Exploring Numerical Data (E.N.D.) is a software resource for instructors and students in a university/college level social sciences introductory statistics course; it consists of text material, review questions, and calculation utilities.

Text Material.  The text sections are focused expositions of the substantive content of the topics.  Instructors, and printed matter such a standard text, may convey a fuller treatment of some topics; E.N.D. is intended to supplement these presentations without getting in their way.  That said, most of my students use E.N.D. as their main resource; instructors who have developed their own package of hand-out materials will find E.N.D. an excellent and economical accessory.  The presentation of topics in E.N.D. is couched in orthodox language and notation and is therefore compatible with virtually any text and fits well into typical introductory statistics courses.  My personal bias is to emphasize the conceptual aspects of statistics rather than devote excessive time to mechanical calculations.

Review Questions.  Review exercises enable students to test their mastery of concepts and computation routines.  The review questions are styled in a multiple-choice (seven alternatives) format and require, in turn, understanding of relevant concepts, computational skills from partially developed data, and understanding of the rules for decision making in science.  The review exercises are accompanied by computational solutions and/or text feedback for incorrect alternatives.  The current version of E.N.D (2.2) contains 365 review exercises which constitute a resource for thorough preparation for tests and examinations.  My own students regard the review questions as most valuable.

Calculation Utilities.  Many of the topic units contain a calculation utility.  The utilities can serve as convenient tools for homework assignments but their principle value as instructional devices is to act as vehicles by which instructors may demonstrate, and students may explore, various descriptive and analytic procedures.  Functions are provided to enable the creation and storage of permanent data files.


Introducing E.N.D. - 13 pages/screens
    Using E.N.D.
    Screen Settings
    Hard Drive Installation
    Example Review Question
    Handling Data
    Copyright & Limitations
    Bug List & Feedback

Unit 1: Learning the Language - 57 pages/screens
    Terms and Definitions
    Review Questions I
    Types of Measurement
    Review Questions II
    Summation Notation
    Review Questions III
    Key Terms Summary

Unit 2: Organizing Data - 43 pages/screens
    Frequency Distributions
    Exact Limits
    Stem & Leaf Displays
    Review Questions
    Key Terms Summary
    Frequency Distribution Calculation Utility
    Stem & Leaf Calculation Utility
    Histogram / Frequency Polygon Calculation Utility

Unit 3: Describing Data - 62 pages/screens
    Review Questions I
    Review Questions II
    Key Terms Summary
    Descriptive Statistics Calculation Utility

Unit 4: Normal Distribution - 43 pages/screens
    Normal Distribution
    Review Questions
    Key Terms Summary
    Normal Distribution Calculation Utility

Unit 5: Probability - 41 pages/screens
    This or That
    This and That
    Review Questions
    Key Terms Summary

Unit 6: Statistical Distributions - 43 pages/screens
    Random Samples
    Sampling Distributions
    t Distributions
    Review Questions
    Key Terms Summary

Unit 7: Confidence Intervals - 30 pages/screens
    Confidence Intervals
    Review Questions
    Key Terms Summary
    Confidence Interval Calculation Utility

Unit 8: Hypothesis Testing - 45 pages/screens
    Hypotheses in Science
    Type I and Type II Error
    Review Questions
    Key Terms Summary

Unit 9: One Sample t-Test - 39 pages/screens
    One Sample t-Test
    Underlying Assumptions
    Confidence Interval Approach
    Review Questions
    Key Terms Summary
    One Sample t-Test Calculation Utility

Unit 10: Two Sample t-Tests - 67 pages/screens
    Independent Samples t-Test
    Related Samples t-Test
    Underlying Assumptions
    Confidence Interval for the Difference Between Means
    Confidence Interval for the Mean Difference
    Review Questions
    Key Terms Summary
    Independent Samples t-Test Calculation Utility
    Related  Samples t-Test Calculation Utility

Unit 11: Analysis of Variance - 39 pages/screens
    F Distributions
    One Factor ANOVA
    Underlying Assumptions
    Après ANOVA (multiple comparisons and strength of effect)
    Review Questions
    Key Terms Summary
    One Factor ANOVA Calculation Utility

Unit 12: Correlation - 54 pages/screens
    Describing Correlation
    Calculation / Interpretation
    Variance Interpretation
    Concluding Remarks
    Review Questions
    Key Terms Summary
    Correlation Calculation and Plotting Utility

Unit 13: Linear Regression - 24 pages/screens
    Predicting Y from X
    Confidence Intervals about Predicted Y
    Review Questions
    Key Terms Summary
    Regression Calculation and Plotting Utility

Unit 14: Chi-Square Tests - 51 pages/screens
    Goodness of Fit Test
    Review Questions I
    Test of Independence
    Review Questions II
    Key Terms Summary
    Goodness of Fit Calculation Utility
    Test of Independence Calculation Utility

Data Files Management - 4 pages/screens
    Data Files Directory
    Single Variable Files
    Paired Variables Files

Endex - 11 pages/screens
One of the new aspects of version 3.0 is called "Endex".  It is a master glossary of 200+ terms/concepts and a navigating index providing mouse-click access to relevant discussions in the E.N.D. units.  Students struggling to learn the terminology and concepts will find Endex most useful.

Exploring Numerical Data is written in ToolBook II (Asymetrix Corp.) and is available on a CD; the CD is self-contained and runs on computers using the Windows 95 and later operating systems (sorry, there is no MacIntosh version).

This is a partial screen capture of the opening page of Unit 9: One-Sample t-Test.

This is a partial screen capture of the calculation utility in Unit 9.

This is a partial screen capture of a review exercise in Unit 9.


In my thirty plus years as a statistics instructor I devoted much time and effort trying to make this subject comprehendible and non-threatening to students.  These efforts included a text (now out of print); E.N.D. is another attempt at this goal.


A few words and images cannot adequately describe Exploring Numerical Data; there is nothing like it currently available.  Earlier  versions of  Exploring Numerical Data were distributed by ITP Nelson (Canada) Publishers and was available bundled with several texts or stand alone.  If you would like to obtain a copy please contact your ITP Nelson sales representative, or me at  horvatht@sympatico.ca .

T. Horvath Ph.D.
Windsor, ON   Canada