This file contains documentation of standard output printed by smartpca.  For
general documentation of the smartpca program, see README in this directory.

Parameter values: smartpca prints basic info on parameter values used.

Outliers: smartpca prints a list of outlier individuals removed, if any.

Tracy-Widom statistics: the column of interest is the "p-value" column which
  indicates the statistical significance of each principal component.
  To get Tracy-Widom statistics, you must recompile smartpca in your 
  local src/ directory (and move it to bin/), 
  or just run twstats (see README file in POPGEN directory).

eigbestsnp:  the SNP of maximum weight.  SNP weights are proportional to 
  the correlation (across samples) between each SNP and each PC.  
  Equivalently, PC coordinates of a given sample can be computed as the
  weighted sum of normalized SNP genotypes.

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POPULATION GENETIC STATISTICS (relevant to studying relationships between
populations whose labels are explicitly specified in input indiv file) --

Average divergence between populations: smartpca prints a divergence matrix
  describing divergence between each pair of populations.  Details:
  From the covariance matrix X  whose eigenvectors were computed
  we can compute a "distance" d for each pair of individuals (i,j):
  d(i,j) = X(i,i) + X(j,j) - 2X(i,j)
  For each pair of populations (a,b)
  now define
  D(a,b) = \sum d(i,j) (in pop a, in pop b) / (| popa | * | pop b| )
  an average distance.  We then normalize D so that the diagonal has
  mean 1 and publish D.
  
Fst statistics: prints fst estimate between each pair of populations, 
  along with standard error of the estimate.  
  [If there is only 1 population, no fst statistics are printed.]
  [If phylipoutname parameter is specified, this information is instead 
  printed to an output file in PHYLIP format.  See ./README for details.]

Anova statistics for population differences along each eigenvector:
  For each eigenvector, a P-value for statistical significance of differences
    between each pair of populations along that eigenvector is printed.
    +++ is used to highlight P-values less than 1e-06.
    *** is used to highlight P-values between 1e-06 and 1e-03.
    If there are more than 2 populations, an overall P-value is also printed
      for that eigenvector.
    If there are more than 2 populations, the populations with minimum (minv)
      and maximum (maxv) eigenvector coordinate are also printed.
  [If there is only 1 population, no Anova statistics are printed.]

Statistical significance of differences between populations:
  For each pair of populations, the above Anova statistics are summed
  across eigenvectors.  The result is approximately chisq with
  d.o.f. equal to the number of eigenvectors.  The chisq statistic and
  its p-value are printed.
  [If there is only 1 population, no statistics are printed.]

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Questions? nickp@broad.mit.edu
