D91623405 D92525008

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D91623405 ???D92525008 ???

• Simple statistics tools for gene expression
  arrays
• http//microarray.cpmc.columbia.edu/pavlidis
  /pub/stats/web/
• NIA Array Analysis Tool.htm
• http//lgsun.grc.nia.nih.gov/ANOVA/index.html
• Perl module (StatisticsKruskalWallis,ttest)
• Mann-Whitney U Test 1http//eatworms.swmed.edu/
  leon/core_2002/stats/formulas.htmutest
• the Rank Products methods of Breitling et
  alrankproducts_FDR.pl
• Multiclass discovery in array data.htm
• http//www.thep.lu.se/markus/software/classdisco
  verer/index.html.

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Simple statistics tools for gene expression
arrays-1

• Analysis of variance and t-tests
• ttest Do a two-sided ttest with or without Welch
  correction. This program include some
  nonparametric tests as options (the Mann-Whitney
  "U" test and the rank-transformed t-test).
• anova-oneway
• Do a one-way analysis of variance with a balanced
  design.
• anova-twoway-norep
• Do a two-way analysis of variance, when there
  are no replicates.
• anova-twoway-withrep
• Do a two-way analysis of variance, when there are
  replicates with a balanced design.

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Command lines to run the analyses on the test
files

• ttest -r testdata.txt ttest-layout.txt gt
  testdata-ttest.out
• anova-oneway -r testdata.txt anova-oneway-layout
  .txt gt testdata-anova-oneway.out
• anova-twoway-withrep -r testdata.txt
  anova-twoway-withrep-layout.txt gt
  testdata-anova-twoway-withrep.out

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testdata.txt 12(sameple) x30(gene)
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Layout(ttest, anova-oneway, anova-twoway-withre
p)
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ttest.out ttest -r testdata.txt
ttest-layout.txt gt testdata-ttest.out
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ttest

• Perform various two-sided statistical analyses of
  data that is divided into two groups, including
  the Student's t-test.
• -r format line needs to be removed
• -w use Welch approximate t
• -m do mann-whitney U (a.k.a. Wilcoxon) test
• -rank use rank transformation of the data
• -l log transform the data
• ttest -r -rank affydatafile.txt
  affydatafile-layout /usr/local/bin/sort -gk 3
  gt! test.rank.out

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anova-oneway.outanova-oneway -r testdata.txt
anova-oneway-layout.txt gt testdata-anova-oneway.o
ut
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anova-twoway-withrep.outanova-twoway-withrep
-r testdata.txt anova-twoway-withrep-layout.txt gt
testdata-anova-twoway-withrep.out
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NIA Array Analysis Tool-anova_oneway
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NIA Array Analysis Tool-anova_oneway

• The major advantage of ANOVA versus simple t-test
  is that variances are averaged over all factor
  levels, thus the statistics become more stable.
• In ANOVA we calculate the F-statistics which is
  then used to estimate P-value and determine if
  the variation between means is significant.
• Testing multiple hypotheses with ANOVA (as in the
  case of microarray data) may require some
  modifications in ANOVA like variance averaging,
  and FDR.

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Comparing 2 tissues with 1-dye arraysInput
Example (2 tissues, 1-dye arrays)
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Comparing multiple tissues with 2-dye
arraysInput Example (3 tissues, 2-dye arrays)
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Comparing 2 tissues with 2-dye arraysInput
Example (2 tissues, 2-dye arrays, dye swap)
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Comparing multiple tissues with 2-dye
arraysExample(3 tissues, 2-dye arrays, universal
reference(UR))
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Visualization of a data set with no
replicationsExample of an input file (1-dye
arrays)
Because your data has no replications, no
statistical analysis will be done. Only
visualization will be available by pair-wise
comparison of tissues, PAC, and hierarchical
clustering. Note that hierarchical clustering is
available only if you have not more than 20
tissues for comparison.
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Kruskal-Wallis test-1

• Perl module, use to test if differences exist
  between 3 or more independant groups of unequal
  sizes.
• StatisticsKruskalWallis
• Also includes the post-hoc Newman-Keuls test, to
  test if the differences between pairs of the
  tested group are significant

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Kruskal-Wallis test-2input and output

• use StatisticsKruskalWallis use strict
• my _at_group_1 (6.4,6.8,7.2,8.3,8.4,9.1,9.4,9.7),
  
• _at_group_2 (2.5,3.7,4.9,5.4,5.9,8.1,8
  .2),
• _at_group_3 (1.3,4.1,4.9,5.2,5.5,8.2)
  
• my kw new StatisticsKruskalWallis
• kw-gtload_data('group 1',_at_group_1)
• kw-gtload_data('group 2',_at_group_2)
• kw-gtload_data('group 3',_at_group_3)
• my (H,p_value) kw-gtperform_kruskal_wallis_tes
  t
• print "Kruskal Wallis statistic is H\n"
• print "p value for test is p_value\n"

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Kruskal-Wallis test-3Newman-Keuls test

• (q,p) kw-gtpost_hoc('Newman-Keuls','group
  1','group 2')
• print "Newman-Keuls statistic for groups 1,2 is
  q, p value p\n"
• (q,p) kw-gtpost_hoc('Newman-Keuls','group
  2','group 3')
• print "Newman-Keuls statistic for groups 2,3 is
  q, p value p\n"

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Kruskal-Wallis test-4 kruskalwallis.perl

• Jussi Karlgren, SICS, 2003. jussi_at_sics.se
• Usage kruskalwallis.perl -c ltCategorial_Columngt
  -v ltValue_Columngt
• require "getopts.pl"
• print "Kruskal-Wallis test statistic H - refer
  to khi2 tables with df degrees of freedom.\n"

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Ttestperl module

• my ttest new StatisticsTTest
• ttest-gtset_significance(90)
• ttest-gtload_data(\_at_r1,\_at_r2)
• ttest-gtoutput_t_test()
• ttest-gtset_significance(99)
• ttest-gtprint_t_test()

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Mann-Whitney U Test 1http//eatworms.swmed.edu/
leon/core_2002/stats/formulas.htmutest
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Mann-Whitney U Test 2(Wilcoxon Rank Sum Test)

• http//eatworms.swmed.edu/leon/core_2002/stats/fo
  rmulas.htmutest
• Utest.c
• Utable.pl

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Multiclass discovery in array data-1http//www.th
ep.lu.se/markus/software/classdiscoverer/index.ht
ml.
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Multiclass discovery in array data-2

• An unsupervised classification method for
  discovery of classes in array data.
• For two classes the Wilcoxon test is used to
  find discriminatory genes. For more than two
  classes the Kruskal-Wallis test is used.
• The Perl modules AlgorithmNumericalShuffle,
  POSIX, StatisticsDistributions, Storable, and
  TieRefHash.

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• For discovery of two classes, P values from
  random permutation tests are stored in the file
  'pvalues.data' in binary format using the CPAN
  module Storable. If 'pvalues.data' is not
  compatible with your system you have to generate
  one using the included 'generate_pvalues.pl'
  program.
• The file 'pvalues.data' contains results for
  which the total number of experiments is
  maximally 100. If you are analysing a data set
  with more than 100 experiments and do not want to
  perform the permutation tests every time, you
  have to modify the subroutine 'new' in
  'WilcoxonTest.pm'.
• Y. Liu and M. Ringner, Multiclass discovery in
  array data, BMC Bioinformatics 5, 70 (2004)
• class_discoverer.pl - multiclass discovery in
  array data
• Genes Exp_1 Exp_2 Exp_3 Exp_4
• Gene_1 0 0 0 0
• Gene_2 1 1 1
• Gene_3 -1 -1 -1 -1
• Gene_4 0 1 2 3