An Explanation of Statistical Tools from DocumentingExcellence.com A consulting practice focusing on working with colleges', organizations', and individuals' utilization of quantitative and qualitative assessment tools to analyze and document their quality outcomes through providing staff development, research design and analysis, and psychometric evaluations.
Statistical Tools TOC Conceptual Issues Measurment Issues Conceptual focus Measurement Focus Effectivenes Evaluating - Single variable Descriptive statistics Validity, Reliabiltiy, Cause & Effect Sound Reasoning Cause and Effect Reporting Modeling Correlation Regression & Correlation Statistical Control Unemployment & Crime Model Reduction Assessment Examples FAQ Glossaary Consulting Services

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Introduction to Statistical Tools

At some point most quantitative assessments use statistical tools.  When the word "statistics" is mentioned many people have one of two reactions.  "That was the best class I ever had!" or "That is the course that almost ended my college studies!"

Understanding and evaluation of many assessment efforts require some use of statistics.  So, I've written a brief primer describing the central ideas we use in examining data.  Since the application of statistics can become complex, and computers now make the calculations accessible, I've tried to explain each concept in terms of what is measured and how to use the statistical findings.

The following pages are organized first into a section that focuses on considering a single variable (evaluation), a second section that focuses on relationships between two or more variables (modeling), and thirdly an overview of outcomes assessment processes.

1. Focusing of what is being measured
   1. Competency and testing
   2. Learning domains
   3. Item construction
   4. Item assessment
   5. Scale construction
      1. Item Coherence with a scale
2. Focusing on how it is being measured
   1. Focus on measurement scales' characteristics
      1. Qualitative measurement
         1. Dichotomies
         2. Nominal categories
         3. Ordinal, ranks
      2. Quantitative measurment
         1. Interval scales
         2. Ratio scales
   2. Measurement processes
   3. Distribution of data
      1. Normal distribution
      2. Skewed distributions
      3. Uniform distributions
      4. Bi-modal distributions
3. Evaluating single variable data
   1. Descriptive statistics
      1. Averages
      2. Distribution
      3. Variance
      4. Standard deviation
      • Comparison of N-1 formula for a sample and N for a population.
      5. Standard error
      6. Confidence interval
      • Application of standard deviation (SD), standard error (SE), and confidence intervals (CI)
      7. Margin of error
      8. Z-score
   2. Criteria for evaluating measurement scale data
      1. Reliability
      2. Validity
      3. Clarifying reliability and validit
4. Finding differences between classifications of cases
   1. Confidence interval
5. Modeling relationships among variables
   1. Correlation
   2. Regression and Correlation
   3. Control for external variables
   4. Statistical controls
   5. Cause and effect
   6. Example of why control of extranious variables is important: Unemployment and Crime
   7. Model reduction
      1. Reduced Math model
      2. Reduced Scientific thinkng model
      3. Reduced Critical thinking model
      4. Reduced Writing model
      5. Reduced College Reading model
6. Conceptual issues in tests and measurment:
   1. Focusing on measurment
      1. Focusing on what is being measured - conceptually.
      2. Focusing on how measurments are used in statistics based on the characteristics of the concepts being measured.
      3. Focusing on measurement effectiveness.
   2. Sound and appropriate reasoning.
   3. Cause and effect reasoning
   4. Probabilty and determinism when considering effects and prediction
7. Outcomes assessment procedures
   1. General education assessments
      1. Successful solutions, a brief overview
      2. Assessment success - process comparisons
      3. Getting Real: Implementing General Education Assessment that Works
      4. Using Standarized Tests for Assessment of General Educaiton outcomes
      5. Using a Rubric for asssessmen of General Education outcomes
   2. Articulating measurments with outcome statements
   3. Discipline assessments
   4. Classroom assessments
   5. Reporting assessment findings
8. Effective instrument development
   1. Understanding validity and reliability
   2. Assessment of an instrument's reliability
   3. Assessment of an instrument's validity
   4. Distiquishing differences among classifications
   5. Outline of a report to an instrument developer
   6. Outline of an instrument summary - Public statement of findings
9. FAQ
10. Glossary

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Copyright © 2013 by Peter T. Klassen, Ph.D. Principal, www.DocumentingExcellence.com
26 January, 2013