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Psychology 202a Advanced Psychological Statistics

Psychology 202a Advanced Psychological Statistics. October 1, 2014. The Plan for Today. The Z test Assumptions The two-sample Z test The t test Evaluating normality The Quantile-Quantile plot. Using the central limit theorem for inference. The one-sample Z test Example:

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Psychology 202a Advanced Psychological Statistics

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  1. Psychology 202aAdvanced Psychological Statistics October 1, 2014

  2. The Plan for Today • The Z test • Assumptions • The two-sample Z test • The t test • Evaluating normality • The Quantile-Quantile plot

  3. Using the central limit theorem for inference • The one-sample Z test • Example: • s= 10, n = 25, M = 105

  4. Assumptions of the Z test • Independent observations. • s is known. • Distribution is normal or sample is sufficiently large. • Problem: those assumptions are virtually never actually met.

  5. The two-sample Z test • Example: s1= s2= 10, n1 = n2 = 25, M1= 103, M2 = 108.

  6. Two-sample Z test (cont.)

  7. Assumptions of the two-sample Z test • Independent observations within groups. • Independent observations between groups. • s is known for both populations. • Distribution is normal or sample is sufficiently large in both populations.

  8. The one-sample t test • Solution to not knowing s : substitute an estimate of the standard deviation. • Class example. • The t test in SAS.

  9. Assumptions of the t test • Independent observations. • Distribution is normal. • The idea of robustness.

  10. Assessing the assumptions • Independence • Look at procedure, not at data • Normality • Graphical methods • Stem-and-leaf plots, histograms • The normal quantile-quantile plot

  11. Understanding the Q-Q plot • Manual Q-Q plots • Using R's “qqnorm” function • The 'plot' subcommand in SAS's proc univariate

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