[R] non-parametric permutation and signed paired-difference distributions

[Weidong Gu]

On Fri, Oct 14, 2011 at 11:38 AM, Michael Friendly <friendly at yorku.ca> wrote:
> Hi all
> Consider the classic data below from Darwin on the heights of 15 pairs of
> zea mays (corn) plants
> either cross-fertilized or self-fertilized, where the goal is to see if it
> makes a difference.
>
>> head(ZeaMays)
>  pair pot  cross   self   diff
> 1    1   1 23.500 17.375  6.125
> 2    2   1 12.000 20.375 -8.375
> 3    3   1 21.000 20.000  1.000
> 4    4   2 22.000 20.000  2.000
> 5    5   2 19.125 18.375  0.750
> 6    6   2 21.500 18.625  2.875
> ...
>
> I'd like to illustrate two types of non-parametric tests of whether the
> mean(diff) = 0.
>
> (a) Permutation test, where the values of, say self are permuted and
> diff=cross - self
> is calculated for each permutation.  There are 15! permutations, but a
> reasonably
> large number of random permutations would suffice.
>
> (b) Test based on assigning each abs(diff) a + or - sign, and calculating
> the mean(diff).
> There are 2^15 such possible values, but again, a reasonably large number of
> random
> samples would do.
>

What do you mean by 'assigning each abs(diff) a + or - sign, and
calculating the mean(diff)'?
abs(diff) should be all positive, right?

> This is obviously a case for apply and friends, but I can't quite see how to
> set it up.
>
> The complete data:
>
>> dput(ZeaMays)
> structure(list(pair = 1:15, pot = structure(c(1L, 1L, 1L, 2L,
> 2L, 2L, 3L, 3L, 3L, 3L, 3L, 4L, 4L, 4L, 4L), .Label = c("1",
> "2", "3", "4"), class = "factor"), cross = c(23.5, 12, 21, 22,
> 19.125, 21.5, 22.125, 20.375, 18.25, 21.625, 23.25, 21, 22.125,
> 23, 12), self = c(17.375, 20.375, 20, 20, 18.375, 18.625, 18.625,
> 15.25, 16.5, 18, 16.25, 18, 12.75, 15.5, 18), diff = c(6.125,
> -8.375, 1, 2, 0.75, 2.875, 3.5, 5.125, 1.75, 3.625, 7, 3, 9.375,
> 7.5, -6)), row.names = c(NA, -15L), .Names = c("pair", "pot",
> "cross", "self", "diff"), class = "data.frame")
>
>
>
> -- Michael Friendly Email: friendly AT yorku DOT ca Professor, Psychology
> Dept. York University Voice: 416 736-5115 x66249 Fax: 416 736-5814 4700
> Keele Street Web: http://www.datavis.ca Toronto, ONT M3J 1P3 CANADA
>
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