Li, Jari, and Mike,
If you *really* don't like nonparametics, try a permutation t-test. Here's the
code for Mike's data, as well as the output I got after running it with 9999
permutations:
> #input the data into x, use g to determine the groups that data go into
> x<-c(13,0,10,2,0,0,1,0,0,1,5,0,0,1,0,0,0,0,0,0,0,1)
> g<-factor(c(1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2))
>
> #set up a matix a with nothing in it
> a<-c()
>
> #split x into two groups, defined by g
> x.g <- split(x,g)
> x.g
$`1`
[1] 13 0 10 2 0 0 1 0 0 1 5
$`2`
[1] 0 0 1 0 0 0 0 0 0 0 1
>
> # do a t-test, report the results
> z <- t.test(x.g$"1",x.g$"2", var.equal = TRUE)
> z
Two Sample t-test
data: x.g$"1" and x.g$"2"
t = 1.9807, df = 20, p-value = 0.06154
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-0.1449011 5.5994465
sample estimates:
mean of x mean of y
2.9090909 0.1818182
>
> #permute the data, split again and report
> xperm <- sample(x,NROW(x))
> xperm
[1] 0 1 1 0 13 1 0 0 10 0 0 0 1 0 0 0 0 5 0 0 0 2
> xperm.g <- split(xperm,g)
> xperm.g
$`1`
[1] 0 1 1 0 13 1 0 0 10 0 0
$`2`
[1] 0 1 0 0 0 0 5 0 0 0 2
>
> #permute the data 9999 times, and every time,
> # compute a t-value, store its absolute value in matrix a
> for(i in 1:9999) {
+ xperm <- sample(x,NROW(x))
+ xperm.g <- split(xperm,g)
+ z <- t.test(xperm.g$"1",xperm.g$"2", var.equal = TRUE)
+ a[i] <- abs(z$statistic)
+ }
>
> #recompute the absolute value of the t-value,
> # store it in the 10000 position of the array, report the matrix a
> x.g <- split(x,g)
> z <- t.test(x.g$"1",x.g$"2")
> a[10000] <- abs(z$statistic)
> #a
> #show rank of your actual t-value against
> # all the other t-values from the permutations
> rank(a)[10000]
[1] 9517.5
>
> #calculate p-value as proportion of t-values from permuations that
> # are greater than your actual t-value;
> # what is the chance that your t could be found just by chance?, or
> # "How likely is it that if the null hypothesis were true, I would
> # observe a value this extreme just due to chance?"
> # It is worth knowing that Fisher used randomization tests to test the value
> of
> # the t-test, F-tests, etc.
> p <- (10000-rank(a)[10000])/10000
> p
[1] 0.04825
So note that the P you get from this is less than 0.05!
Like any permutation test, the P is only approximate.
Cheers, Rick
On Mar 24, 2014, at 8:45 AM, Li Wen
<li....@environment.nsw.gov.au<mailto:li....@environment.nsw.gov.au>> wrote:
HI, Jari
The default in the Welch t test (an adaptive student's t test) doesn't assume
equal variance; but student's t-test do assume normal distribution.
Cheers
Li
-----Original Message-----
From:
r-sig-ecology-boun...@r-project.org<mailto:r-sig-ecology-boun...@r-project.org>
[mailto:r-sig-ecology-boun...@r-project.org] On Behalf Of Jari Oksanen
Sent: Monday, 24 March 2014 10:43 PM
To: Richard Boyce;
r-sig-ecology@r-project.org<mailto:r-sig-ecology@r-project.org>
Subject: Re: [R-sig-eco] report out by t.test
Except that t-test does not assume that *observations* are normally
distributed, nor that variances are equal.
Avoid non-parametric tests: they assume too much of data properties.
For var.equal assumption in t.test, see ?t.test.
Cheers, Jari Oksanen
________________________________________
From:
r-sig-ecology-boun...@r-project.org<mailto:r-sig-ecology-boun...@r-project.org>
[r-sig-ecology-boun...@r-project.org<mailto:r-sig-ecology-boun...@r-project.org>]
on behalf of Richard Boyce [boy...@nku.edu<mailto:boy...@nku.edu>]
Sent: 24 March 2014 13:23
To: r-sig-ecology@r-project.org<mailto:r-sig-ecology@r-project.org>
Subject: Re: [R-sig-eco] report out by t.test
Mike,
There is no way that your data meet the assumptions of a t-test (normal
distributions, equal variance). A nonparametric Mann-Whitney (aka Wilcoxon)
test is much better suited to your data.
Here's what I got when I ran it:
Q<-c(13,0,10,2,0,0,1,0,0,1,5)
WD<-c(0,0,1,0,0,0,0,0,0,0,1)
wilcox.test(Q,WD)
Wilcoxon rank sum test with continuity correction
data: Q and WD
W = 86.5, p-value = 0.05119
alternative hypothesis: true location shift is not equal to 0
Warning message:
In wilcox.test.default(Q, WD) : cannot compute exact p-value with ties
This has a p-value quite close to 0.05, giving some evidence that there's a
difference between your groups. Note that this you have different null and
alternative hypothesis: groups are the same vs. groups are different.
Rick Boyce
On Mar 24, 2014, at 7:00 AM,
r-sig-ecology-requ...@r-project.org<mailto:r-sig-ecology-requ...@r-project.org><mailto:r-sig-ecology-requ...@r-project.org>
wrote:
Message: 1
Date: Sun, 23 Mar 2014 14:21:41 -0700
From: Michael Marsh
<sw...@blarg.net<mailto:sw...@blarg.net><mailto:sw...@blarg.net>>
To:
r-sig-ecology@r-project.org<mailto:r-sig-ecology@r-project.org><mailto:r-sig-ecology@r-project.org>
Subject: [R-sig-eco] report out by t.test
Message-ID:
<532f5065.7030...@blarg.net<mailto:532f5065.7030...@blarg.net><mailto:532f5065.7030...@blarg.net>>
Content-Type: text/plain; charset=ISO-8859-1; format=flowed
I test differences between frequency of hits of exotic annual forbs in plots on
two sites, Q and WD.
Q<-c(13,0,10,2,0,0,1,0,0,1,5)
WD<-c(0,0,1,0,0,0,0,0,0,0,1)
t.test(Q,WD)
Welch Two Sample t-test
data: Q and WD
t = 1.9807, df = 10.158, p-value = 0.07533 alternative hypothesis: true
difference in means is not equal to 0
95 percent confidence interval:
-0.3342006 5.7887460
sample estimates:
mean of x mean of y
2.9090909 0.1818182
The p-value is greater than 0.05, thus does not reach the 95% confidence level,
yet the difference in means is reported as not equal to 0.
Am I encountering a one-sided versus two sided comparison that I don't
understand, or is ther another explanation?
Mike Marsh
================================
Richard L. Boyce, Ph.D.
Director, Environmental Science Program
Professor
Department of Biological Sciences, SC 150 Northern Kentucky University Nunn
Drive Highland Heights, KY 41099 USA
859-572-1407 (tel.)
859-572-5639 (fax)
boy...@nku.edu<mailto:boy...@nku.edu><mailto:boy...@nku.edu>
http://www.nku.edu/~boycer/
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Highland Heights, KY 41099 USA
859-572-1407 (tel.)
859-572-5639 (fax)
boy...@nku.edu<mailto:boy...@nku.edu>
http://www.nku.edu/~boycer/
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exciting discoveries." - A.A. Milne
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