ESCI 340 computer lab:  Friday 24 January 2014

Variance test, Paired-sample t-test, Wilcoxon test



> # Variance ratio test using D.fir dbh data:



> dbh.edge <- c(87.5, 95.1, 75, 88.3, 83, 92.7, 88.5, 96, 118.9, 62.5)

> dbh.int <- c(115.2, 80, 91.6, 63, 112, 107, 52.1, 102.4, 99, 68.0)

> par(mfrow = c(2,1))

> hist(dbh.edge, xlim=c(50, 120), xlab="DBH, edge trees (m)", main="")

> hist(dbh.int, xlim=c(50, 120), xlab="DBH, interior trees (m)", main="")

> var(dbh.edge)

[1] 214.5028

> var(dbh.int)

[1] 487.2623

> fcalc <- var(dbh.int) / var(dbh.edge)

> fcalc

[1] 2.27159

> # P(2-tailed) > 0.50





> # Paired-sample t-test using moss cover/maple data 



> # Paired moss cover data: up vs. down slope, B-l maples

> m.up <- c(70, 100, 95, 70, 90, 50, 60, 90, 90, 1)

> m.up

 [1]  70 100  95  70  90  50  60  90  90   1

> m.down <- c(0, 1, 2, 15, 0, 3, 20, 0, 5, 0)



> m.up

 [1]  70 100  95  70  90  50  60  90  90   1

> m.down <- c(0, 1, 2, 15, 0, 3, 20, 0, 5, 0)

> m.down

 [1]  0  1  2 15  0  3 20  0  5  0

> m.diff <- m.up - m.down

> m.diff

 [1] 70 99 93 55 90 47 40 90 85  1

> mean(m.diff)

[1] 67

> se.diff <- sd(m.diff) / sqrt(10)

> se.diff

[1] 9.843215

> t.diff <- mean(m.diff) / se.diff

> t.diff

[1] 6.806719



> # Are paired differences distributed normally? (t-test assumption)

> par(mfrow = c(1,1))

> hist(m.diff)

> # No; 3 reasons: asymmetric, bimodal, few values near mean

> # Consequently, use non-parametric (Wilcoxon) test

> m.diff

 [1] 70 99 93 55 90 47 40 90 85  1

> sort(m.diff)   # show differences in ascending order

 [1]  1 40 47 55 70 85 90 90 93 99

> # positive ranks are values 1 ... 10; no negative ranks

> sum(c(1:10))

[1] 55

> # T+ = 55, T- = 0

> # Use T-

> P(2-tailed) < 0.005