Chapter 2

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Chapter 2
2010-09-20 17:01:49
Test Measurement

Chapter 2: The Basic Mathematics of Measurement
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  1. Nominal Scales
    Qualitative system for categorizing objects or people i.e Female =1, Male = 2
  2. Ordinal Scales
    • Allows you to rank people or objects according to the quantity of a characteristic i.e
    • Class Rank
  3. Interval Scales
    Allows ranking on a scale with equal units i.e IQs, GRE scores
  4. Ratio Scales
    Properties of interval scales with a true zero point ie height in inches, weight in pounds
  5. Distribution
    A set of scores
  6. Measures of Central Tendency
    • 1) Mean
    • 2) Median
    • 3) Mode
  7. Measures of Variability
    • 1) Range
    • 2) Variance
    • 3) Standard Deviation
  8. Variance
  9. Variance
    Measure of variability in distribution of scores
  10. Standard deviation
    Used in interpreting scores: square root of variance
  11. Correlation Coefficient
    mathematical measure of the relationship between two variables:

    • range -1.0 to + 1.0
    • sign indicates the patter of the relationship
    • size indicates the strength of the relationship
  12. Scatterplots
    graph depicting the relationship between two variables. Each mark in the scatterplot actually represents two scores, an individual's scores on the X and Y variable
  13. Major Types of Correlations(4)
    • 1) Pearson Product-Moment Correlation
    • 2) Spearman Rank-Difference Correlation
    • 3) Point-Biserial Correlation
    • 4) Biserial Correlation
  14. Pearson Product-Moment Correlation
    Both variables continuous and on an Interval or Ratio Scale
  15. Spearman Rank-Difference Correlation:
    both variables on an Ordinal Scale
  16. Point-Biserial Correlation
    ONe variable continuous and on Interval/Ratio scale, the other a genuine dichotomy
  17. Biserial Correlation
    Both variables continuous and on Interval/Ratio scale, but one is reduced o two categories
  18. Factors that effect correlations
    • 1) If another type of relationship exists, traditional correlations may underestimate the correlation
    • 2) If there is a restriction of range in either variable, the magnitude of the correlation will be reduced
  19. Qualitative interpretation of correlations
    • < .3 Weak
    • .3 - .7 Moderate
    • > .7 Strong
  20. Statistical Significance of Correlations
    determined both by the size of the correlation coefficient and the size of the sample
  21. Coefficient of Determiniation(r squared)
    The proportion of variance on one variable that is determined or predicatble from the other variable
  22. Coefficient of Nondetermination (1 - r squared)
    The proportion of variance in one variable that is not determined or predicatable from the other variable
  23. Linear Regression
    • A statistical technique for predicting scores on one variable given a score on another
    • Predicts criterion scores based on a perfect linear relationship
    • Strong correlations result in accurate predictions; weak correlations resul in less accurate predictions

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