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Review of Basics

Review of Basics. REVIEW OF BASICS PART I. Measurement Descriptive Statistics Frequency Distributions. Measured Scores. Any measured score represents: True underlying score Measurement error Lower measurement error means higher reliability . Statistical Models.

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Review of Basics

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  1. Review of Basics

  2. REVIEW OF BASICS PART I • Measurement • Descriptive Statistics • Frequency Distributions

  3. Measured Scores • Any measured score represents: • True underlying score • Measurement error • Lower measurement error means higher reliability

  4. Statistical Models • How well can we represent the data? • Outcomei = modeli + errori • The model may be as simple as the mean of the data set, but often takes the form of a linear equation: • Y = mX+ b

  5. MEASUREMENT SCALES • What assumptions can you make about a score? • Many statistics require a certain measurement scale. • The measurement scale is a property of the data.

  6. 1. Nominal Scale • Numbers classify into groups. • Math, other than counting, is not meaningful.

  7. 2. Ordinal Scale • Numbers are rank orders. • Math, other than counting, is not meaningful.

  8. 3. Interval Scale • Numbers represent amounts, with equal intervals between numbers. • Math, other than ratio comparisons, is meaningful.

  9. 4. Ratio Scale • Numbers represent amounts, with equal intervals and a true zero • true zero: score of zero represents a complete absence • Math, including ratios, is meaningful.

  10. Why You Can’t do Ratios on an Interval Scale

  11. The Same Temperatures on Another Interval Scale

  12. The Same Temperatures on a Ratio Scale (Rankine = F + 459.6)

  13. The Same Temperatures on a Ratio Scale (Kelvin = C + 273.15)

  14. DESCRIPTIVE STATISTICS • Central Tendency • Variability • Frequency Distributions

  15. Central Tendency – Typical Score • mean: arithmetic average • median: middle score • mode: most frequent score

  16. Variability – Spread of Scores • deviation: difference between observed score and model (e.g., mean) • sum of squares(SS): sum of squared differences from the mean

  17. Variability • variance: average squared difference from the mean • standard deviation: average unsquared difference from the mean

  18. FREQUENCY DISTRIBUTIONS • frequency: number of times a score occurs in a distribution • frequency distribution: list of scores with the frequency of each score indicated

  19. Normal Distributions • symmetrical • equal mean, median, and mode • bell-shaped

  20. Why Be Normal? • Many variables are affected by many random factors. • Effects of random factors tend to balance out.

  21. Skewness • Extent to which scores are piled more on one end of the distribution than the other • positive skew • negative skew

  22. Skewness • Skewness = 0 for a normal distribution • Skewness < 0 for a negatively skewed distribution • Skewness > 0 for a positively skewed distribution

  23. Kurtosis • Extent to which scores pile at the ends of the distribution • Platykurtic: flat • Leptokurtic: steep

  24. Kurtosis • Kurtosis = 0 for a normal distribution • Kurtosis < 0 when the distribution is flatter than a normal • Kurtosis > 0 when the distribution is steeper than a normal

  25. Review Question! • Think of a variable that you would expect to have a skewed distribution. Why would you expect it to be skewed? Do you expect it to be positively or negatively skewed?

  26. Choosing Stats A researcher manipulates whether participants are put in a conflict situation or not (a confederate either agrees or disagrees with the participant). The participants are then given a survey which measures their level of self-confidence. The researcher would like to know whether conflict affects level of self-confidence.

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