5. Agenda
1. R
2.
3.
4.
5. R
Saturday, November 26, 11 8
6. Agenda
1. R
2.
3.
4.
5. R
Saturday, November 26, 11 9
7. •
• Ross Ihaka & Robert Gentleman (R & R)
• Ross Ihaka and Robert Gentleman. R: A language for data analysis and graphics.
Journal of Computational and Graphical Statistics, 5(3):299-314, 1996.
• http://biostat.mc.vanderbilt.edu/twiki/pub/Main/Je reyHorner/JCGSR.pdf
•
Saturday, November 26, 11 10
16. • Windows: : http://cran.md.tsukuba.ac.jp/bin/windows/base/
• Download R 2.14.0 for Windows
• Mac OS X: http://cran.md.tsukuba.ac.jp/bin/macosx/
• R-2.14.0.pkg (latest version)
Saturday, November 26, 11 19
141. t
> like <- c(6,10,6,10,7,8,7,9,10,4)
> dislike <- c(3,5,6,4,4,8,4,5,4,7)
> t.test(like,dislike,var.equal=TRUE)
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142. t
> t.test(like,dislike,var.equal=TRUE)
Two Sample t-test
data: like and dislike
t = 3.3041, df = 18, p-value = 0.003946
alternative hypothesis: true difference in
means is not equal to 0 #
95 percent confidence interval: #
0.9831754 4.4168246
sample estimates:
mean of x mean of y
7.7 5.0
Saturday, November 26, 11 145
143. t ...
“
t Welch t
Welch t ”
http://aoki2.si.gunma-u.ac.jp/lecture/Average/bunsan1.html
Saturday, November 26, 11 146
145. ! !
― Welch ―
• http://oku.edu.mie-u.ac.jp/~okumura/blog/node/2262
• http://aoki2.si.gunma-u.ac.jp/lecture/BF/index.html
• Donald W. Zimmerman, ``Some properties of preliminary tests of equality of variances in
the two-sample location problem'', The Journal of General Psychology,Vol.123, pp.217-231
(1996)
• The unequal variance t-test is an underused alternative to Student's t-test and the Mann-
Whitney U test -- Ruxton 17 (4): 688 -- Behavioral Ecology
• : Mann-Whitney U http://qdai.way-
nifty.com/qjes/2005/02/mannwhitneyu.html
Saturday, November 26, 11 148
146. ...
> t.test(like,dislike,var.equal=FALSE)
Welch Two Sample t-test
data: like and dislike
t = 3.3041, df = 16.795, p-value = 0.004249
alternative hypothesis: true difference in
means is not equal to 0
95 percent confidence interval:
0.9743014 4.4256986
sample estimates:
mean of x mean of y
7.7 5.0
Saturday, November 26, 11 149
147. t t ...
•t t ...
• Student t
t
• s^2
s t ...
• %E3%82%B4%E3%82%BB%E3%83%83%E3%83%88
http://ja.wikipedia.org/wiki/%E3%82%A6%E3%82%A3%E3%83%AA%E3%82%A2%E3%83%A0%E3%83%BB
• http://ja.wikipedia.org/wiki/%E8%87%AA%E7%94%B1%E5%BA%A6
• http://mat.isc.chubu.ac.jp/fpr/fpr1997/0119.html
• http://www.pol.geophys.tohoku.ac.jp/~hanawa/ori/ori/054.html
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