Generates a matrix of fixed differences and associated statistics for populations taken pairwise
Source:R/gl.fixed.diff.r
gl.fixed.diff.RdThis script takes SNP data or sequence tag P/A data grouped into populations in a genlight object (DArTSeq) and generates a matrix of fixed differences between populations taken pairwise
Usage
gl.fixed.diff(
x,
tloc = 0,
test = FALSE,
delta = 0.02,
alpha = 0.05,
reps = 1000,
mono.rm = TRUE,
pb = FALSE,
verbose = NULL
)Arguments
- x
Name of the genlight object containing SNP genotypes or tag P/A data (SilicoDArT) or an object of class 'fd' [required].
- tloc
Threshold defining a fixed difference (e.g. 0.05 implies 95:5 vs 5:95 is fixed) [default 0].
- test
If TRUE, calculate p values for the observed fixed differences [default FALSE].
- delta
Threshold value for the true population minor allele frequency (MAF) from which resultant sample fixed differences are considered true positives [default 0.02].
- alpha
Level of significance used to display non-significant differences between populations as they are compared pairwise [default 0.05].
- reps
Number of replications to undertake in the simulation to estimate probability of false positives [default 1000].
- mono.rm
If TRUE, loci that are monomorphic across all individuals are removed before beginning computations [default TRUE].
- pb
If TRUE, show a progress bar on time consuming loops [default FALSE].
- verbose
Verbosity: 0, silent or fatal errors; 1, begin and end; 2, progress log; 3, progress and results summary; 5, full report [default 2 or as specified using gl.set.verbosity].
Value
A list of Class 'fd' containing the gl object and square matrices, as follows:
$gl – the output genlight object;
$fd – raw fixed differences;
$pcfd – percent fixed differences;
$nobs – mean no. of individuals used in each comparison;
$nloc – total number of loci used in each comparison;
$expfpos – if test=TRUE, the expected count of false positives for each comparison [by simulation];
$sdfpos – if test=TRUE, the standard deviation of the count of false positives for each comparison [by simulation];
$prob – if test=TRUE, the significance of the count of fixed differences [by simulation])
Details
A fixed difference at a locus occurs when two populations share no alleles or where all members of one population has a sequence tag scored, and all members of the other population has the sequence tag absent. The challenge with this approach is that when sample sizes are finite, fixed differences will occur through sampling error, compounded when many loci are examined. Simulations suggest that sample sizes of n1=5 and n2=5 are adequate to reduce the probability of [experiment-wide] type 1 error to negligible levels [ploidy=2]. A warning is issued if comparison between two populations involves sample sizes less than 5, taking into account allele drop-out.
Optionally, if test=TRUE, the script will test the fixed differences between final OTUs for statistical significance, using simulation, and then further amalgamate populations that for which there are no significant fixed differences at a specified level of significance (alpha). To avoid conflation of true fixed differences with false positives in the simulations, it is necessary to decide a threshold value (delta) for extreme true allele frequencies that will be considered fixed for practical purposes. That is, fixed differences in the sample set will be considered to be positives (not false positives) if they arise from true allele frequencies of less than 1-delta in one or both populations. The parameter delta is typically set to be small (e.g. delta = 0.02).
NOTE: The above test will only be calculated if tloc=0, that is, for analyses of absolute fixed differences. The test applies in comparisons of allopatric populations only. For sympatric populations, use gl.pval.sympatry().
An absolute fixed difference is as defined above. However, one might wish to score fixed differences at some lower level of allele frequency difference, say where percent allele frequencies are 95,5 and 5,95 rather than 100:0 and 0:100. This adjustment can be done with the tloc parameter. For example, tloc=0.05 means that SNP allele frequencies of 95,5 and 5,95 percent will be regarded as fixed when comparing two populations at a locus.
Author
Custodian: Arthur Georges – Post to https://groups.google.com/d/forum/dartr
Examples
# \donttest{
fd <- gl.fixed.diff(testset.gl, tloc=0, verbose=3 )
#> Starting gl.fixed.diff
#> Processing genlight object with SNP data
#> Comparing populations for absolute fixed differences
#> Warning: Monomorphic loci retained, used in calculations
#> Populations, aggregations and sample sizes
#> EmmacBrisWive EmmacBurdMist EmmacBurnBara EmmacClarJack
#> 10 10 11 5
#> EmmacClarYate EmmacCoopAvin EmmacCoopCully EmmacCoopEulb
#> 5 10 10 10
#> EmmacFitzAllig EmmacJohnWari EmmacMaclGeor EmmacMaryBoru
#> 10 10 11 6
#> EmmacMaryPetr EmmacMDBBowm EmmacMDBCond EmmacMDBCudg
#> 4 10 10 10
#> EmmacMDBForb EmmacMDBGwyd EmmacMDBMaci EmmacMDBMurrMung
#> 11 9 10 10
#> EmmacMDBSanf EmmacNormJack EmmacNormLeic EmmacNormSalt
#> 10 6 1 1
#> EmmacRichCasi EmmacRoss EmmacRussEube EmmacTweeUki
#> 10 10 10 10
#> EmsubRopeMata EmvicVictJasp
#> 5 5
#> Warning: Fixed differences can arise through sampling error if sample sizes are small
#> Some sample sizes are small (N < 10, minimum in dataset = 1 )
#> Recommend manually amalgamating populations or setting test=TRUE to allow evaluation of statistical significance
#> Comparing populations pairwise -- this may take time. Please be patient
#> Completed: gl.fixed.diff
#>
fd <- gl.fixed.diff(testset.gl, tloc=0, test=TRUE, delta=0.02, reps=100, verbose=3 )
#> Starting gl.fixed.diff
#> Processing genlight object with SNP data
#> Comparing populations for absolute fixed differences
#> Warning: Monomorphic loci retained, used in calculations
#> Populations, aggregations and sample sizes
#> EmmacBrisWive EmmacBurdMist EmmacBurnBara EmmacClarJack
#> 10 10 11 5
#> EmmacClarYate EmmacCoopAvin EmmacCoopCully EmmacCoopEulb
#> 5 10 10 10
#> EmmacFitzAllig EmmacJohnWari EmmacMaclGeor EmmacMaryBoru
#> 10 10 11 6
#> EmmacMaryPetr EmmacMDBBowm EmmacMDBCond EmmacMDBCudg
#> 4 10 10 10
#> EmmacMDBForb EmmacMDBGwyd EmmacMDBMaci EmmacMDBMurrMung
#> 11 9 10 10
#> EmmacMDBSanf EmmacNormJack EmmacNormLeic EmmacNormSalt
#> 10 6 1 1
#> EmmacRichCasi EmmacRoss EmmacRussEube EmmacTweeUki
#> 10 10 10 10
#> EmsubRopeMata EmvicVictJasp
#> 5 5
#> Warning: Fixed differences can arise through sampling error if sample sizes are small
#> Some sample sizes are small (N < 10, minimum in dataset = 1 )
#> Comparing populations pairwise -- this may take time. Please be patient
#> EmmacBrisWive vs EmmacBurdMist [p = 0.0969 ,ns]
#> EmmacBrisWive vs EmmacBurnBara [p = 0.8722 ,ns]
#> EmmacBrisWive vs EmmacClarJack [p = 0.9351 ,ns]
#> EmmacBrisWive vs EmmacFitzAllig [p = 0.106 ,ns]
#> EmmacBrisWive vs EmmacMaryBoru [p = 0.8162 ,ns]
#> EmmacBrisWive vs EmmacMaryPetr [p = 0.9256 ,ns]
#> EmmacBrisWive vs EmmacMDBMaci [p = 0.727 ,ns]
#> EmmacBrisWive vs EmmacRichCasi [p = 0.9009 ,ns]
#> EmmacBrisWive vs EmmacTweeUki [p = 0.7834 ,ns]
#> EmmacBurdMist vs EmmacBurnBara [p = 0.6691 ,ns]
#> EmmacBurdMist vs EmmacFitzAllig [p = 0.8109 ,ns]
#> EmmacBurdMist vs EmmacJohnWari [p = 0.7057 ,ns]
#> EmmacBurdMist vs EmmacMaclGeor [p = 0.6093 ,ns]
#> EmmacBurdMist vs EmmacMaryBoru [p = 0.6815 ,ns]
#> EmmacBurdMist vs EmmacMaryPetr [p = 0.6643 ,ns]
#> EmmacBurdMist vs EmmacMDBCond [p = 0.1683 ,ns]
#> EmmacBurdMist vs EmmacMDBGwyd [p = 0.056 ,ns]
#> EmmacBurdMist vs EmmacMDBMaci [p = 0.8806 ,ns]
#> EmmacBurdMist vs EmmacNormSalt [p = 0.5438 ,ns]
#> EmmacBurdMist vs EmmacRichCasi [p = 0.8812 ,ns]
#> EmmacBurdMist vs EmmacRoss [p = 0.7234 ,ns]
#> EmmacBurdMist vs EmmacTweeUki [p = 0.7253 ,ns]
#> EmmacBurnBara vs EmmacClarJack [p = 0.8156 ,ns]
#> EmmacBurnBara vs EmmacClarYate [p = 0.8284 ,ns]
#> EmmacBurnBara vs EmmacCoopAvin [p = 0.5475 ,ns]
#> EmmacBurnBara vs EmmacFitzAllig [p = 0.709 ,ns]
#> EmmacBurnBara vs EmmacJohnWari [p = 0.735 ,ns]
#> EmmacBurnBara vs EmmacMaclGeor [p = 0.7245 ,ns]
#> EmmacBurnBara vs EmmacMaryBoru [p = 0.7388 ,ns]
#> EmmacBurnBara vs EmmacMaryPetr [p = 0.7448 ,ns]
#> EmmacBurnBara vs EmmacMDBBowm [p = 0.7847 ,ns]
#> EmmacBurnBara vs EmmacMDBCond [p = 0.8388 ,ns]
#> EmmacBurnBara vs EmmacMDBCudg [p = 0.7698 ,ns]
#> EmmacBurnBara vs EmmacMDBForb [p = 0.8033 ,ns]
#> EmmacBurnBara vs EmmacMDBGwyd [p = 0.7866 ,ns]
#> EmmacBurnBara vs EmmacMDBMaci [p = 0.7969 ,ns]
#> EmmacBurnBara vs EmmacMDBMurrMung [p = 0.875 ,ns]
#> EmmacBurnBara vs EmmacMDBSanf [p = 0.8442 ,ns]
#> EmmacBurnBara vs EmmacNormJack [p = 0.9108 ,ns]
#> EmmacBurnBara vs EmmacNormLeic [p = 0.2927 ,ns]
#> EmmacBurnBara vs EmmacNormSalt [p = 0.7437 ,ns]
#> EmmacBurnBara vs EmmacRichCasi [p = 0.9062 ,ns]
#> EmmacBurnBara vs EmmacRoss [p = 0.6378 ,ns]
#> EmmacBurnBara vs EmmacTweeUki [p = 0.7541 ,ns]
#> EmmacClarJack vs EmmacClarYate [p = 0.6552 ,ns]
#> EmmacClarJack vs EmmacMaclGeor [p = 0.6332 ,ns]
#> EmmacClarJack vs EmmacMaryPetr [p = 0.8225 ,ns]
#> EmmacClarJack vs EmmacMDBBowm [p = 0.7243 ,ns]
#> EmmacClarJack vs EmmacMDBCond [p = 0.793 ,ns]
#> EmmacClarJack vs EmmacMDBCudg [p = 0.6565 ,ns]
#> EmmacClarJack vs EmmacMDBForb [p = 0.7701 ,ns]
#> EmmacClarJack vs EmmacMDBGwyd [p = 0.7244 ,ns]
#> EmmacClarJack vs EmmacRichCasi [p = 0.6378 ,ns]
#> EmmacClarJack vs EmmacTweeUki [p = 0.6616 ,ns]
#> EmmacClarYate vs EmmacMaclGeor [p = 0.6062 ,ns]
#> EmmacClarYate vs EmmacMaryPetr [p = 0.8231 ,ns]
#> EmmacClarYate vs EmmacMDBBowm [p = 0.7866 ,ns]
#> EmmacClarYate vs EmmacMDBCond [p = 0.8451 ,ns]
#> EmmacClarYate vs EmmacMDBCudg [p = 0.6931 ,ns]
#> EmmacClarYate vs EmmacMDBForb [p = 0.8444 ,ns]
#> EmmacClarYate vs EmmacMDBGwyd [p = 0.7545 ,ns]
#> EmmacClarYate vs EmmacMDBMaci [p = 0.8079 ,ns]
#> EmmacClarYate vs EmmacRichCasi [p = 0.6288 ,ns]
#> EmmacClarYate vs EmmacTweeUki [p = 0.6729 ,ns]
#> EmmacCoopAvin vs EmmacCoopCully [p = 0.6187 ,ns]
#> EmmacCoopAvin vs EmmacCoopEulb [p = 0.6173 ,ns]
#> EmmacCoopCully vs EmmacCoopEulb [p = 0.6569 ,ns]
#> EmmacFitzAllig vs EmmacJohnWari [p = 0.8013 ,ns]
#> EmmacFitzAllig vs EmmacMaclGeor [p = 0.6518 ,ns]
#> EmmacFitzAllig vs EmmacMaryBoru [p = 0.6815 ,ns]
#> EmmacFitzAllig vs EmmacMaryPetr [p = 0.7503 ,ns]
#> EmmacFitzAllig vs EmmacMDBBowm [p = 0.8598 ,ns]
#> EmmacFitzAllig vs EmmacMDBCond [p = 0.814 ,ns]
#> EmmacFitzAllig vs EmmacMDBCudg [p = 0.7026 ,ns]
#> EmmacFitzAllig vs EmmacMDBGwyd [p = 0.8316 ,ns]
#> EmmacFitzAllig vs EmmacMDBMaci [p = 0.8035 ,ns]
#> EmmacFitzAllig vs EmmacMDBMurrMung [p = 0.8363 ,ns]
#> EmmacFitzAllig vs EmmacMDBSanf [p = 0.731 ,ns]
#> EmmacFitzAllig vs EmmacNormJack [p = 0.7437 ,ns]
#> EmmacFitzAllig vs EmmacNormSalt [p = 0.578 ,ns]
#> EmmacFitzAllig vs EmmacRichCasi [p = 0.9491 ,ns]
#> EmmacFitzAllig vs EmmacRoss [p = 0.7931 ,ns]
#> EmmacFitzAllig vs EmmacTweeUki [p = 0.8406 ,ns]
#> EmmacJohnWari vs EmmacMaclGeor [p = 0.7358 ,ns]
#> EmmacJohnWari vs EmmacMaryBoru [p = 0.733 ,ns]
#> EmmacJohnWari vs EmmacMaryPetr [p = 0.7147 ,ns]
#> EmmacJohnWari vs EmmacMDBMaci [p = 0.8098 ,ns]
#> EmmacJohnWari vs EmmacNormJack [p = 0.6999 ,ns]
#> EmmacJohnWari vs EmmacNormSalt [p = 0.5495 ,ns]
#> EmmacJohnWari vs EmmacRichCasi [p = 0.836 ,ns]
#> EmmacJohnWari vs EmmacRoss [p = 0.5838 ,ns]
#> EmmacJohnWari vs EmmacRussEube [p = 0.7985 ,ns]
#> EmmacJohnWari vs EmmacTweeUki [p = 0.6442 ,ns]
#> EmmacMaclGeor vs EmmacMaryBoru [p = 0.6978 ,ns]
#> EmmacMaclGeor vs EmmacMaryPetr [p = 0.6836 ,ns]
#> EmmacMaclGeor vs EmmacMDBBowm [p = 0.7569 ,ns]
#> EmmacMaclGeor vs EmmacMDBCond [p = 0.7814 ,ns]
#> EmmacMaclGeor vs EmmacMDBCudg [p = 0.6629 ,ns]
#> EmmacMaclGeor vs EmmacMDBForb [p = 0.8257 ,ns]
#> EmmacMaclGeor vs EmmacMDBGwyd [p = 0.7314 ,ns]
#> EmmacMaclGeor vs EmmacMDBMaci [p = 0.7854 ,ns]
#> EmmacMaclGeor vs EmmacNormLeic [p = 0.057 ,ns]
#> EmmacMaclGeor vs EmmacNormSalt [p = 0.6099 ,ns]
#> EmmacMaclGeor vs EmmacRichCasi [p = 0.6382 ,ns]
#> EmmacMaclGeor vs EmmacRoss [p = 0.72 ,ns]
#> EmmacMaclGeor vs EmmacRussEube [p = 0.058 ,ns]
#> EmmacMaclGeor vs EmmacTweeUki [p = 0.5768 ,ns]
#> EmmacMaryBoru vs EmmacMaryPetr [p = 0.7824 ,ns]
#> EmmacMaryBoru vs EmmacMDBBowm [p = 0.8344 ,ns]
#> EmmacMaryBoru vs EmmacMDBCond [p = 0.8597 ,ns]
#> EmmacMaryBoru vs EmmacMDBCudg [p = 0.7412 ,ns]
#> EmmacMaryBoru vs EmmacMDBGwyd [p = 0.8213 ,ns]
#> EmmacMaryBoru vs EmmacMDBMaci [p = 0.8587 ,ns]
#> EmmacMaryBoru vs EmmacMDBMurrMung [p = 0.8736 ,ns]
#> EmmacMaryBoru vs EmmacMDBSanf [p = 0.814 ,ns]
#> EmmacMaryBoru vs EmmacNormJack [p = 0.8278 ,ns]
#> EmmacMaryBoru vs EmmacNormLeic [p = 0.142 ,ns]
#> EmmacMaryBoru vs EmmacNormSalt [p = 0.5946 ,ns]
#> EmmacMaryBoru vs EmmacRichCasi [p = 0.8755 ,ns]
#> EmmacMaryBoru vs EmmacRoss [p = 0.6949 ,ns]
#> EmmacMaryBoru vs EmmacTweeUki [p = 0.7872 ,ns]
#> EmmacMaryPetr vs EmmacMDBBowm [p = 0.8647 ,ns]
#> EmmacMaryPetr vs EmmacMDBCond [p = 0.8188 ,ns]
#> EmmacMaryPetr vs EmmacMDBCudg [p = 0.769 ,ns]
#> EmmacMaryPetr vs EmmacMDBForb [p = 0.8518 ,ns]
#> EmmacMaryPetr vs EmmacMDBGwyd [p = 0.8452 ,ns]
#> EmmacMaryPetr vs EmmacMDBMaci [p = 0.8089 ,ns]
#> EmmacMaryPetr vs EmmacMDBMurrMung [p = 0.8537 ,ns]
#> EmmacMaryPetr vs EmmacMDBSanf [p = 0.7822 ,ns]
#> EmmacMaryPetr vs EmmacNormJack [p = 0.7536 ,ns]
#> EmmacMaryPetr vs EmmacNormLeic [p = 0.0609 ,ns]
#> EmmacMaryPetr vs EmmacNormSalt [p = 0.7047 ,ns]
#> EmmacMaryPetr vs EmmacRichCasi [p = 0.885 ,ns]
#> EmmacMaryPetr vs EmmacRoss [p = 0.6162 ,ns]
#> EmmacMaryPetr vs EmmacTweeUki [p = 0.814 ,ns]
#> EmmacMDBBowm vs EmmacMDBCond [p = 0.5985 ,ns]
#> EmmacMDBBowm vs EmmacMDBCudg [p = 0.5479 ,ns]
#> EmmacMDBBowm vs EmmacMDBForb [p = 0.5864 ,ns]
#> EmmacMDBBowm vs EmmacMDBGwyd [p = 0.5727 ,ns]
#> EmmacMDBBowm vs EmmacMDBMaci [p = 0.5998 ,ns]
#> EmmacMDBBowm vs EmmacMDBMurrMung [p = 0.6269 ,ns]
#> EmmacMDBBowm vs EmmacMDBSanf [p = 0.5685 ,ns]
#> EmmacMDBBowm vs EmmacNormJack [p = 0.9044 ,ns]
#> EmmacMDBBowm vs EmmacNormLeic [p = 0.9664 ,ns]
#> EmmacMDBBowm vs EmmacNormSalt [p = 0.8513 ,ns]
#> EmmacMDBBowm vs EmmacRoss [p = 0.0542 ,ns]
#> EmmacMDBCond vs EmmacMDBCudg [p = 0.6072 ,ns]
#> EmmacMDBCond vs EmmacMDBForb [p = 0.6413 ,ns]
#> EmmacMDBCond vs EmmacMDBGwyd [p = 0.679 ,ns]
#> EmmacMDBCond vs EmmacMDBMaci [p = 0.6227 ,ns]
#> EmmacMDBCond vs EmmacMDBMurrMung [p = 0.62 ,ns]
#> EmmacMDBCond vs EmmacMDBSanf [p = 0.6014 ,ns]
#> EmmacMDBCond vs EmmacNormJack [p = 0.851 ,ns]
#> EmmacMDBCond vs EmmacNormLeic [p = 0.2825 ,ns]
#> EmmacMDBCond vs EmmacNormSalt [p = 0.8187 ,ns]
#> EmmacMDBCond vs EmmacRichCasi [p = 0.0898 ,ns]
#> EmmacMDBCudg vs EmmacMDBForb [p = 0.6048 ,ns]
#> EmmacMDBCudg vs EmmacMDBGwyd [p = 0.6058 ,ns]
#> EmmacMDBCudg vs EmmacMDBMaci [p = 0.5726 ,ns]
#> EmmacMDBCudg vs EmmacMDBMurrMung [p = 0.5828 ,ns]
#> EmmacMDBCudg vs EmmacMDBSanf [p = 0.5797 ,ns]
#> EmmacMDBCudg vs EmmacNormJack [p = 0.8051 ,ns]
#> EmmacMDBCudg vs EmmacNormLeic [p = 0.1976 ,ns]
#> EmmacMDBCudg vs EmmacNormSalt [p = 0.7818 ,ns]
#> EmmacMDBForb vs EmmacMDBGwyd [p = 0.5599 ,ns]
#> EmmacMDBForb vs EmmacMDBMaci [p = 0.6206 ,ns]
#> EmmacMDBForb vs EmmacMDBMurrMung [p = 0.6338 ,ns]
#> EmmacMDBForb vs EmmacMDBSanf [p = 0.6601 ,ns]
#> EmmacMDBGwyd vs EmmacMDBMaci [p = 0.574 ,ns]
#> EmmacMDBGwyd vs EmmacMDBMurrMung [p = 0.5757 ,ns]
#> EmmacMDBGwyd vs EmmacMDBSanf [p = 0.5921 ,ns]
#> EmmacMDBGwyd vs EmmacNormJack [p = 0.9025 ,ns]
#> EmmacMDBGwyd vs EmmacNormLeic [p = 0.3769 ,ns]
#> EmmacMDBGwyd vs EmmacNormSalt [p = 0.8689 ,ns]
#> EmmacMDBGwyd vs EmmacRichCasi [p = 0.0508 ,ns]
#> EmmacMDBMaci vs EmmacMDBMurrMung [p = 0.5936 ,ns]
#> EmmacMDBMaci vs EmmacMDBSanf [p = 0.6011 ,ns]
#> EmmacMDBMaci vs EmmacNormJack [p = 0.8701 ,ns]
#> EmmacMDBMaci vs EmmacNormLeic [p = 0.2775 ,ns]
#> EmmacMDBMaci vs EmmacNormSalt [p = 0.8091 ,ns]
#> EmmacMDBMaci vs EmmacRichCasi [p = 0.8464 ,ns]
#> EmmacMDBMaci vs EmmacRoss [p = 0.7999 ,ns]
#> EmmacMDBMaci vs EmmacTweeUki [p = 0.7523 ,ns]
#> EmmacMDBMurrMung vs EmmacMDBSanf [p = 0.5575 ,ns]
#> EmmacMDBMurrMung vs EmmacNormJack [p = 0.8694 ,ns]
#> EmmacMDBMurrMung vs EmmacNormLeic [p = 0.2211 ,ns]
#> EmmacMDBMurrMung vs EmmacNormSalt [p = 0.8265 ,ns]
#> EmmacMDBMurrMung vs EmmacRichCasi [p = 0.0691 ,ns]
#> EmmacMDBSanf vs EmmacNormJack [p = 0.7783 ,ns]
#> EmmacMDBSanf vs EmmacNormLeic [p = 0.1643 ,ns]
#> EmmacMDBSanf vs EmmacNormSalt [p = 0.7087 ,ns]
#> EmmacMDBSanf vs EmmacRichCasi [p = 0.0611 ,ns]
#> EmmacNormJack vs EmmacNormLeic [p = 0.7209 ,ns]
#> EmmacNormJack vs EmmacNormSalt [p = 0.6791 ,ns]
#> EmmacNormJack vs EmmacRichCasi [p = 0.7859 ,ns]
#> EmmacNormJack vs EmmacRoss [p = 0.7515 ,ns]
#> EmmacNormJack vs EmmacRussEube [p = 0.8755 ,ns]
#> EmmacNormJack vs EmmacTweeUki [p = 0.7565 ,ns]
#> EmmacNormLeic vs EmmacNormSalt [p = 0.8724 ,ns]
#> EmmacNormLeic vs EmmacRichCasi [p = 0.8646 ,ns]
#> EmmacNormLeic vs EmmacRussEube [p = 0.9669 ,ns]
#> EmmacNormLeic vs EmmacTweeUki [p = 0.8549 ,ns]
#> EmmacNormSalt vs EmmacRichCasi [p = 0.7169 ,ns]
#> EmmacNormSalt vs EmmacRoss [p = 0.6053 ,ns]
#> EmmacNormSalt vs EmmacRussEube [p = 0.6212 ,ns]
#> EmmacNormSalt vs EmmacTweeUki [p = 0.6647 ,ns]
#> EmmacRichCasi vs EmmacRoss [p = 0.8848 ,ns]
#> EmmacRichCasi vs EmmacRussEube [p = 0.2642 ,ns]
#> EmmacRichCasi vs EmmacTweeUki [p = 0.5997 ,ns]
#> EmmacRoss vs EmmacTweeUki [p = 0.7679 ,ns]
#> Completed: gl.fixed.diff
#>
# }