Hypothesis Testing

Chapters 1,2,4,5, and 6 covered.  Chapter 3 is 'bonus'.  

Bayesian (boo) vs. Frequentists (yea!):

http://oikosjournal.wordpress.com/2011/10/11/frequentist-vs-bayesian-statistics-resources-to-help-you-choose/

Bayes' Theorem explained:

http://betterexplained.com/articles/an-intuitive-and-short-explanation-of-bayes-theorem/ 

For R programmers check the following link:

http://meandering-through-mathematics.blogspot.com/2011/05/bayesian-probability.html

Resource summing up hypothesis testing:
http://www.sjsu.edu/faculty/gerstman/StatPrimer/hyp-test.pdf

Type I and Type II error:
Type I- Falsely rejecting the null hypothesis.  To accept the significance of our result mistakenly.
Type II- The opposite.  Falsely rejecting the significance of a result.  Falsely accepting the null hypothesis.

For a video on type I error:

http://www.khanacademy.org/math/probability/statistics-inferential/hypothesis-testing/v/type-1-errors

(Aside ** A link for the Bonferroni correction explained:

http://www.aaos.org/news/aaosnow/apr12/research7.asp  )


The null hypothesis for s's and g's:
http://www.null-hypothesis.co.uk/science//item/what_is_a_null_hypothesis

What is a model anyway?:
http://www.sportsci.org/resource/stats/models.html

Stats 1/25/2013

Big N little n What begins with those?
Nine new neckties and a nightshirt and a nose.

Big N = Population.    Little n = sample.

(n-1) explained:

http://sinairv.wordpress.com/2011/08/21/sample-variance-vs-population-variance-bessels-correction/

And if you are really bored at night:

http://en.wikipedia.org/wiki/Bessel's_correction

http://en.wikipedia.org/wiki/Friedrich_Bessel

Dividing standard deviation by the mean is the coefficient of variation.  Great for analyzing variation between populations. 

Standard Error of the Mean (SEM) = 

**(n-1) again for samples.**

Standard error is what is typically used instead of standard deviations.  As such, error bars in graphs are typically calculated using the standard error.  

Kurtosis:

Next week!!  Hypothesis testing and the assumption of our distributions.

http://mathworld.wolfram.com/HypothesisTesting.html

Stats 1/18/2013

How to Look at Graphs: Frequency Distribuions

Bin size...can turn bins into classes
Random distribution should be a clumped distribution.  This is because one that appears evenly dispersed may be hyper-dispersed, which is a non random separation of the data. For an example, check out this site:  http://2600hertz.wordpress.com/2010/03/12/how-random-is-random/

Mean, Median, and Mode:
http://www.fgse.nova.edu/edl/secure/stats/lesson1.htm

Geometric Mean:
http://www.cliffsnotes.com/study_guide/Geometric-Mean.topicArticleId-18851,articleId-18817.html

Range show distance between most extreme values.  

And the standard (NOT AVERAGE) deviation:

NOTE** the n-1 (vs. n) is used for samples versus the entire population.  See fudge factors next week

Or the variance:

Thus: http://en.wikipedia.org/wiki/68-95-99.7_rule

To compare deviations of two different populations that may be on different scales:

To analyze which of two samples from two different populations differs 'more' from the mean:

TYPES OF DISTRIBUTIONS:

Poisson:

http://eprints.ma.man.ac.uk/894/02/0-19-852868-X.pdf

m=8 is a special case called the normal distribution.

Friendly fudge factor next week!!

There are three kinds of lies: lies, damned lies, and statistics

There are three kinds of lies: lies, damned lies, and statistics -Marky Mark Twain




















An observation (~individual) defined:
http://epp.eurostat.ec.europa.eu/statistics_explained/index.php/Glossary:Observation_unit

A sample (~population) defined:
http://www.stats.gla.ac.uk/steps/glossary/sampling.html

"PCA principle components analysis is regression in more than two dimensions" - Francisco Moore

Repeated measures will be revisited and can be seen here:
http://biostat.mc.vanderbilt.edu/wiki/pub/Main/ClinStat/repmeas.PDF

Types of variables:
http://www.unesco.org/webworld/idams/advguide/Chapt1_3.htm

Meristic for fish people:
http://en.wikipedia.org/wiki/Meristics

A paper on error and philosophy:
http://www.ets.org/Media/Research/pdf/PICANG12.pdf


'Never ever ever ever ever used a derived variable in stats.  Unless you have to.  Distributions get wonky. '  paraphrased  -Francisco B.G. Moore the University of Akron Summit on Statistical Analysis 1-16-13