moss_bartlett.txt

				JFM  2/8/2012



Bartlett's test for equality of variances,

using moss cover data on 4 kinds of surfaces.  

Data collected by ESCI 340 students on 1/23/2012.

Calculations in R.



> # Enter data

> moss.df <- c(10, 30, 0, 40, 5, 0, 25, 50, 0, 12)

> length(moss.df)   # Check that sample size = 10

[1] 10

> moss.bm <- c(60, 100, 15, 10, 80, 100, 100, 60, 70, 0)

> moss.bm

 [1]  60 100  15  10  80 100 100  60  70   0

> moss.rock <- c(30, 50, 100, 70, 100, 100, 7, 90,0, 60)

> moss.rock

 [1]  30  50 100  70 100 100   7  90   0  60

> moss.log <- c(30, 90, 25, 60, 0, 100, 45, 100, 10, 85)

> moss.log

 [1]  30  90  25  60   0 100  45 100  10  85



> # Sample variances:

> v.df <- var(moss.df)

> v.df

[1] 326.1778

> v.bm <- var(moss.bm)

> v.bm

[1] 1491.389

> v.rock <- var(moss.rock)

> v.rock

[1] 1467.122

> v.log <- var(moss.log)

> v.log

[1] 1430.278



> # Pooled variance:

> v.p <- var(c(moss.df, moss.bm, moss.rock, moss.log))

> v.p

[1] 1417.410



> moss.B <- log(v.p)*36 - 9*(log(v.df) + log(v.bm) +

+   log(v.rock) + log(v.log))

> moss.B

[1] 12.37282

> # Correction factor

> moss.c <- 1 + (1/9)*(4/9 - 1/36)

> moss.c

[1] 1.046296

> moss.Bc <- moss.B / moss.c

> moss.Bc

[1] 11.82535



> # Compare with Chi-squared statistic w/ k-1 degrees of freedom

> # Chi-sq_0.01,3 = 11.345     Chi-sq_0.005,3 = 12.838 

> # 0.01 > P > 0.005

> 1 - pchisq(moss.Bc, df = 3)          # precise P-value

[1] 0.008006024