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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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slide1

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

hypothesis testing on variances one sample
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.

hypothesis testing on variances two samples
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.

non parametric statistics
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.
wilcoxon rank sum test
Wilcoxon Rank-Sum Test

m=12 n=15

Rank sum W=212

W=

for each type of parametric test there s a non parametric version
For each type of parametric test there’s a non-parametric version.

http://www.tufts.edu/~gdallal/npar.htm

statistical data analysis final notes
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.)
power law distribution
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

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