comment on

And furthering the work of esteemed monk tlm above, the difference is explained completely by whether or not your final step divides by (N-1) or by N.

   Data Set    Div(N-1)   Div N
 ------------ ---------- -------
  condition1    50.73     49.56
  condition2    44.34     43.32
  condition3    52.05     50.85
  condition4    56.39     55.10

use strict;
use warnings;
use List::Util 'sum';

sub sample_sd {
  die unless @_ and ref $_[ 0 ] eq 'ARRAY' and @{ $_[ 0 ] } > 1;
  my $data = shift;
  my $sum = sum @$data;
  my $n = @$data;
  my $mean = $sum/$n;
  my $sq_dev = sum map $_*$_, map $_ - $mean, @$data;
  return sqrt( ( $sq_dev )/( $n - 1 ) );
}

sub sample_sd2 {
  die unless @_ and ref $_[ 0 ] eq 'ARRAY' and @{ $_[ 0 ] } > 1;
  my $data = shift;
  my $sum = sum @$data;
  my $n = @$data;
  my $mean = $sum/$n;
  my $sq_dev = sum map $_*$_, map $_ - $mean, @$data;
  return sqrt( ( $sq_dev )/( $n ) );
}


while ( <DATA> ) {
  my @data = split;
  my $label = shift @data;
  my $sd = sample_sd( \@data );
  my $sd2 = sample_sd2( \@data );
  printf "$label %.2f  %.2f\n", $sd, $sd2;
}

__DATA__
condition1 397 322 350 346 338 324 461 477 432 373 386 412 475 360.5 3
+84 324 424 319 454.5 412 387 370
condition2 360.5 318.5 356 316.5 330 296.5 444 474 416.5 355 320 401.5
+ 363.5 332 363 324 388 312 344 372 347.5 338
condition3 372 354 358 311 336.5 297 485 461 407.5 365 342 428 494 343
+.5 372 324 379.5 345 389 384 363 346
condition4 324 305.5 364 320 327.5 288.5 432.5 434 447 369 315 397.5 5
+15 339 405 330 396 319 345 381.5 340 317
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Update: Which is exactly what the following posts (at least) had attempted to tell you: Re^2: standard deviation accuracy question Re: standard deviation accuracy question and Re^2: standard deviation accuracy question

-Scott

In reply to Re^2: standard deviation accuracy question by 5mi11er
in thread standard deviation accuracy question by Anonymous Monk

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