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Central Tendency and Variability: Understanding Scores and The Normal Curve

This quick review provides an overview of central tendency measures—mean, median, and mode—and the characteristics of distributions, including normal and skewed shapes. It discusses how to evaluate scores with raw scores and z-scores, illustrating the significance of z-transformation for comparing different variables. Additionally, it covers theoretical probability distributions (Z, F, T) for hypothesis testing and understanding experimental outcomes. Key aspects of the standard normal curve, including critical values and probability ranges, are highlighted for practical application.

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Central Tendency and Variability: Understanding Scores and The Normal Curve

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Presentation Transcript

  1. Quick Review • Central tendency: Mean, Median, Mode • Shape: Normal, Skewed, Modality • Variability: Standard Deviation, Variance

  2. Quick Review

  3. Evaluating scores • Raw score of X: • -Measure of absolute standing • Difficult to interpret • Z-SCORE • - Measure of relative standing

  4. Z-Transformation • Transforming all raw scores in a distribution does not change the shape of a distribution, it does change the mean and the standard deviation

  5. Z Transformation • Z transformation provides a common metric to compare scores on different variables • Given X , find Z • Given Z , find X

  6. Find Z

  7. Find X

  8. -THEORETICAL PROBABILITY DISTRIBUTIONS (Z, F, T) -Used for testing hypothesis -Provide a way of determining probability of an obtained sample result (experimental outcome) -Usually, the probably that experimental result occurred by chance given null distribution

  9. A THEORETICAL PROBABILITY DISTRIBUTION The standard normal curve: - Bell-Shaped, symmetrical, asymptotic - Mean, Median and Mode all equal - Mean = 0; SD (δ) = 1; Variance (δ2) = 1

  10. Area under curve  probability Z is continuous so one can only compute probability for a range of values THE NORMAL CURVE

  11. BASIC RULES TO REMEMBER: THE (STANDARD) NORMAL CURVE

  12. BASIC RULES TO REMEMBER: 50% above Z=0, 50% below Z = 0 34% between Z=0 & Z= 1 / between Z=0 & Z = -1 68% between Z = -1 and Z = +1 96% between Z = -2 and Z = +2 99% between Z = -3 and Z = +3 THE (STANDARD) NORMAL CURVE

  13. TWO-TAILED CRITICAL VALUES 5% + and -1.96 1% + and – 2.58 THE (STANDARD) NORMAL CURVE

  14. ONE-TAILED CRITICAL VALUES 5% + OR - 1.645 1% + OR – 2.33 THE NORMAL CURVE

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