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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_STARS_Bullying_Study_alt.wasp
Title produced by softwareChi-Square Test
Date of computationTue, 04 Dec 2012 08:31:53 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/04/t1354627926wgve3zl9x1fzw44.htm/, Retrieved Fri, 09 May 2025 13:59:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=196225, Retrieved Fri, 09 May 2025 13:59:16 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact274

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Chi Square Measure of Association- Free Statistics Software (Calculator)] [Bullying by Gender] [2009-11-23 19:30:44] [98fd0e87c3eb04e0cc2efde01dbafab6]
- R P   [Chi Square Measure of Association- Free Statistics Software (Calculator)] [Bullying by Gende...] [2009-11-24 18:28:32] [b98453cac15ba1066b407e146608df68]
- R       [Chi Square Measure of Association- Free Statistics Software (Calculator)] [STARS Bullying Study] [2009-11-25 00:02:16] [98fd0e87c3eb04e0cc2efde01dbafab6]
-           [Chi Square Measure of Association- Free Statistics Software (Calculator)] [are boys bullied ...] [2009-11-26 12:36:30] [9dc333cea70095e4d9c08ad15f70f6c6]
- RM          [Chi-Square Test] [Week 9 Q1 are boy...] [2012-12-04 12:41:37] [4dc91430d64c29b80ea298de98509adb]
-   P           [Chi-Square Test] [WS9 Q2 Are the bo...] [2012-12-04 13:15:05] [4dc91430d64c29b80ea298de98509adb]
-   P             [Chi-Square Test] [WS9 Q2 ] [2012-12-04 13:22:35] [4dc91430d64c29b80ea298de98509adb]
-   P                 [Chi-Square Test] [WS9 Q3] [2012-12-04 13:31:53] [7c48a7d6ebd2bfa3a852549e2ff25361] [Current]
-   P                   [Chi-Square Test] [WS9 Q4] [2012-12-04 13:42:00] [4dc91430d64c29b80ea298de98509adb]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
'g'	'Many'	'Often'	'Both'	'Outside'	'Same'	'Boys'	'Usually'	'Usually'	'Yes'	'Yes'	'Rarely'
'g'	'Few'	'Not_bul'	'Physical'	'Outside'	'Same'	'Boys'	'Usually'	'Rarely'	'Yes'	'No'	'Dont_bul'
'g'	'Many'	'Rarely'	'Mental'	'Outside'	'Same'	'Girls'	'Dont_know'	'Dont_know'	'Yes'	'No'	'Dont_bul'
'g'	'Many'	'Rarely'	'Mental'	'Not_bul'	'Differnt'	'Boys'	'Dont_know'	'Rarely'	'No'	'Yes'	'Dont_bul'
'b'	'Many'	'Not_bul'	'Physical'	'Not_bul'	'Not_bul'	'Not_bul'	'Dont_know'	'Dont_know'	'Not_bul'	'Not_bul'	'Dont_bul'
'b'	'Many'	'Not_bul'	'Physical'	'Outside'	'Differnt'	'Boys'	'Dont_know'	'Dont_know'	'No'	'No'	'Dont_bul'
'b'	'One'	'Not_bul'	'Not_bul'	'Not_bul'	'Same'	'Not_bul'	'Dont_know'	'Dont_know'	'Not_bul'	'Not_bul'	'Dont_bul'
'g'	'Many'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Dont_know'	'Dont_know'	'Not_bul'	'Not_bul'	'Dont_bul'
'g'	'Few'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Rarely'	'Rarely'	'Not_bul'	'Not_bul'	'Dont_bul'
'b'	'One'	'Rarely'	'Mental'	'Inside'	'Same'	'Boys'	'Dont_know'	'Rarely'	'No'	'No'	'Dont_bul'
'g'	'Many'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Dont_know'	'Rarely'	'Not_bul'	'Not_bul'	'Dont_bul'
'b'	'Few'	'Often'	'Mental'	'Outside'	'Both'	'Boys'	'Rarely'	'Sometimes'	'No'	'No'	'Dont_bul'
'g'	'Many'	'Often'	'Mental'	'Outside'	'Same'	'Both'	'Usually'	'Sometimes'	'No'	'Yes'	'Dont_bul'
'b'	'One'	'Often'	'Both'	'Outside'	'Differnt'	'Boys'	'Rarely'	'Sometimes'	'No'	'No'	'Dont_bul'
'g'	'Many'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Dont_know'	'Rarely'	'Not_bul'	'Not_bul'	'Dont_bul'
'g'	'Many'	'Not_bul'	'Mental'	'Not_bul'	'Not_bul'	'Not_bul'	'Dont_know'	'Dont_know'	'Not_bul'	'Not_bul'	'Dont_bul'
'b'	'Many'	'Rarely'	'Mental'	'Not_bul'	'Differnt'	'Boys'	'Sometimes'	'Sometimes'	'Not_bul'	'Not_bul'	'Dont_bul'
'b'	'Many'	'Rarely'	'Both'	'Both'	'Both'	'Boys'	'Rarely'	'Usually'	'Yes'	'Yes'	'Rarely'
'b'	'Many'	'Not_bul'	'Mental'	'Outside'	'Differnt'	'Boys'	'Dont_know'	'Usually'	'No'	'No'	'Dont_bul'
'g'	'Many'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Sometimes'	'Sometimes'	'Yes'	'Yes'	'Dont_bul'
'b'	'Few'	'Rarely'	'Not_bul'	'Outside'	'Differnt'	'Boys'	'Dont_know'	'Dont_know'	'No'	'No'	'Dont_bul'
'b'	'Few'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Usually'	'Dont_know'	'Not_bul'	'Not_bul'	'Dont_bul'
'g'	'Few'	'Not_bul'	'Not_bul'	'Inside'	'Same'	'Boys'	'Rarely'	'Dont_know'	'No'	'Yes'	'Dont_bul'
'g'	'Few'	'Often'	'Mental'	'Outside'	'Differnt'	'Girls'	'Dont_know'	'Dont_know'	'No'	'No'	'Dont_bul'
'b'	'Many'	'Often'	'Both'	'Outside'	'Differnt'	'Boys'	'Usually'	'Rarely'	'No'	'Yes'	'Rarely'
'b'	'Few'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Dont_know'	'Rarely'	'Not_bul'	'Not_bul'	'Dont_bul'
'b'	'Many'	'Not_bul'	'Mental'	'Not_bul'	'Not_bul'	'Boys'	'Dont_know'	'Usually'	'Yes'	'No'	'Dont_bul'
'b'	'Few'	'Rarely'	'Both'	'Outside'	'Differnt'	'Boys'	'Dont_know'	'Dont_know'	'Yes'	'Yes'	'Dont_bul'
'b'	'Many'	'Often'	'Both'	'Outside'	'Same'	'Boys'	'Dont_know'	'Sometimes'	'No'	'No'	'Dont_bul'
'g'	'Few'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Dont_know'	'Dont_know'	'Not_bul'	'Not_bul'	'Dont_bul'
'b'	'Many'	'Often'	'Both'	'Both'	'Same'	'Both'	'Usually'	'Usually'	'Yes'	'Yes'	'Often'
'g'	'One'	'Often'	'Mental'	'Outside'	'Differnt'	'Both'	'Sometimes'	'Usually'	'No'	'Yes'	'Dont_bul'
'b'	'Many'	'Often'	'Both'	'Both'	'Differnt'	'Both'	'Usually'	'Rarely'	'Yes'	'Yes'	'Dont_bul'
'g'	'Many'	'Rarely'	'Physical'	'Outside'	'Differnt'	'Boys'	'Dont_know'	'Dont_know'	'No'	'No'	'Dont_bul'
'b'	'Few'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Dont_know'	'Sometimes'	'Not_bul'	'Not_bul'	'Dont_bul'
'g'	'Many'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Dont_know'	'Rarely'	'Not_bul'	'Not_bul'	'Dont_bul'
'b'	'Many'	'Often'	'Mental'	'Inside'	'Differnt'	'Boys'	'Sometimes'	'Sometimes'	'No'	'Yes'	'Dont_bul'
'g'	'Many'	'Often'	'Mental'	'Inside'	'Differnt'	'Both'	'Dont_know'	'Usually'	'Yes'	'Yes'	'Often'
'b'	'Many'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Dont_know'	'Dont_know'	'Not_bul'	'Not_bul'	'Dont_bul'
'g'	'Few'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Dont_know'	'Dont_know'	'Not_bul'	'Not_bul'	'Dont_bul'
'g'	'None'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Dont_know'	'Sometimes'	'Not_bul'	'Not_bul'	'Dont_bul'
'b'	'Many'	'Rarely'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Dont_know'	'Rarely'	'Not_bul'	'Not_bul'	'Dont_bul'
'g'	'Few'	'Rarely'	'Both'	'Not_bul'	'Same'	'Girls'	'Rarely'	'Rarely'	'No'	'Yes'	'Rarely'
'g'	'Many'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Dont_know'	'Sometimes'	'Not_bul'	'Not_bul'	'Dont_bul'
'b'	'Few'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Dont_know'	'Dont_know'	'Not_bul'	'Not_bul'	'Dont_bul'
'g'	'Many'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Dont_know'	'Rarely'	'Not_bul'	'Not_bul'	'Rarely'
'b'	'Few'	'Rarely'	'Physical'	'Outside'	'Differnt'	'Boys'	'Rarely'	'Sometimes'	'Yes'	'No'	'Rarely'
'g'	'Many'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Dont_know'	'Dont_know'	'Not_bul'	'Not_bul'	'Dont_bul'
'g'	'Few'	'Often'	'Mental'	'Outside'	'Differnt'	'Girls'	'Usually'	'Rarely'	'No'	'Yes'	'Dont_bul'
'g'	'Many'	'Often'	'Both'	'Outside'	'Differnt'	'Both'	'Dont_know'	'Sometimes'	'Yes'	'Yes'	'Rarely'
'b'	'Few'	'Rarely'	'Physical'	'Outside'	'Differnt'	'Boys'	'Usually'	'Dont_know'	'No'	'No'	'Dont_bul'
'g'	'Few'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Dont_know'	'Dont_know'	'Not_bul'	'Not_bul'	'Dont_bul'
'b'	'Many'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Dont_know'	'Dont_know'	'Not_bul'	'Not_bul'	'Dont_bul'
'g'	'Many'	'Rarely'	'Mental'	'Both'	'Both'	'Boys'	'Sometimes'	'Sometimes'	'No'	'No'	'Rarely'
'b'	'Many'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Sometimes'	'Rarely'	'Not_bul'	'Not_bul'	'Rarely'
'b'	'Few'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Dont_know'	'Sometimes'	'Not_bul'	'Not_bul'	'Dont_bul'
'g'	'Many'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Usually'	'Sometimes'	'Not_bul'	'Not_bul'	'Dont_bul'
'g'	'Many'	'Rarely'	'Mental'	'Outside'	'Same'	'Girls'	'Sometimes'	'Usually'	'No'	'Yes'	'Dont_bul'
'g'	'Many'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Usually'	'Dont_know'	'Not_bul'	'Not_bul'	'Dont_bul'
'g'	'Many'	'Often'	'Not_bul'	'Outside'	'Same'	'Boys'	'Usually'	'Sometimes'	'Yes'	'Yes'	'Dont_bul'
'g'	'Many'	'Often'	'Mental'	'Both'	'Both'	'Girls'	'Usually'	'Usually'	'No'	'Yes'	'Often'
'g'	'Many'	'Rarely'	'Mental'	'Outside'	'Same'	'Girls'	'Dont_know'	'Rarely'	'Yes'	'Yes'	'Often'
'b'	'Many'	'Often'	'Both'	'Both'	'Differnt'	'Boys'	'Sometimes'	'Sometimes'	'No'	'Yes'	'Dont_bul'
'b'	'Many'	'Rarely'	'Both'	'Outside'	'Differnt'	'Boys'	'Sometimes'	'Dont_know'	'No'	'Yes'	'Rarely'
'g'	'None'	'Rarely'	'Not_bul'	'Outside'	'Not_bul'	'Girls'	'Dont_know'	'Dont_know'	'Yes'	'No'	'Dont_bul'
'b'	'One'	'Rarely'	'Mental'	'Outside'	'Same'	'Boys'	'Dont_know'	'Dont_know'	'Yes'	'No'	'Rarely'
'g'	'Few'	'Rarely'	'Mental'	'Outside'	'Same'	'Girls'	'Dont_know'	'Rarely'	'Yes'	'Yes'	'Often'
'b'	'Few'	'Often'	'Mental'	'Outside'	'Same'	'Boys'	'Usually'	'Dont_know'	'No'	'Yes'	'Rarely'
'b'	'Many'	'Not_bul'	'Mental'	'Not_bul'	'Not_bul'	'Not_bul'	'Rarely'	'Rarely'	'Not_bul'	'Not_bul'	'Dont_bul'
'b'	'Many'	'Often'	'Physical'	'Inside'	'Same'	'Boys'	'Rarely'	'Sometimes'	'No'	'Yes'	'Often'
'g'	'Few'	'Rarely'	'Mental'	'Outside'	'Same'	'Girls'	'Rarely'	'Rarely'	'No'	'Yes'	'Dont_bul'
'b'	'Many'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Dont_know'	'Dont_know'	'Not_bul'	'Not_bul'	'Dont_bul'
'g'	'Many'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Usually'	'Sometimes'	'Not_bul'	'Not_bul'	'Dont_bul'
'b'	'Many'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Usually'	'Dont_know'	'Not_bul'	'Not_bul'	'Dont_bul'
'g'	'Few'	'Rarely'	'Both'	'Both'	'Both'	'Both'	'Usually'	'Usually'	'Yes'	'Yes'	'Rarely'
'g'	'Many'	'Rarely'	'Mental'	'Both'	'Both'	'Both'	'Sometimes'	'Sometimes'	'No'	'Yes'	'Rarely'
'g'	'Many'	'Not_bul'	'Mental'	'Not_bul'	'Not_bul'	'Not_bul'	'Dont_know'	'Sometimes'	'Not_bul'	'Not_bul'	'Dont_bul'
'b'	'Many'	'Rarely'	'Mental'	'Outside'	'Same'	'Boys'	'Sometimes'	'Sometimes'	'No'	'No'	'Rarely'
'b'	'Many'	'Rarely'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Rarely'	'Sometimes'	'Not_bul'	'Not_bul'	'Dont_bul'
'b'	'Many'	'Rarely'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Sometimes'	'Sometimes'	'Not_bul'	'Not_bul'	'Dont_bul'
'b'	'Many'	'Often'	'Mental'	'Outside'	'Same'	'Boys'	'Usually'	'Sometimes'	'No'	'No'	'Dont_bul'
'g'	'One'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Dont_know'	'Dont_know'	'Not_bul'	'Not_bul'	'Dont_bul'
'g'	'Many'	'Rarely'	'Mental'	'Outside'	'Same'	'Both'	'Dont_know'	'Sometimes'	'No'	'No'	'Rarely'
'g'	'Few'	'Not_bul'	'Mental'	'Both'	'Same'	'Both'	'Sometimes'	'Sometimes'	'No'	'No'	'Dont_bul'
'g'	'Few'	'Often'	'Physical'	'Outside'	'Differnt'	'Both'	'Dont_know'	'Dont_know'	'Yes'	'Yes'	'Dont_bul'
'b'	'Few'	'Often'	'Not_bul'	'Outside'	'Same'	'Boys'	'Usually'	'Dont_know'	'No'	'No'	'Rarely'
'b'	'Few'	'Often'	'Physical'	'Not_bul'	'Differnt'	'Boys'	'Rarely'	'Rarely'	'Yes'	'No'	'Rarely'
'g'	'Many'	'Not_bul'	'Mental'	'Inside'	'Same'	'Not_bul'	'Sometimes'	'Sometimes'	'Yes'	'No'	'Dont_bul'
'b'	'Many'	'Often'	'Mental'	'Inside'	'Differnt'	'Boys'	'Dont_know'	'Sometimes'	'No'	'Yes'	'Rarely'
'b'	'Many'	'Rarely'	'Mental'	'Both'	'Both'	'Boys'	'Dont_know'	'Dont_know'	'Yes'	'Yes'	'Rarely'
'g'	'Few'	'Often'	'Mental'	'Both'	'Same'	'Girls'	'Rarely'	'Dont_know'	'No'	'Yes'	'Rarely'
'g'	'Many'	'Often'	'Mental'	'Both'	'Same'	'Girls'	'Sometimes'	'Dont_know'	'Yes'	'Yes'	'Dont_bul'
'b'	'Many'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Dont_know'	'Dont_know'	'Not_bul'	'Not_bul'	'Dont_bul'
'g'	'Many'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Dont_know'	'Dont_know'	'Not_bul'	'Not_bul'	'Dont_bul'
'b'	'Many'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Usually'	'Rarely'	'Not_bul'	'Not_bul'	'Dont_bul'
'g'	'Many'	'Not_bul'	'Mental'	'Not_bul'	'Not_bul'	'Not_bul'	'Dont_know'	'Rarely'	'Not_bul'	'Not_bul'	'Dont_bul'
'g'	'Many'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Dont_know'	'Rarely'	'Not_bul'	'Not_bul'	'Dont_bul'
'g'	'Few'	'Often'	'Mental'	'Outside'	'Not_bul'	'Both'	'Usually'	'Rarely'	'No'	'Yes'	'Dont_bul'
'g'	'One'	'Often'	'Both'	'Both'	'Both'	'Girls'	'Sometimes'	'Sometimes'	'Yes'	'Yes'	'Dont_bul'
'g'	'Many'	'Often'	'Mental'	'Outside'	'Same'	'Girls'	'Dont_know'	'Sometimes'	'No'	'Yes'	'Rarely'
'g'	'Many'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Usually'	'Sometimes'	'Not_bul'	'Not_bul'	'Dont_bul'
'g'	'Many'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Sometimes'	'Dont_know'	'Not_bul'	'Not_bul'	'Dont_bul'
'b'	'Many'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Usually'	'Sometimes'	'Not_bul'	'Not_bul'	'Dont_bul'
'g'	'Many'	'Rarely'	'Mental'	'Both'	'Same'	'Girls'	'Sometimes'	'Sometimes'	'Yes'	'Yes'	'Dont_bul'
'g'	'Many'	'Often'	'Mental'	'Both'	'Both'	'Boys'	'Dont_know'	'Dont_know'	'Yes'	'No'	'Dont_bul'
'b'	'Few'	'Rarely'	'Mental'	'Both'	'Both'	'Boys'	'Sometimes'	'Sometimes'	'No'	'No'	'Dont_bul'
'b'	'Many'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Dont_know'	'Dont_know'	'Not_bul'	'Not_bul'	'Dont_bul'
'g'	'Many'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Dont_know'	'Dont_know'	'Not_bul'	'Not_bul'	'Dont_bul'
'b'	'Many'	'Often'	'Physical'	'Both'	'Differnt'	'Boys'	'Sometimes'	'Sometimes'	'Not_bul'	'No'	'Dont_bul'
'g'	'Many'	'Often'	'Both'	'Inside'	'Same'	'Girls'	'Dont_know'	'Sometimes'	'Yes'	'Yes'	'Often'
'g'	'Many'	'Rarely'	'Physical'	'Outside'	'Same'	'Boys'	'Sometimes'	'Sometimes'	'No'	'No'	'Dont_bul'
'b'	'Many'	'Often'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Dont_know'	'Dont_know'	'Not_bul'	'Not_bul'	'Rarely'
'g'	'Many'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Dont_know'	'Dont_know'	'Not_bul'	'Not_bul'	'Dont_bul'
'b'	'Few'	'Often'	'Both'	'Outside'	'Both'	'Boys'	'Sometimes'	'Rarely'	'Yes'	'No'	'Dont_bul'
'b'	'Many'	'Often'	'Not_bul'	'Outside'	'Both'	'Boys'	'Sometimes'	'Sometimes'	'No'	'No'	'Often'
'b'	'Few'	'Rarely'	'Physical'	'Outside'	'Same'	'Boys'	'Rarely'	'Rarely'	'No'	'No'	'Dont_bul'
'b'	'Many'	'Not_bul'	'Both'	'Outside'	'Differnt'	'Boys'	'Sometimes'	'Rarely'	'No'	'No'	'Dont_bul'
'g'	'Many'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Dont_know'	'Dont_know'	'Not_bul'	'Not_bul'	'Dont_bul'
'g'	'Many'	'Often'	'Both'	'Both'	'Both'	'Boys'	'Dont_know'	'Sometimes'	'No'	'Yes'	'Dont_bul'
'b'	'Many'	'Rarely'	'Both'	'Outside'	'Both'	'Boys'	'Dont_know'	'Sometimes'	'No'	'Yes'	'Rarely'
'b'	'Many'	'Often'	'Physical'	'Outside'	'Same'	'Boys'	'Rarely'	'Rarely'	'No'	'Yes'	'Rarely'
'g'	'Many'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Dont_know'	'Dont_know'	'Not_bul'	'Not_bul'	'Dont_bul'
'g'	'Many'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Dont_know'	'Dont_know'	'Not_bul'	'Not_bul'	'Dont_bul'
'g'	'Few'	'Rarely'	'Mental'	'Inside'	'Same'	'Girls'	'Dont_know'	'Sometimes'	'No'	'No'	'Rarely'
'g'	'One'	'Often'	'Mental'	'Both'	'Same'	'Girls'	'Dont_know'	'Rarely'	'No'	'Yes'	'Rarely'
'g'	'Few'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Sometimes'	'Sometimes'	'Not_bul'	'Not_bul'	'Rarely'
'b'	'Many'	'Rarely'	'Mental'	'Outside'	'Differnt'	'Boys'	'Dont_know'	'Sometimes'	'No'	'No'	'Dont_bul'
'g'	'Few'	'Rarely'	'Mental'	'Outside'	'Same'	'Boys'	'Rarely'	'Rarely'	'No'	'Yes'	'Rarely'
'g'	'Many'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Dont_know'	'Sometimes'	'Not_bul'	'Not_bul'	'Dont_bul'
'b'	'Many'	'Rarely'	'Mental'	'Both'	'Both'	'Boys'	'Rarely'	'Sometimes'	'Yes'	'No'	'Often'
'g'	'Many'	'Rarely'	'Physical'	'Outside'	'Differnt'	'Boys'	'Sometimes'	'Dont_know'	'Yes'	'Yes'	'Dont_bul'
'g'	'Many'	'Rarely'	'Both'	'Outside'	'Both'	'Boys'	'Sometimes'	'Dont_know'	'No'	'Yes'	'Dont_bul'
'g'	'Many'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Sometimes'	'Sometimes'	'Not_bul'	'Not_bul'	'Rarely'
'g'	'Many'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Rarely'	'Usually'	'Not_bul'	'Not_bul'	'Dont_bul'
'b'	'Many'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Sometimes'	'Sometimes'	'Not_bul'	'Not_bul'	'Often'
'g'	'Many'	'Often'	'Mental'	'Outside'	'Same'	'Girls'	'Rarely'	'Sometimes'	'No'	'No'	'Rarely'
'b'	'Many'	'Rarely'	'Physical'	'Outside'	'Same'	'Boys'	'Sometimes'	'Dont_know'	'Yes'	'Yes'	'Dont_bul'
'b'	'Many'	'Rarely'	'Mental'	'Outside'	'Differnt'	'Boys'	'Dont_know'	'Rarely'	'No'	'No'	'Rarely'
'g'	'Few'	'Often'	'Mental'	'Outside'	'Both'	'Both'	'Usually'	'Dont_know'	'Yes'	'No'	'Dont_bul'
'g'	'Many'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Dont_know'	'Dont_know'	'Not_bul'	'Not_bul'	'Dont_bul'
'b'	'Many'	'Not_bul'	'Both'	'Outside'	'Not_bul'	'Not_bul'	'Dont_know'	'Sometimes'	'Not_bul'	'Not_bul'	'Rarely'
'g'	'Few'	'Often'	'Mental'	'Outside'	'Differnt'	'Boys'	'Dont_know'	'Dont_know'	'No'	'No'	'Dont_bul'
'b'	'Many'	'Rarely'	'Mental'	'Outside'	'Both'	'Boys'	'Dont_know'	'Usually'	'No'	'No'	'Dont_bul'
'g'	'Few'	'Rarely'	'Mental'	'Both'	'Same'	'Boys'	'Dont_know'	'Sometimes'	'No'	'No'	'Dont_bul'
'g'	'Few'	'Often'	'Mental'	'Outside'	'Same'	'Girls'	'Dont_know'	'Sometimes'	'No'	'Yes'	'Dont_bul'
'b'	'Many'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Usually'	'Dont_know'	'Not_bul'	'Not_bul'	'Dont_bul'
'g'	'Many'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Usually'	'Sometimes'	'Not_bul'	'Not_bul'	'Dont_bul'
'g'	'One'	'Rarely'	'Mental'	'Outside'	'Same'	'Girls'	'Dont_know'	'Rarely'	'No'	'No'	'Dont_bul'
'b'	'Many'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Dont_know'	'Dont_know'	'Not_bul'	'Not_bul'	'Dont_bul'
'b'	'Many'	'Often'	'Both'	'Outside'	'Same'	'Boys'	'Usually'	'Sometimes'	'No'	'Yes'	'Dont_bul'
'g'	'Few'	'Often'	'Both'	'Outside'	'Same'	'Boys'	'Sometimes'	'Sometimes'	'No'	'Yes'	'Rarely'
'g'	'Many'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Dont_know'	'Usually'	'Not_bul'	'Not_bul'	'Dont_bul'
'g'	'Few'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Sometimes'	'Dont_know'	'Not_bul'	'Not_bul'	'Dont_bul'
'b'	'Many'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Sometimes'	'Rarely'	'Not_bul'	'Not_bul'	'Dont_bul'
'g'	'Many'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Dont_know'	'Dont_know'	'Not_bul'	'Not_bul'	'Dont_bul'
'g'	'Many'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Dont_know'	'Dont_know'	'Not_bul'	'Not_bul'	'Dont_bul'
'g'	'Many'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Dont_know'	'Dont_know'	'Not_bul'	'Not_bul'	'Dont_bul'
'b'	'Many'	'Rarely'	'Both'	'Outside'	'Same'	'Boys'	'Dont_know'	'Sometimes'	'No'	'No'	'Dont_bul'
'b'	'Many'	'Often'	'Mental'	'Outside'	'Both'	'Boys'	'Sometimes'	'Sometimes'	'No'	'No'	'Rarely'
'g'	'Many'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Dont_know'	'Dont_know'	'Not_bul'	'Not_bul'	'Dont_bul'
'b'	'Many'	'Rarely'	'Mental'	'Outside'	'Same'	'Boys'	'Dont_know'	'Sometimes'	'No'	'No'	'Rarely'
'g'	'None'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Dont_know'	'Sometimes'	'Not_bul'	'Not_bul'	'Dont_bul'
'b'	'Many'	'Often'	'Mental'	'Outside'	'Same'	'Boys'	'Dont_know'	'Sometimes'	'No'	'No'	'Rarely'
'b'	'Many'	'Rarely'	'Physical'	'Outside'	'Same'	'Boys'	'Rarely'	'Sometimes'	'No'	'No'	'Dont_bul'
'b'	'Few'	'Rarely'	'Mental'	'Outside'	'Same'	'Boys'	'Usually'	'Rarely'	'Yes'	'No'	'Dont_bul'
'g'	'Many'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Dont_know'	'Sometimes'	'Not_bul'	'Not_bul'	'Dont_bul'
'b'	'Many'	'Often'	'Mental'	'Outside'	'Differnt'	'Boys'	'Sometimes'	'Rarely'	'No'	'No'	'Rarely'
'g'	'Many'	'Often'	'Both'	'Both'	'Both'	'Boys'	'Sometimes'	'Dont_know'	'No'	'No'	'Rarely'
'b'	'Many'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Dont_know'	'Sometimes'	'Not_bul'	'Not_bul'	'Often'
'g'	'One'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Dont_know'	'Dont_know'	'Not_bul'	'Not_bul'	'Dont_bul'
'b'	'Many'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Sometimes'	'Usually'	'Not_bul'	'Not_bul'	'Dont_bul'
'b'	'Many'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Usually'	'Dont_know'	'Not_bul'	'Not_bul'	'Dont_bul'
'g'	'Many'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Usually'	'Dont_know'	'Not_bul'	'Not_bul'	'Dont_bul'
'g'	'Many'	'Often'	'Mental'	'Not_bul'	'Not_bul'	'Both'	'Sometimes'	'Sometimes'	'Yes'	'Yes'	'Dont_bul'
'b'	'Many'	'Rarely'	'Physical'	'Outside'	'Same'	'Boys'	'Dont_know'	'Sometimes'	'Yes'	'Yes'	'Dont_bul'
'b'	'Many'	'Often'	'Mental'	'Inside'	'Not_bul'	'Both'	'Sometimes'	'Sometimes'	'No'	'Yes'	'Often'
'g'	'Many'	'Rarely'	'Mental'	'Inside'	'Same'	'Boys'	'Dont_know'	'Sometimes'	'No'	'No'	'Dont_bul'
'g'	'Few'	'Often'	'Not_bul'	'Outside'	'Same'	'Both'	'Dont_know'	'Dont_know'	'Not_bul'	'Not_bul'	'Dont_bul'
'b'	'Many'	'Rarely'	'Physical'	'Outside'	'Differnt'	'Boys'	'Sometimes'	'Sometimes'	'Yes'	'Yes'	'Rarely'
'g'	'Many'	'Rarely'	'Both'	'Both'	'Both'	'Both'	'Sometimes'	'Sometimes'	'No'	'No'	'Dont_bul'
'b'	'Many'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Dont_know'	'Rarely'	'Not_bul'	'Not_bul'	'Dont_bul'
'b'	'Many'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Sometimes'	'Sometimes'	'Not_bul'	'Not_bul'	'Dont_bul'
'g'	'Many'	'Rarely'	'Mental'	'Outside'	'Differnt'	'Boys'	'Rarely'	'Sometimes'	'No'	'No'	'Dont_bul'
'b'	'Few'	'Rarely'	'Mental'	'Outside'	'Differnt'	'Boys'	'Dont_know'	'Dont_know'	'No'	'Yes'	'Dont_bul'
'g'	'Many'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Dont_know'	'Dont_know'	'Not_bul'	'Not_bul'	'Dont_bul'
'b'	'Many'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Usually'	'Dont_know'	'Not_bul'	'Not_bul'	'Dont_bul'
'g'	'Many'	'Not_bul'	'Mental'	'Not_bul'	'Not_bul'	'Not_bul'	'Sometimes'	'Sometimes'	'Not_bul'	'Not_bul'	'Dont_bul'
'b'	'Few'	'Rarely'	'Physical'	'Not_bul'	'Differnt'	'Boys'	'Usually'	'Sometimes'	'No'	'No'	'Dont_bul'
'g'	'Many'	'Not_bul'	'Mental'	'Not_bul'	'Not_bul'	'Not_bul'	'Dont_know'	'Rarely'	'Not_bul'	'Not_bul'	'Dont_bul'
'g'	'Many'	'Often'	'Both'	'Both'	'Same'	'Both'	'Dont_know'	'Sometimes'	'No'	'Yes'	'Often'
'b'	'Many'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Usually'	'Usually'	'Not_bul'	'Not_bul'	'Dont_bul'
'g'	'Many'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Usually'	'Dont_know'	'Not_bul'	'Not_bul'	'Dont_bul'
'b'	'Many'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Not_bul'	'Dont_know'	'Usually'	'Not_bul'	'Not_bul'	'Dont_bul'

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=196225&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=196225&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=196225&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net






Tabulation of Results
how_often_bullied x gender_of_bully
BothBoysGirlsNot_bul
Not_bul16080
Often1327111
Rarely437103

\begin{tabular}{lllllllll}
\hline
Tabulation of Results \tabularnewline
how_often_bullied  x  gender_of_bully \tabularnewline
  & Both & Boys & Girls & Not_bul \tabularnewline
Not_bul & 1 & 6 & 0 & 80 \tabularnewline
Often & 13 & 27 & 11 & 1 \tabularnewline
Rarely & 4 & 37 & 10 & 3 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=196225&T=1

[TABLE]
[ROW][C]Tabulation of Results[/C][/ROW]
[ROW][C]how_often_bullied  x  gender_of_bully[/C][/ROW]
[ROW][C] [/C][C]Both[/C][C]Boys[/C][C]Girls[/C][C]Not_bul[/C][/ROW]
[C]Not_bul[/C][C]1[/C][C]6[/C][C]0[/C][C]80[/C][/ROW]
[C]Often[/C][C]13[/C][C]27[/C][C]11[/C][C]1[/C][/ROW]
[C]Rarely[/C][C]4[/C][C]37[/C][C]10[/C][C]3[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=196225&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=196225&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Tabulation of Results
how_often_bullied x gender_of_bully
BothBoysGirlsNot_bul
Not_bul16080
Often1327111
Rarely437103






Tabulation of Expected Results
how_often_bullied x gender_of_bully
BothBoysGirlsNot_bul
Not_bul8.1131.559.4737.87
Often4.8518.865.6622.63
Rarely5.0419.595.8823.5

\begin{tabular}{lllllllll}
\hline
Tabulation of Expected Results \tabularnewline
how_often_bullied  x  gender_of_bully \tabularnewline
  & Both & Boys & Girls & Not_bul \tabularnewline
Not_bul & 8.11 & 31.55 & 9.47 & 37.87 \tabularnewline
Often & 4.85 & 18.86 & 5.66 & 22.63 \tabularnewline
Rarely & 5.04 & 19.59 & 5.88 & 23.5 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=196225&T=2

[TABLE]
[ROW][C]Tabulation of Expected Results[/C][/ROW]
[ROW][C]how_often_bullied  x  gender_of_bully[/C][/ROW]
[ROW][C] [/C][C]Both[/C][C]Boys[/C][C]Girls[/C][C]Not_bul[/C][/ROW]
[C]Not_bul[/C][C]8.11[/C][C]31.55[/C][C]9.47[/C][C]37.87[/C][/ROW]
[C]Often[/C][C]4.85[/C][C]18.86[/C][C]5.66[/C][C]22.63[/C][/ROW]
[C]Rarely[/C][C]5.04[/C][C]19.59[/C][C]5.88[/C][C]23.5[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=196225&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=196225&T=2

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Tabulation of Expected Results
how_often_bullied x gender_of_bully
BothBoysGirlsNot_bul
Not_bul8.1131.559.4737.87
Often4.8518.865.6622.63
Rarely5.0419.595.8823.5






Statistical Results
Pearson's Chi-squared test
Chi Square Statistic162.69
Degrees of Freedom6
P value0

\begin{tabular}{lllllllll}
\hline
Statistical Results \tabularnewline
Pearson's Chi-squared test \tabularnewline
Chi Square Statistic & 162.69 \tabularnewline
Degrees of Freedom & 6 \tabularnewline
P value & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=196225&T=3

[TABLE]
[ROW][C]Statistical Results[/C][/ROW]
[ROW][C]Pearson's Chi-squared test[/C][/ROW]
[ROW][C]Chi Square Statistic[/C][C]162.69[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]6[/C][/ROW]
[ROW][C]P value[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=196225&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=196225&T=3

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Statistical Results
Pearson's Chi-squared test
Chi Square Statistic162.69
Degrees of Freedom6
P value0


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 3 ; par2 = 7 ; par3 = Pearson Chi-Square ;
Parameters (R input):
par1 = 3 ; par2 = 7 ; par3 = Pearson Chi-Square ;
R code (references can be found in the software module):
cat1 <- as.numeric(par1) #
cat2<- as.numeric(par2) #
simulate.p.value=FALSE
if (par3 == 'Exact Pearson Chi Square by simulation') simulate.p.value=TRUE
x <- t(x)
(z <- array(unlist(x),dim=c(length(x[,1]),length(x[1,]))))
(table1 <- table(z[,cat1],z[,cat2]))
(V1<-dimnames(y)[[1]][cat1])
(V2<-dimnames(y)[[1]][cat2])
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Tabulation of Results',ncol(table1)+1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,paste(V1,' x ', V2),ncol(table1)+1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, ' ', 1,TRUE)
for(nc in 1:ncol(table1)){
a<-table.element(a, colnames(table1)[nc], 1, TRUE)
}
a<-table.row.end(a)
for(nr in 1:nrow(table1) ){
a<-table.element(a, rownames(table1)[nr], 1, TRUE)
for(nc in 1:ncol(table1) ){
a<-table.element(a, table1[nr, nc], 1, FALSE)
}
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')
(cst<-chisq.test(table1, simulate.p.value=simulate.p.value) )
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Tabulation of Expected Results',ncol(table1)+1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,paste(V1,' x ', V2),ncol(table1)+1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, ' ', 1,TRUE)
for(nc in 1:ncol(table1)){
a<-table.element(a, colnames(table1)[nc], 1, TRUE)
}
a<-table.row.end(a)
for(nr in 1:nrow(table1) ){
a<-table.element(a, rownames(table1)[nr], 1, TRUE)
for(nc in 1:ncol(table1) ){
a<-table.element(a, round(cst$expected[nr, nc], digits=2), 1, FALSE)
}
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Statistical Results',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, cst$method, 2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Chi Square Statistic', 1, TRUE)
a<-table.element(a, round(cst$statistic, digits=2), 1,FALSE)
a<-table.row.end(a)
if(!simulate.p.value){
a<-table.row.start(a)
a<-table.element(a, 'Degrees of Freedom', 1, TRUE)
a<-table.element(a, cst$parameter, 1,FALSE)
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a, 'P value', 1, TRUE)
a<-table.element(a, round(cst$p.value, digits=2), 1,FALSE)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable2.tab')