Repeated measures ANOVA

2009-01-03T18:01:30Z

88.192.37.9: /* Why use? */

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The purpose of this tutorial is teach the use of '''repeated measures ANOVAs''', including one-way repeated measures, 2-way within-subjects ANOVA, and mixed designs. Practical exercises are based on using [[SPSS]].
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==Overview==
The '''repeated measures design''' is also known as a '''within-subject design'''. In this design, participants may present scores for:
# A measure repeated over '''''time'''''<br>(e.g., [[w:Self-confidence|self-confidence]] before, after, and following-up a psycho-social intervention), and/or
# A measure repeated cross more than one '''''condition'''''<br>(e.g., experimental and control conditions), and/or
# Several related, comparable measures<br>(e.g., sub-scales of an [[IQ]] test).

Repeated-measures designs can also be understood as an extension of the '''paired-samples t-test''' (to include comparison between more than two repeated measures).

Repeated-measures designs may also be combined with between-subjects factors to create mixed-design ANOVA. Multiple repeated-measures designs can also be tested using '''MANOVAs'''.

==Why to use?==
By collecting data from the same participants under repeated conditions:
* Individual differences can be reduced/eliminated as a source of between-groups differences (which helps to create a more powerful test).
* Inferential testing becomes more powerful (the sample size is not divided between conditions/groups)

==Possible designs==
# '''One-way repeated measures''' - repeated measures across one [[IV]]
# '''Two-way repeated measures''' - repeated measures across two IVs
# '''Two-way mixed split-plot design (SPANOVA)''' - repeated measures on one IV, independent groups on another IV

==Assumptions==
Most of the assumptions for between-subjects ANOVA design apply, however the key variation is that instead of the '''homogeneity of variance assumption''', repeated-measures designs have the assumption of '''Sphericity''' which means that the variance of the population difference scores for any two conditions should be the same as the variance of the population difference scores for any other two conditions.
# Tested by [[w:Mauchly's sphericity test|Mauchly's sphericity test]].
# When the significance level of Mauchly’s test is < 0.05 then sphericity cannot be assumed.
# Note: the sphericity assumption is only relevant to the univariate (one-way) RM ANOVA. This assumption is commonly violated and so it is generally not recommended to use the univariate analyses – the ''p''-values tend to be inaccurate to the extent that this assumption is violated. The alternative, a multivariate test, does not require the assumption of sphericity and is therefore recommended. The multivariate test is conducted on difference scores and evaluates whether the population means for the sets of difference scores are simultaneously equal to zero.

In addition, for SPANOVA, consider '''homogeneity of intercorrelations''':
# The pattern of intercorrelations across the levels of the repeated measures factor should be consistent from level to level of the between subjects factor
# Tested using Box's ''M'' statistic.

==Exercises==
# One-way repeated measures ANOVA:
#* [http://www.pearsoned.com.au/wpsBridge/francis5/files/AQUES.sav AQUES.sav] - Francis 3.3.7, p. 66 (5th ed.)
# Two-way repeated measures
#* [http://www.pearsoned.com.au/wpsBridge/francis5/files/Repmeas.sav Repmeas.sav] - Francis 3.3.8.2, p. 76 (5th ed.)
# Mixed ANOVA
#* [http://www.pearsoned.com.au/wpsBridge/francis5/files/AQUES.sav AQUES.sav] - Francis 3.3.8.3, p. 81 (5th ed.)

==Example write-up==

==Background==
The researcher wanted to determine whether the average husband wants to express his worries to his wife more or less the longer they are married. The researcher developed the Desire to Express Worry scale (DEW) and had 30 husbands answer the questionnaire when they initially got married, and then after 5, 10, and 15 years of marriage.

==Results==
A one-way within-subjects analysis of variance (ANOVA) was conducted with the within-subjects factor being Time (four levels indicating the number of years married) and the dependent variable being the Desire to Express Worry Scale (DEW) scores. The means and standard deviations for the DEW scors are presented in Table 1. The assumptions for ANOVA were met (explain in more detail).

The ANOVA indicated a significant time effect, Wilks’ <math>\lambda</math> = 0.62, ''F'' (3,27) = 5.57, ''p'' = .004, multivariate <math>\eta^2</math> =.38. Follow-up polynomial contrasts indicated a significant linear effect with means decreasing over time, ''F'' (1,29) = 11.56, ''p'' =.002, <math>\eta</math><math>_p^2</math> =.29. Higher-order polynomial contrasts were not significant. Men were increasingly less likely to desire to express worry to their wives with increasing years of marriage. It should be noted that there was little change in the means from 0 to 5 years, and therefore the the significant trend was due to changes after 5 years of marriage. These results suggest that men are more eager to express worry to their wives early in marriage, and that this desire decreases after 5 years of marrriage(also add a Figure and possibly pairwise, Cohen's ''d'' effect sizes).

Table 1<br>
''Means and Standard Deviations for DEW Scores''
<center>
{|
|-
! Number of years married
! ''M''
! ''SD''
|-
| 0 years
| 65.8
| 9.23
|-
| 5 years
| 65.43
| 10.69
|-
| 10 years
| 63.1
| 10.68
|-
| 15 years
| 61.93
| 12.57
|}
</center>
Note: [[Skewness]] and [[kurtosis]] should be added to the table. Perhaps a marginal total would also be appropriate.

==References==
* Baguley, T. (2004). ''[http://www.abdn.ac.uk/~psy317/personal/files/teaching/spheric.htm An introduction to sphericity]''.
==See also==
* [[Mixed-design ANOVA‎]]
* [[w:Repeated measures design|Repeated measures design]] (Wikipedia)
* [[w:Sphericity#Sphericity in statistics|Sphericity]] (Wikipedia)

==External links==
===University of Canberra===
* [http://ucspace.canberra.edu.au/display/RMPE/Repeated+measures+ANOVA Repeated measures ANOVA] (ucspace)
** [http://ucspace.canberra.edu.au/download/attachments/45090985/RM+ANOVA+Notes.doc Repeated measures ANOVA Notes] (Handout)

===Other===
* [http://davidmlane.com/hyperstat/within-subjects.html Chapter 14 Within-Subjects ANOVA] (HyperStat Online)

===Effect sizes===
* [http://wilderdom.com/301/Cohensd.xls Cohensd.xls]

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Sisu

2007-04-20T19:41:32Z

88.192.149.254:

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[[Image:Monument to the Finnish sisu.jpg|thumb|left|280px|"Monument to the Finnish sisu" on a [[fell]] in [[Lapland]]]]

'''Sisu''' is a [[Finnish language|Finnish]] term that could be roughly translated into [[English language|English]] as strength of will, determination, perseverance, and acting rationally in the face of adversity. The equivalent in English is "to have guts", and indeed, the word derives from ''sisus'', which means something inner or interior. However, sisu has a long-term element in it; it is not momentary courage, but the ability to sustain the same. To [[anthropology|anthropologists]], it is an appropriate invention for a cold northern land, dotted by thousands of lakes, and long under threat of being overwhelmed, militarily, linguistically and otherwise, by more powerful neighbours. Similar concepts exist among other cold-weather peoples, such as the [[Inuit]] and [[Chukchi people|Chukchi]].

Due to its cultural significance, ''Sisu'' is a common element of [[brand name]]s in [[Finland]]. For example, there are [[Sisu Auto|Sisu brand cars]] (and [[Sisu XA-180|armored vehicles]]), a brand of strong-tasting candy manufactured by [http://www.leaf.fi Leaf], and an anti-Swedish language, anti-immigration nationalist organisation [http://www.suomensisu.org Suomen Sisu]. Mount Sisu is the name of a mountain discovered by mountain climber [[Veikka Gustafsson]] in the Antarctic.

The term is commonly used in everyday speech to describe stoic toughness. It is widely understood in the [[Upper Peninsula of Michigan|Upper Peninsula]] of [[Michigan]], which is home to a large concentration of Finnish-Americans. For instance: ''Even after cutting his hand open and getting 12 stitches, he didn't shed a tear. Wow! He's got sisu!'' This has extended to include a popular bumper sticker saying simply "Sisu". By analogy, the term has picked up new meanings. Depending on context, "sisu" can refer to spunk, attitude, self-confidence, and so on. However, sisu is not [[bravery]], nor strength, and needs to be distinguished from [[courage]], especially when talking about the military. In contrast, sisu is an ability to finish the task and get things done, as defined by [[Roman Schatz]] in his book ''From Finland with Love'' (2005) and decisiveness. Usually sisu means will and decisiveness to get the things done against impossible odds, or to succeed when given the [[chinaman's chance]].

Sisu can be either good or bad, but the usual meaning is good. Bad sisu (Finnish ''paha sisu'') means malice combined with ruthlessness and implacability: it means relentless strive for mischief, persecution and vengeance (compare [[chutzpah]]). It is in a sense the mirror image of good sisu. Finnish expression ''pahansisuinen'' implies "audacious", "implacable", "full of affrontery", "malevolent" etc with aggressive overtones. The verb ''sisuuntua'' refers to getting angry, but with an element of determination and even being unforgiving. The idiom ''meni sisu kaulaan'' ("the sisu went to the throat [or neck]") returns to the original meaning, "innards"; "get a lump in one's throat", as in become too intimidated to act.

==External link==
*[http://www.washingtonpost.com/wp-dyn/content/article/2006/03/22/AR2006032201943.html Washington Post: The Finnish Line], about Finnish fortitude and resilience

[[Category:Finnish culture]]
[[Category:Upper Peninsula of Michigan]]

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[[fr:Sisu]]
[[ru:Сису]]
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Repeated measures ANOVA

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