Archive:MANOVA - Revision history

wikademia>Wikademia: moved MANOVA to Archive:MANOVA

2009-06-13T06:49:21Z

← Older revision	Revision as of 06:49, 13 June 2009
(No difference)

wikademia>Wikademia at 16:05, 29 April 2009

2009-04-29T16:05:42Z

← Older revision		Revision as of 16:05, 29 April 2009
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	* The purpose of this tutorial is to teach use of '''multivariate analysis of variance (MANOVA)''', with practical exercises based on using [[SPSS]].		* The purpose of this tutorial is to teach use of '''multivariate analysis of variance (MANOVA)''', with practical exercises based on using [[SPSS]].
	* Note that the MANOVA procedure is not available with the Studentware version of SPSS.		* Note that the MANOVA procedure is not available with the Studentware version of SPSS.
	~~{{RoundBoxBottom}}~~
	~~{{TOCright}}~~
	==What is MANOVA?==		==What is MANOVA?==
	* Developed as a theoretical construct by [[Wikipedia:Samuel S. Wilks\|Samual S. Wilks]] in 1932 (Biometrika).		* Developed as a theoretical construct by [[Wikipedia:Samuel S. Wilks\|Samual S. Wilks]] in 1932 (Biometrika).

wikademia>Wikademia at 16:05, 29 April 2009

2009-04-29T16:05:26Z

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	{{~~RoundBoxTop\|theme=2}}~~		{{ntnes}}
	~~{{tutorial}}~~
	~~{{50%done~~}}
	* The purpose of this tutorial is to teach use of '''multivariate analysis of variance (MANOVA)''', with practical exercises based on using [[SPSS]].		* The purpose of this tutorial is to teach use of '''multivariate analysis of variance (MANOVA)''', with practical exercises based on using [[SPSS]].
	* Note that the MANOVA procedure is not available with the Studentware version of SPSS.		* Note that the MANOVA procedure is not available with the Studentware version of SPSS.

wikademia>Wikademia: Text replace - 'w:' to 'Wikipedia:'

2009-04-11T18:17:26Z

Text replace - 'w:' to 'Wikipedia:'

← Older revision		Revision as of 18:17, 11 April 2009
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	{{TOCright}}		{{TOCright}}
	==What is MANOVA?==		==What is MANOVA?==
	* Developed as a theoretical construct by [[w:Samuel S. Wilks\|Samual S. Wilks]] in 1932 (Biometrika).		* Developed as a theoretical construct by [[Wikipedia:Samuel S. Wilks\|Samual S. Wilks]] in 1932 (Biometrika).
	* An extension of univariate [[ANOVA]] procedures to situations in which there are two or more related [[DV\|dependent variables]] (ANOVA analyses only a single DV at a time). DVs should be correlated (but not overly so; otherwise they should be combined) or conceptually related.		* An extension of univariate [[ANOVA]] procedures to situations in which there are two or more related [[DV\|dependent variables]] (ANOVA analyses only a single DV at a time). DVs should be correlated (but not overly so; otherwise they should be combined) or conceptually related.
	* The MANOVA procedure identifies (inferentially) whether:		* The MANOVA procedure identifies (inferentially) whether:

wikademia>Wikademia: moved Advanced ANOVA/MANOVA to MANOVA

2009-04-10T18:51:17Z

moved Advanced ANOVA/MANOVA to MANOVA

← Older revision	Revision as of 18:51, 10 April 2009
(No difference)

wikademia>Jtneill: /* Multivariate test statistics */

2008-08-27T16:54:24Z

Multivariate test statistics

← Older revision		Revision as of 16:54, 27 August 2008
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	# Considers differences over all the characteristic roots		# Considers differences over all the characteristic roots
	# More robust than Wilks'; should be used when sample size decreases, unequal cell sizes or homogeneity of covariances is violated		# More robust than Wilks'; should be used when sample size decreases, unequal cell sizes or homogeneity of covariances is violated

			==Tests of between-subject effects==
			* If there is a significant multivariate effect, examine the '''Tests of Between-Subjects Effects''' for each of the DVs.
			* Since there are multiple tests, control for the Type I error-rate (e.g., use a Bonferroni adjusment - divide the original alpha level by the number of tests).

	==Effect sizes==		==Effect sizes==

wikademia>Jtneill: /* Test statistics */

2008-08-27T16:50:38Z

Test statistics

← Older revision		Revision as of 16:50, 27 August 2008
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	#* If this assumption is violated, use a more conservative critical <math>/alpha</math> level for determining significance for that variable in the univariate ''F''-test. Tabachnick and Fidell suggest .025 or .01 rather than the conventional .05 level.		#* If this assumption is violated, use a more conservative critical <math>/alpha</math> level for determining significance for that variable in the univariate ''F''-test. Tabachnick and Fidell suggest .025 or .01 rather than the conventional .05 level.

	==~~Test~~ statistics==		==Multivariate test statistics==
	Choose from among these multivariate test statistics to assess whether there are statistically significant differences across the levels of the IV(s) for a linear combination of DVs. In general Wilks' <math>/lambda</math> is recommended unless there are problems with small ''N'', unequal ''n''s, violations of assumptions, etc. in which case Pillai's trace is more robust (Tabachnick & Fidell):		Choose from among these multivariate test statistics to assess whether there are statistically significant differences across the levels of the IV(s) for a linear combination of DVs. In general Wilks' <math>/lambda</math> is recommended unless there are problems with small ''N'', unequal ''n''s, violations of assumptions, etc. in which case Pillai's trace is more robust (Tabachnick & Fidell):
	;Roy's greatest characteristic root		;Roy's greatest characteristic root

wikademia>Jtneill: /* Effect sizes */

2008-08-27T16:50:16Z

Effect sizes

← Older revision		Revision as of 16:50, 27 August 2008
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	==Effect sizes==		==Effect sizes==
	Also use [[effect size]]s to evaluate strength of the effects (particularly for significant effects):		Also use [[effect size]]s to evaluate strength of the effects (particularly for significant effects):
	* ~~Univariate~~ ANOVA: ~~<math>\eta^2</math> gives the proportion of variance in the DV that is attributable to different levels of an IV~~		* Multivariate ANOVA:
	* ~~Multivariate ANOVA:~~ Wilks' <math>\lambda</math> - multivariate <math>\eta^2</math>: Wilks' <math>\lambda</math> reflects the ratio of within-group variance across all discriminant functions to total variance across all discriminant functions.		** Wilks' <math>\lambda</math> - multivariate <math>\eta^2</math>: Wilks' <math>\lambda</math> reflects the ratio of within-group variance across all discriminant functions to total variance across all discriminant functions.
			* Univariate ANOVA:
			** <math>\eta^2</math> gives the proportion of variance in the DV that is attributable to different levels of an IV

	==Follow-up testing==		==Follow-up testing==

wikademia>Jtneill: /* Test statistics */

2008-08-27T16:49:30Z

Test statistics

← Older revision		Revision as of 16:49, 27 August 2008
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	==Test statistics==		==Test statistics==
	Choose from among these test statistics to assess differences across the levels of the IV(s) for ~~the~~ DVs:		Choose from among these multivariate test statistics to assess whether there are statistically significant differences across the levels of the IV(s) for a linear combination of DVs. In general Wilks' <math>/lambda</math> is recommended unless there are problems with small ''N'', unequal ''n''s, violations of assumptions, etc. in which case Pillai's trace is more robust (Tabachnick & Fidell):
	;Roy's greatest characteristic root		;Roy's greatest characteristic root
	# Tests for differences on only the first discriminant function		# Tests for differences on only the first discriminant function

wikademia>Jtneill: /* Assumptions / # '''Homogeneity of error variances (Levene's test)''' # If this assumption is violated, use a more conservative critical $/alpha$ level for determining significance for

2008-08-27T16:46:00Z

Assumptions: # '''Homogeneity of error variances (Levene's test)''' #* If this assumption is violated, use a more conservative critical <math>/alpha</math> level for determining significance for

← Older revision		Revision as of 16:46, 27 August 2008
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	#* The ''F'' test from Box’s ''M'' statistics should be interpreted cautiously because it is a highly sensitive test of the violation of the multivariate normality assumption, particularly with large sample sizes.		#* The ''F'' test from Box’s ''M'' statistics should be interpreted cautiously because it is a highly sensitive test of the violation of the multivariate normality assumption, particularly with large sample sizes.
	#* MANOVA is fairly robust to this assumption where there are equal sample sizes for each cell.		#* MANOVA is fairly robust to this assumption where there are equal sample sizes for each cell.
			# '''Homogeneity of error variances (Levene's test)'''
			#* If this assumption is violated, use a more conservative critical <math>/alpha</math> level for determining significance for that variable in the univariate ''F''-test. Tabachnick and Fidell suggest .025 or .01 rather than the conventional .05 level.

	==Test statistics==		==Test statistics==

Archive:MANOVA - Revision history

wikademia>Wikademia: moved MANOVA to Archive:MANOVA

wikademia>Wikademia at 16:05, 29 April 2009

wikademia>Wikademia at 16:05, 29 April 2009

wikademia>Wikademia: Text replace - 'w:' to 'Wikipedia:'

wikademia>Wikademia: moved Advanced ANOVA/MANOVA to MANOVA

wikademia>Jtneill: /* Multivariate test statistics */

wikademia>Jtneill: /* Test statistics */

wikademia>Jtneill: /* Effect sizes */

wikademia>Jtneill: /* Test statistics */

wikademia>Jtneill: /* Assumptions */ # '''Homogeneity of error variances (Levene's test)''' #* If this assumption is violated, use a more conservative critical /alpha level for determining significance for

wikademia>Jtneill: /* Assumptions / # '''Homogeneity of error variances (Levene's test)''' # If this assumption is violated, use a more conservative critical $/alpha$ level for determining significance for