Prove? Nothing.

•  Error in Hypothesis Testing

  • Type I Error

  • Type II Error

• Selecting an Alpha Level

• Reporting the Results of Statistical Tests

• Assumptions

• Directional Tests

• Hypotheses for Directional Tests

• The Critical Region in Directional Tests

• Which One Do I Use?

• Putting It All Together: A Review of Hypothesis Testing

X.  The t-Statistic [For Single Samples]

• Overview

• Why Do We Have Different Tests to Do the Same Thing?

• How is t Different from z?

  • Degrees of Freedom

  • The t Distribution

• Hypothesis Testing with the t-Statistic [Cheat Sheet]

  • Directional Testing with the t-Statistic

• Assumptions

XI.  The t-Test for Two Independent Samples

• Overview

• Pooled Variance

• Degrees of Freedom

• Computation of the t-Statistic for Independent Samples

• Reporting the t-Statistic for Independent Samples

• Power and Effect Size

• Assumptions

XII.  The t-Test for Two Related Samples

• Overview

• Appropriate Experimental Designs

• Advantages and Disadvantages

• Hypothesis Testing with the Dependent Samples t-Test [Cheat Sheet]

• Power and Effect Size

• Assumptions

XIII.  Analysis of Variance [ANOVA]

• Overview

• Type I Errors and Multiple Tests

• Hypotheses for ANOVA

• Partitioning Variance

• ANOVA Notation Conventions

• Computing the Test Statistic [Cheat Sheet]

• The F Distribution

• Reporting ANOVA Results

• Power and Effect Size

• Assumptions

• Post Hoc Tests

  • Planned v. Unplanned Comparisons

  • Tukey's HSD Test [Cheat Sheet]

  • Scheffé Test [Cheat Sheet]

XIV.  Correlation and Regression

• Overview

• Computation of the Pearson Correlation [Cheat Sheet]

• Interpretation of the Pearson Correlation

• Uses of Correlation

• Correlation and Causation

• Outliers

• Coefficient of Determination

• Hypothesis Testing with the Pearson Correlation

• Reporting Correlations

• Assumptions

• The Spearman Correlation

  • Logic

  • Calculation of the Spearman Correlation [Cheat Sheet]

• Introduction to Regression

  • Linear Equations

  • The Least Squares Solution

XV.  The Chi-Square Statistic

• Parametric and Nonparametric Tests

• The Goodness of Fit Test

  • Definition

  • Hypothesis

  • Computation [Cheat Sheet]

  • The Chi-Square Distribution

  • Power and Effect Size

• The Test for Independence

  • Hypotheses

  • Computation of Chi-square for Independence [Cheat Sheet]

  • Power and Effect Size

  • Assumptions

XVI.  Introduction to Advanced ANOVA Designs

• Overview

• Repeated Measures Designs

  • The Logic of the Related Measures ANOVA

  • Power and Effect Size

• Two-factor Designs

  • The Logic of Two Factor Designs

  • Power and Effect Size

• Mixed Designs

  • Logic of Mixed Designs

  • Power and Effect Size in Mixed Designs

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