The Normal Curve and Sampling Error Chapter 6 The Normal Curve and Sampling Error

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.

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.

More than 95% of scores fall between ± 2 SD Z of 1.96 is the 95% value

Z Scores

Computing Confidence Intervals

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

T Score

Skewed Distribution

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

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

SPSS Interpretation of Skew From 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

Confidence Intervals

Using SE for Confidence Interval

Computing Confidence Intervals