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Reject H o Accept H o

Left Tailed Right Tailed Two tailed . Reject H o. Reject H o. Reject H o Accept H o. Accept H o Reject H o. Accept H o. http://library.beau.org/gutenberg/1/0/9/6/10962/10962-h/images/069.png.

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Reject H o Accept H o

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  1. Left Tailed Right Tailed Two tailed Reject Ho Reject Ho Reject Ho Accept Ho Accept Ho Reject Ho Accept Ho http://library.beau.org/gutenberg/1/0/9/6/10962/10962-h/images/069.png http://www.pindling.org/Math/Statistics/Textbook/Chapter8_two_population_inference/proportion_independent.htm

  2. Hypothesis testing on variances: one sample New method reduces variances in product 1.41<1.5; How small is enough? Suppose Hois true (σ²= 1.5), how likely is it to observe S²≤1.41 ? Chi-sq. with n-1 D.F. Use table: There’s good chance of observing 1.41 in a random sample, even if the true population variance is 1.5. No reason to reject Ho: No significant evidence of reduced variance.

  3. Hypothesis testing on variances: two samples Variance unequal in two populations F dist. with 15 and 24 D.F. Use table: Reject Ho at α=0.2: Variances are not equal.

  4. Non-parametric statistics • All hypothesis testing so far deals with parametersµ, σof certain distributions. • Non-parametric statistics: raw data is converted into ranks. All subsequent analyses are done on these ranks. • Do not require original data to be normal. • Sum of ranks are approximately normally distributed.

  5. Wilcoxon Rank-Sum Test m=12 n=15 Rank sum W=212 W=

  6. For each type of parametric test there’s a non-parametric version. http://www.tufts.edu/~gdallal/npar.htm

  7. Statistical data analysis: final notes • All tests based on T dist. requires normality in original population. When sample size is big (>30), applicable even not normal. • Tests based on Chi-sq. & F dist. are sensitive to violation of normality. Test of normality. • Some datasets are normal only after log-transformation. • Use non-parametric tests when data not normal. • Watch out for outliers! (box plot helps) • It never hurts to visualize your data!! • Yes, you can do it! (Wiki, google, RExcel etc.)

  8. Power law distribution • Density function: • Word usage, internet, www, city sizes, protein interactions, income distribution • Active research in physics, computer science, linguistics, geophysics, sociology, &economics. Zipf’s law: My 381 students http://special.newsroom.msu.edu/back_to_school/index.html

  9. Thanks!

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