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What stat?

Simulation & Gaming:
An Interdisciplinary Journal



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From  http://davidmlane.com/hyperstat/

HyperStat Online Statistics Textbook

RVLS Home | Glossary | Free Statistical Analysis Tools | Instructional Demos | Exercises and Problems | Statistics Help

  1. Introduction to Statistics
  2. Describing Univariate Data
  3. Describing Bivariate Data
  4. Introduction to Probability
  5. Normal Distribution
  6. Sampling Distributions
  7. Point Estimation
  8. Confidence Intervals
  9. The Logic of Hypothesis Testing
  10. Testing Hypotheses with Standard Errors
  11. Power
  12. Introduction to Between-Subjects ANOVA
  13. Factorial Between-Subjects ANOVA
  14. Within-Subjects/Repeated Measures ANOVA
  15. Prediction
  16. Chi Square
  17. Distribution-Free Tests
  18. Measuring Effect Size

© 1993-2005 David M. Lane,  Associate Professor of Psychology, Statistics, and Management at Rice University

From   http://onlinestatbook.com

Online Statistics: An Interactive Multimedia Course of Study

Online Statistics: A Multimedia Course of Study is an introductory-level statistics book. The material is presented both as a standard textbook and as a multimedia presentation. The book features interactive demonstrations and simulations, case studies, and an analysis lab.

Table of Contents

  1. Introduction
  2. Graphing Distributions
  3. Summarizing Distributions
  4. Describing Bivariate Data
  5. Probability
  6. Normal Distributions
  7. Sampling Distributions
  8. Estimation
  9. Logic of Hypothesis Testing
  10. Testing Means
  11. Power
  12. Prediction
  13. ANOVA
  14. Chi Square
  15. Case Studies
  16. Calculators
  17. Glossary

Full Table of Contents

Title Page
List of Simulations and Demonstrations

  1. Introduction
    1. What are Statistics?
    2. Importance of Statistics
    3. Descriptive Statistics
    4. Inferential Statistics
    5. Sampling Demonstration
    6. Variables
    7. Percentiles
    8. Measurement
      1. Levels of Measurement
      2. Measurement Demonstration
      3. Basics of Data Collection
    9. Distributions
    10. Summation Notation
    11. Linear Transformations
    12. Exercises
    13. PDF Files (in .zip archive)
  2. Graphing Distributions
    1. Introduction
    2. Qualitative Variables
    3. Quantitative Variables
      1. Stem and Leaf Displays
      2. Histograms
      3. Frequency Polygons
      4. Box Plots
      5. Box Plot Demonstration
      6. Bar Charts
      7. Line Graphs
    4. Exercises
    5. PDF Files (in .zip archive)
  3. Summarizing Distributions
    1. Central Tendency
      1. What is Central Tendency
      2. Measures of Central Tendency
      3. Balance Scale Simulation
      4. Absolute Difference Simulation
      5. Squared Differences Simulation
      6. Median and Mean
      7. Mean and Median Simulation
      8. Additional Measures
      9. Comparing measures
    2. Variability
      1. Measures of Variability
      2. Variability Demo
      3. Estimating Variance Simulation
    3. Shape
    4. Comparing Distributions Demo
    5. Effects of Transformations
    6. Variance Sum Law I
    7. Exercises
    8. PDF Files (in .zip archive)
  4. Describing Bivariate Data
    1. Introduction to Bivariate Data
    2. Values of the Pearson Correlation
    3. Guessing Correlations Simulation
    4. Properties of Pearson's r
    5. Computing Pearson's r
    6. Restriction of Range Demo
    7. Variance Sum Law II
    8. Exercises
    9. PDF Files (in .zip archive)

  5. Probability
    1. Introduction
    2. Basic Concepts
    3. Conditional Probability Demo
    4. Gamblers Fallacy Simulation
    5. Birthday Demonstration
    6. Binomial Distribution
    7. Binomial Demonstration
    8. Base Rates
    9. Bayes' Theorem Demonstration
    10. Monty Hall Problem Demonstration
    11. Exercises
    12. PDF Files (in .zip archive)
  6. Normal Distributions
    1. Introduction
    2. History
    3. Areas of Normal Distributions
    4. Varieties of Normal Distribution Demo
    5. Standard Normal
    6. Normal Approximation to the Binomial
    7. Normal Approximation Demo
    8. Exercises
    9. PDF Files (in .zip archive)
  7. Sampling Distributions
    1. Introduction
    2. Basic Demo
    3. Sample Size Demo
    4. Central Limit Theorem Demo
    5. Sampling Distribution of the Mean
    6. Sampling Distribution of Difference Between Means
    7. Sampling Distribution of Pearson's r
    8. Sampling Distribution of a Proportion
    9. Exercises
    10. PDF Files (in .zip archive)
  8. Estimation
    1. Introduction
    2. Degrees of Freedom
    3. Characteristics of Estimators
    4. Bias and Variability Simulation
    5. Confidence Intervals
      1. Introduction
      2. Confidence Interval for the Mean
      3. t distribution
      4. Confidence Interval Simulation
      5. Confidence Interval for the Difference Between Means
      6. Confidence Interval for Pearson's Correlation
      7. Confidence Interval for a Proportion
    6. Exercises
    7. PDF Files (in .zip archive)

  9. Logic of Hypothesis Testing
    1. Introduction
    2. Significance Testing
    3. Type I and Type II Errors
    4. One- and Two-Tailed Tests
    5. Interpreting Significant Results
    6. Interpreting Non-Significant Results
    7. Steps in Hypothesis Testing
    8. Signficance Testing and Confidence Intervals
    9. Misconceptions
    10. Exercises
    11. PDF Files (in .zip archive)
  10. Testing Means
    1. Single Mean
    2. t Distribution Demo
    3. Difference between Two Means (Independent Groups)
    4. Robustnes Simulation
    5. All Pairwise Comparisons Among Means
    6. Specific Comparisons
    7. Difference between Two Means (Correlated Pairs)
    8. Correlated t Simulation
    9. Specific Comparisons (Correlated Observations)
    10. Pairwise Comparisons (Correlated Observations)
    11. Exercises
    12. PDF Files (in .zip archive)
  11. Power
    1. Introduction
    2. Example Calculations
    3. Power Demo 1
    4. Power Demo 2
    5. Factors Affecting Power
    6. Exercises
    7. PDF Files (in .zip archive)

  12. Prediction
    1. Introduction to Simple Linear Regression
    2. Linear Fit Demo
    3. Partitioning Sums of Squares
    4. Standard Error of the Estimate
    5. Prediction Line Demo
    6. Inferential Statistics for b and r
    7. Exercises
    8. PDF Files (in .zip archive)

  13. ANOVA
    1. Introduction
    2. ANOVA Designs
    3. One-Factor ANOVA (Between-Subjects)
    4. One-Way Demo
    5. Multi-Factor ANOVA (Between-Subjects)
    6. Unequal Sample Sizes
    7. Tests Supplementing ANOVA
    8. Within-Subjects ANOVA
    9. Power of Within-Subjects Designs Demo
    10. Exercises
    11. PDF Files (in .zip archive)
  14. Chi Square
    1. Chi Square Distribution
    2. One-Way Tables
    3. Testing Distributions Demo
    4. Contingency Tables
    5. 2 x 2 Table Simulation
    6. Exercises
    7. PDF Files (in .zip archive)
  15. Case Studies
    1. Angry Moods
    2. Flatulence
    3. Physicians Reactions to Patient Size
    4. Teacher Ratings
    5. Mediterranean Diet and Health
    6. Smiles and Leniency
    7. Animal Research
    8. ADHD Treatment
    9. Weapons and Aggression
    10. SAT and College GPA
    11. Stereograms
    12. Driving
    13. Guns and Aggression
    14. Stroop Interference
    15. TV Violence
    16. Bias Against Associates of the Obese
  16. Calculators
    1. Analysis Lab
    2. Binomial Distribution
    3. Chi Square Distribution
    4. F Distribution
    5. Inverse Normal Distribution
    6. Inverse t Distribution
    7. Normal Distribution
    8. Power Calculator
    9. r to z'
    10. t Distribution
    11. Studentized Range Distribution
  17. Glossary


From  http://www.statisticssolutions.com/Tips_Resources.htm

Statistical Analyses Explained

Hypothesis Testing…read more

Researchers often seek to infer whether variables are related to each other; hypothesis testing permits one to examine such relationships empirically.

Typically, researchers state a hypothesis as a “null hypothesis (abbreviated as Ho).” That is, there is no difference in the dependent variable by the independent variable.

T-Test…read more

One type of t-test is called an independent sample t-test.
An independent sample t-test is the appropriate statistic when the dependent variable is continuous (i.e., interval or ratio data) and the independent variable is dichotomous (i.e., categorical or nominal)

Analysis of Variance (ANOVA) …read more

Analysis of Variance (ANOVA) is a statistical method to examine if there are differences in a dependent variable by a set of interval independent variables.

The Analysis of Variance (ANOVA) yields Main effects and Interaction effects

Chi-square Test…read more

The chi-square test is a nonparametric statistic that assesses the association between two categorical variables.

The null hypothesis states there is no association between these variables, while the alternative hypothesis states a relationship does exist between the two variables.

Multiple Regression (Stepwise and Hierarchical) …read more

Multiple Regression is used to predict the amount of variance (R2) accounted for in the criterion (dependent variable) from a set of predictors (independent variables).

The predictors can be interval, dichotomous, and/or dummy variables.

Logistic Regression…read more

Logistic Regression is a regression method used when the dependent variable is dichotomous.

Logistic regression is used to predict the likelihood (the odds ratio) of the outcome based on the predictor variables (called covariates in logistic regression).

LISREL…read more

LISREL is a popular software program designed for structural equation modeling.

The LISREL program may be used to handle standard multivariate methods, such as analysis of variance, regression analyses, and multivariate analysis of variance.

Structural Equation Modeling (SEM) …read more

Structural equation modeling (SEM) is a multivariate statistical technique used to examine direct and indirect relationships between one or more independent variables and one or more dependent variables.

Path Analysis …read more

Path analysis examines the direct and indirect effects of variables hypothesized as causes of variables treated as effects.

A method applied to causal models already formulated on the basis of knowledge and theoretical considerations.

SPSS…read more

SPSS is a statistical package for dissertation and thesis graduate students.

SPSS permits graduate students to conduct descriptive statistics, one-way and multivariate ANOVAs, repeated-measures ANOVA, correlation, regression, discriminant analysis, factor analysis, alpha reliability analysis, chi-square test

Statistical Formula…read more

Statistical formulas are used to generate statistics necessary to infer relationships between variables and decide whether statistical hypotheses are supported.

Statistics Solutions uses a wide variety of statistical tests to obtain the necessary statistics.


Correlation…read more

Correlation is a bivariate measure of association (strength) of the relationship between two variables. It varies from 0 (random relationship) to 1 (perfect linear relationship) or -1 (perfect negative linear relationship).

Partial Correlation…read more

Partial correlation is the correlation of two variables while controlling for a third or more other variables. The technique is commonly used in "causal" modeling of small models (3 - 5 variables).

Discriminant Function Analysis…read more

Discriminant function analysis, a.k.a. discriminant analysis or DA, is used to classify cases into the values of a categorical dependent, usually a dichotomy.

Factor Analysis…read more

Factor analysis is used to uncover the latent structure (dimensions) of a set of variables.

Log-linear, logit, and probit models…read more

Log-linear, logit, and probit models extend the principles of generalized linear models (ex., regression) to better treat the case of dichotomous and categorical variables.

Manova…read more

Type I. Used in hierarchical balanced designs where main effects are specified before first-order interaction effects, and first-order interaction effects are specified before second-order interaction errects, etc.

Reliability Analysis…read more

Reliability is the correlation of an item, scale, or instrument with a hypothetical one which truly measures what it is supposed to.

Measures of Association…read more

Association refers to a wide variety of coefficients which measure strength of relationship, defined various ways. In common usage "association" refers to measures of strength of relationship in which at least one of the variables is a dichotomy, nominal, or ordinal.

Dichotomous Association…read more

Association refers to coefficients which gauge the strength of a relationship. Coefficients in this section are designed for use with 2-by-2 tables. Note that measures for larger tables, discussed separately for nominal and ordinal data, may also be used with 2-by-2 tables.

Nominal Association…read more

Association refers to coefficients which gauge the strength of a relationship. Coefficients in this section are designed for use with nominal data.

Nominal-by-Interval Association Eta,…read more

Eta is a coefficient of nonlinear association. For linear relationships, eta equals the correlation coefficient (Pearson's r).

Ordinal Association…read more

Gamma, also called Goodman and Kruskal's gamma, is a symmetric measure which varies from +1 to -1, based on the difference between concordant pairs (P) and discordant pairs (Q).

Testing of Assumptions…read more

Assumptions are covered under each statistical topic. See also the separate section on data levels. This section provides information general to all procedures.

Canonical Correlation…read more

A canonical correlation is the correlation of two canonical (latent) variables, one representing a set of independent variables, the other a set of dependent variables.

Cluster Analysis…read more

Cluster analysis, also called segmentation analysis or taxonomy analysis, seeks to identify homogeneous subgroups of cases in a population.

Correspondence Analysis…read more

Correspondence analysis is a method of factoring categorical variables and displaying them in a property space which maps their association in two or more dimensions.

Data Imputation for Missing Values…read more

Proper handling of missing values is important in all analyses and is critical in some, such as time series analysis.

Data Levels and Measurement…read more

Nominal data has no order, and the assignment of numbers to categories is purely arbitrary (ex., 1=East, 2=North, 3=South, etc.).

Partial Least Squares Regression (PLS)…read more

Partial least squares (PLS) regression (path) analysis is an alternative to OLS regression, canonical correlation, or structural equation modeling (SEM) for analysis of systems of independent and response variables.

Research Designs…read more

Research designs fall into two broad classes: quasi-experimental and experimental.

Significance…read more

Significance is the percent chance that a relationship found in the data is just due to an unlucky sample, such that if we took another sample we might find nothing.

Binomial Test of Significance…read more

The binomial test is an exact probability test, based on the rules of probability, and is used to examine the distribution of a single dichotomy when the researcher has a small sample.

Normal Curve Tests of Means and Proportions…read more

Normal curve means tests, commonly called simply "hypothesis tests," are a basic method of exploring possible differences between two samples, or of testing the null hypothesis that an observed sample mean does not differ significantly from zero.

Fisher Exact Test of Significance…read more

The Fisher exact test of significance is used in place of the chi-square test in small 2-by-2 tables.

Runs Test of Randomness…read more

The one-sample runs test of significance is commonly used as a test of randomness in a sample.

One-Sample Kolmogorov-Smirnov…read more

The Kolmogorov-Smirnov D test is a goodness-of-fit test which tests whether a given distribution is not significantly different from one hypothesized (ex., on the basis of the assumption of a normal distribution).

Tests for Two Independent Samples…read more

This set of significance coefficients tests whether an ordinal or interval variable measured in each of two independent samples can be assumed to come from the same underlying population.

Tests for More Than Two Independent…read more

The tests in this section test whether one can reject the null hypothesis that two or more independent samples come from the same underlying population distribution.

Significance Tests for Two Dependent…read more

The McNemar test assesses the significance of the difference between two dependent samples when the variable of interest is a dichotomy.

Survey Research…read more

Survey research is the method of gathering data from respondents thought to be representative of some population, using an instrument composed of closed structure or open-ended items (questions).

Time Series Analysis…read more

Simple time series design. The usual time series design is simply the collection of quantitative observations at regular intervals through repeated surveys, such as unemployment indexes collected by the Bureau of Labor Statistics.

Event History Analysis, and Survival Analysis…read more

Event history analysis is an umbrella terms for a set of procedures. As such it is a specialized subfield of time series analysis which uses techniques, such as Poisson regression, which are designed to analyze rare events (time series in which most data are non-events).

Two-Stage Least Squares (2SLS)…read more

Two-stage least squares regression (2SLS) is a method of extending regression to cover models which violate ordinary least squares (OLS)

Validity…read more

A study is valid if its measures actually measure what they claim to, and if there are no logical errors in drawing conclusions from the data.

Recommended Sites…read more

We have compiled a list of respected sites that can help out with your verious dissertation needs.

From  http://www.statisticssolutions.com/AreasOfExpertise.htm


Analysis of variance (ANOVA)

Independent sample T-Test

Student’s t test

Statistical Formula

Multivariate Analysis of covariance (MANCOVA)

Discriminant Analysis

Repeated measures analysis

Correlation (Pearson, Kendall, Spearman)

Reliability analysis

Canonical correlations

Multiple regression analysis

Factor analysis

Descriptive statistics

Logistic Regression

AMOS 6.0


Multiple Regression (Stepwise and Hierarchical)

Structural Equation Modeling (SEM)

Path Analysis

Cluster analysis

Effect size

Power analysis

Program evaluation

Time series analysis

Wilcoxon Matched-pairs Sign test

Mann-Whitney U Test

Sign Test

PLS graph



Hypothesis Testing

Partial Correlation

Logistic Regression

Log-linear, logit, and probit models


Measures of Association

Dichotomous Association: Percent Difference, Yule's Q, Yule's Y, Risk, Odds Ratio

Nominal Association: Phi, Contingency Coefficient, Tschuprow's T, Cramer's V, Lambda, Uncertainty Coefficient

Nominal-by-Interval Association Eta, the Correlation Ratio

Ordinal Association: Gamma, Kendall's tau-b and tau-c, Somers' d

Testing of Assumptions

Correspondence Analysis

Data Imputation for Missing Values

Data Levels and Measurement

Research Designs


Binomial Test of Significance

Normal Curve Tests of Means and Proportions

Fisher Exact Test of Significance

Runs Test of Randomness

One-Sample Kolmogorov-Smirnov Goodness-of-Fit Test

Tests for More Than Two Independent Samples: Kruskal-Wallis H, Median, and Jonckheere-Terpstra Tests

Significance Tests for Two Dependent Samples: McNemar, Marginal Homogeneity, Sign, and Wilcoxon Tests

Survey Research

Event History Analysis, and Survival Analysis

Two-Stage Least Squares (2SLS) Regression Analysis



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