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1, 2.6, 2/3, 105.2, 0.0043 1, 3, 0, 245 A, B, C... ; 0 1 0.2, 3/4, 0.99
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R > 1 + 1 > 1 1 > 2 * 2 > 4 / 2 > 3^2 > sqrt(9) > 9^(1/2) ½
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> a < 3.14 > b < c( 1, 2, 3, 4, 5, 6) > x < matrix(nrow = 2, ncol = 3) > data < read.csv( HandSize.csv, header = T) b[3] x[2, 3] data$hl
CSV CSV *.csv R read.csv(.csv, header = T) R write.csv(.csv
[,] > d[d$hl== F,] # d d$hl== F TRUE > d[d$hl== F,]$HL # HL subest() > d.f < subset(d, HL == F ) # d HL== H d.f > d.f$hl
plot(), boxplot(), histogram() plot(hl, data = d) HL boxplot(hl, data = d) plot(hl ~ Sex, data = d) HL Sex plot(hl ~ BL, data = d) histogram(d$hl, breaks = ) breaks
a X 1, X 2,...X n a a X 1 a, X 2 a,...x n a n Σ X i a) # Σ X i a # Σ X i a) 2 # 2
a a f(a) a f(a) = (X 1 a) 2 + (X 2 a) 2 +...(X n a) 2 = X 12 + X 22 +...X n2 2a(X 1 + X 2 +...X n ) + na 2 a f(a) a f(a) a f (a) = 0 2(X 1 + X 2 +...X n ) + 2a = 0 a = (X 1 + X 2 +...X n ) /n
N μ, σ 2 μ σ 2
lm( ) lm()
m0 null Null model μ μ ( x ) 2
m0 P P t = 0 t
HL HL t p α α = 0.05 = 1/20 p α HL
α p p = 0.05 1/20... Type I
m0 P P t = 0 t
( x / > t.cal < (mean(d$hl) 0) / sqrt(var(d$hl)/n) n 1 t n 25
m1 ANOVA lm(hl ~ 1, data = d) lm(hl ~ Sex, data = d)
m1 ANOVA p p t
... lm(hl ~ Sex, data = d) t > var.test(bl.f, BL.m) > t.test(bl.f, BL.m,,var.equal = TRUE) BL.f BL.m t p lm()
...
m2 Y Y p p Y
m3 ANCOVA p 0.05
m4 ANCOVA
HL ~ 1 HL ~ Sex + HL ~ BL + BL HL ~ BL + Sex + BL + ) + BL HL ~ BL + Sex + BL:Sex + BL + ) + BL summary a Intercept b BL a m SexM b m BL:SexM
... p
Model 0: HL ~ 1 Model 1: HL ~ Sex Model 2: HL ~BL HL 16 17 18 19 20 male female HL 16 17 18 19 20 HL 16 17 18 19 20 150 160 170 180 BL 150 160 170 180 BL 150 160 170 180 BL Model 3: HL ~ BL + Sex Model 4: HW ~ BL + Sex + BL:Sex HL 16 17 18 19 20 HL 16 17 18 19 20 150 160 170 180 BL 150 160 170 180 BL
AIC AIC 2 e.g.
AIC AIC Model 3 Model 4
AIC. BL*Sex BL +Sex BL Sex 1 AIC BL*Sex 0.3496 0.105 2.544e 05 8.194e 12 75.8 BL+Sex 0.0554 5.802e 06 1.441e 12 74.8 BL N/A 7.017e 13 76.8 Sex 4.994e 09 95.2 1 129.5
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R MCMC ( ) Crawley: :R
2
anova(h0, h1) 2 h 0 h 1 2 2 p.value = 1 pchisq(2*(mll.h1$value MLL.h0$value), h1 h0 ) F 2