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Reject h o accept h o

Left Tailed Right Tailed Two tailed

Reject Ho

Reject Ho

Reject Ho Accept Ho

Accept Ho Reject Ho

Accept Ho



Hypothesis testing on variances one sample
Hypothesis testing on Two tailed 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 Two tailed 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 Two tailed

  • 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 Two tailed Rank-Sum Test

m=12 n=15

Rank sum W=212


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


Statistical data analysis final notes
Statistical data analysis: final notes version.

  • 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 version.

  • 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



Thanks! version.