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Understanding The Normal Curve and Sampling Error: SD vs SE

Learn the differences between SD and SE, and how to compute confidence intervals using standard scores. Interpret skewness and kurtosis for data analysis. Explore confidence intervals in statistical analysis.

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Understanding The Normal Curve and Sampling Error: SD vs SE

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Presentation Transcript

  1. Chapter 6 The Normal Curve and Sampling Error

  2. Difference between SD & SE? • SD is the sum of the squared deviations from the mean. • SE is the amount of ERROR in the estimate of the population based on the sample.

  3. Need for Standard Scores • In the Olympics the last place finishers are all superior to non-Olympic athletes. • How good is a 4 m long jump in high school? • Given mean = 5, we know that 4 m was below the mean.

  4. More than 95% of scores fall between ± 2 SDZ of 1.96 is the 95% value

  5. Z Scores

  6. Computing Confidence Intervals

  7. Area Under Normal Curve Z = 1.96 is 95% level. 2.5% in each tail. 50 - 2.5 = 47.50

  8. T Score

  9. Skewed Distribution

  10. Interpretation of Skew • Skew is acceptable as long as the Z score is less than 2.0 [p 89]

  11. Interpretation of Kurtosis • Kurtosis is acceptable as long as the Z score is less than 2.0 [p 89]

  12. SPSS Interpretation of SkewFrom Table 6.2 p 87 A skew that is more than twice it’s SE is taken as a departure from symmetry. In this case the Skew of -.988 is not greater than 2 * .637 = 1.274 See p 287 of SPSS Base Manual

  13. Confidence Intervals

  14. Using SE for Confidence Interval

  15. Computing Confidence Intervals

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