nests

http://udel.edu/~mcdonald/statnested.html

http://psych.colorado.edu/~carey/Courses/PSYC5741/handouts/Nested_ANOVA.pdf

http://www3.imperial.ac.uk/pls/portallive/docs/1/1171923.PDF

http://ekhartman.berkeley.edu/work/ANOVA.pdf

http://www.statsoft.com/textbook/anova-manova/

http://animsci.agrenv.mcgill.ca/servers/anbreed/statisticsII/type1.htm

http://en.wikipedia.org/wiki/Degrees_of_freedom_(statistics)

http://www.pindling.org/Math/Statistics/Textbook/Chapter10_ANOVA/ANOVA.htm

http://statwww.epfl.ch/davison/SM/SMsample.pdf

Linear Regression explained on YouTube
http://www.youtube.com/watch?v=ocGEhiLwDVc

Linear Regression in R:
http://www.montefiore.ulg.ac.be/~kvansteen/GBIO0009-1/ac20092010/Class8/Using%20R%20for%20linear%20regression.pdf

Linear Regression in Excel:
http://office.microsoft.com/en-us/excel-help/perform-a-regression-analysis-HA001111963.aspx

Linear Regression in SAS:
http://www2.math.umd.edu/~slud//s798c/Handouts/Lec03Pt5B.pdf

Booting up SaS

Sassy

(*Note:  Though this class is primarily focused on learning and manipulating data using the SAS or JMP statistical packages, I will be programing and posting solutions in R.  I may try to post equivallen solutions in SAS simultaneously for those that are interested in learning both.  R is free and does not require 22 Gazigabytes. )

T-Test:
History for the nerds-
http://en.wikipedia.org/wiki/William_Sealy_Gosset

Basic t-test with calculator-
http://www.stattools.net/tTest_Exp.php

More detailed explanation-
http://simon.cs.vt.edu/SoSci/converted/T-Dist/activity.html

Regression + ANOVA = ANCOVA

Regression:

covariance = 

regression coefficient = 

(*Note:  The n or n-1 will cancel when the cov is divided by the var, thus whether the correction is applied or not is irrelevant)

Regression explained:
http://www.law.uchicago.edu/files/files/20.Sykes_.Regression.pdf

more simply:
http://www.stat.yale.edu/Courses/1997-98/101/linreg.htm
http://easycalculation.com/statistics/learn-regression.php

And explained well:
http://www.sjsu.edu/faculty/gerstman/StatPrimer/regression.pdf

Goodness of fit explained:
http://www.mathworks.com/help/curvefit/evaluating-goodness-of-fit.html

Regression in SAS:
http://www.ats.ucla.edu/stat/sas/webbooks/reg/chapter1/sasreg1.htm
http://www.youtube.com/watch?v=Bzm8TJYFZcs

Regression in R
http://msenux.redwoods.edu/math/R/regression.php

Model I and II regressions:
http://www.mbari.org/staff/etp3/regress/about.htm


WOOOOO!

HW # 1

To those who unfortunately are reading this as opposed to vacationing in Vegas,

Andrew Jones

Biometry

2/3/13

Small Arabinose Negative Lineages vs. Large Arabinose Negative Lineages

Average of Small-

0.765635645
0.890993539
0.860948991
0.886212273
0.859489471
0.934212218
0.945863536
0.999423109
0.899233247
0.787217193
0.938261524
0.984696833
0.83820725
0.827858702

(∑Obs)/n where n = 14.

(1) Mean = .887

(2) Var = (∑(obs-µ)^2)/(n-1)

=(.00016+.000052+.00021+.00053+.00040+.00006+.00040+.00002+.00021+.00289+. 00231+.00028+.00151+.00174)/13

=.00087

Average of Large-

0.887503593
0.907561395
0.914647822
0.877401142
0.920149004
0.907823388
0.880485947
0.896073919
0.88584494
0.954043492
0.852222311
0.9171615
0.861517592
0.942045965
0.916409303

(∑Obs)/n where n = 15.

(1) Mean = .901

(2) Var = (∑(obs-µ)^2)/(n-1)

=(.01473 + .00002 + .00068 +.00000 + .00076 + .00228 + .00346 + .01263 + .00015 + .00996 + .00263 + .00954 + .00238 + .00350)/14

=.00482

(3) Mean of means= (.901 + .887)/2 = 0.895

(4) Variance of Mean of Means((.900-.89)^2 + (.887-.894)^2)/n-1 = .000085

(5) Grand Mean

0.765635645
0.890993539
0.860948991
0.886212273
0.859489471
0.934212218
0.945863536
0.999423109
0.899233247
0.787217193
0.938261524
0.984696833
0.83820725
0.827858702
0.887503593
0.907561395
0.914647822
0.877401142
0.920149004
0.907823388
0.880485947
0.896073919
0.88584494
0.954043492
0.852222311
0.9171615
0.861517592
0.942045965
0.916409303
/19

=.8945

(6) Variance

(.0165 + .00001 + .00112 + .00007 + .00122 + .00158 + .00264 + .01102 + .00002 + .01150 + .00192 + .00814 + .00316 + .00443 + .00005 + .00017 + .00041 + .00029 + .00066 + .00018 + .00020 + .00000 + .00007 + .0036 + .00178 + .00052 + .00108 + .00227 + .00048)/28

=.00268

(7) The Weird One

 Obs- .8945

-0.128817625

-0.003459731

-0.033504279

-0.008240997

-0.034963799 

0.039758948 

0.051410266

0.104969839 

0.004779977

-0.107236077 

0.043808254 

0.090243563

-0.056246020

-0.066594568

-0.006949677 

0.013108125 

0.020194552

-0.017052128 

0.025695734 

0.013370118

-0.013967323

0.001620649

-0.008608330 

0.059590222

-0.042230959 

0.022708230

-0.032935678 

0.047592695

0.021956030

(-0.128817625 + -0.003459731 + -0.033504279 + -0.008240997 + -0.034963799  + 0.039758948  + 0.051410266 + 0.104969839 + 0.004779977 + -0.107236077  + 0.043808254  + 0.090243563 + -0.056246020 + -0.066594568 + -0.006949677  + 0.013108125  + 0.020194552 + -0.017052128  + 0.025695734  + 0.013370118 -+ 0.013967323 + 0.001620649 + -0.008608330 + 0.059590222 + -0.042230959+ 0.022708230 + -0.032935678 + 0.047592695 + 0.021956030)/29

= 1.15 x 10^-17

(8) (-0.128817625- 1.15 x 10^-17)^2 + (-0.003459731- 1.15 x 10^-17) ^2 + (-0.033504279- 1.15 x 10^-17) ^2 + (-0.008240997- 1.15 x 10^-17) ^2 + (-0.034963799- 1.15 x 10^-17) ^2  + (0.039758948- 1.15 x 10^-17) ^2  + (0.051410266- 1.15 x 10^-17) ^2 + (0.104969839- 1.15 x 10^-17) ^2 + (0.004779977- 1.15 x 10^-17) ^2 + (-0.107236077- 1.15 x 10^-17) ^2  + (0.043808254- 1.15 x 10^-17) ^2  + (0.090243563- 1.15 x 10^-17) ^2 + (-0.056246020- 1.15 x 10^-17) ^2 + (-0.066594568- 1.15 x 10^-17) ^2 + (-0.006949677- 1.15 x 10^-17) ^2  + (0.013108125- 1.15 x 10^-17) ^2  + (0.020194552- 1.15 x 10^-17) ^2 + (-0.017052128- 1.15 x 10^-17) ^2  + (0.025695734- 1.15 x 10^-17) ^2  + (0.013370118- 1.15 x 10^-17) ^2 + (0.013967323- 1.15 x 10^-17) ^2 + (0.001620649- 1.15 x 10^-17) ^2 + (-0.008608330- 1.15 x 10^-17) ^2 + (0.059590222- 1.15 x 10^-17) ^2 + (-0.042230959- 1.15 x 10^-17) ^2+ (0.022708230- 1.15 x 10^-17) ^2 + (-0.032935678- 1.15 x 10^-17) ^2 + (0.047592695- 1.15 x 10^-17) ^2 + (0.021956030- 1.15 x 10^-17) ^2

All divided by 29

=0.0026

magic