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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.

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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 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


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

  • 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



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