Information Technology Reference
In-Depth Information
A second source of dependence can occur when participants in an
experimental situation are allowed to communicate with each other about
the task demands of the experiment. Such “contamination” may cause
participants to influence each others behavior. An example of this is a
group problem-solving study.
A third type of dependence situation occurs when the error component
of each observation falls into a cyclical pattern typically due to participants'
data being collected near each other in time and entered sequentially into
the data set. This propinquity of the cases to each other in time, sometimes
referred to as
autocorrelation
, may produce residual error components that
are not independent of each other.
5.2.4 DETERMININGWHEN YOU HAVE VIOLATED ERROR
INDEPENDENCE
Unlike the other two assumptions of normality and equality of vari-
ances, determining when your data have violated the assumption of error
independence involves more complex diagnostic statistical analysis more
typically performed in the domain of multiple regression analysis. For
example, Cohen, Cohen, West, and Aiken (2003) discuss various diag-
nostics for detecting nonindependence of residuals, including plotting
the residuals against an ordered numeric variable such as case number
and computing the
Durbin-Watson
statistic (see Durbin & Watson, 1950,
1951, 1971).
5.2.5 CONSEQUENCE OF VIOLATING ERROR INDEPENDENCE
Hays (1981) and Stevens (2002) both consider independence to be a “very
serious” statistical assumption for ANOVA, one that is often either ignored
or dismissed as relatively inconsequential by investigators in the social
and behavioral sciences. The consequence of violating the independence
assumption is inflation of the targeted alpha (
α
) level. As Stevens (2002)
notes, “Just a small amount of dependence among the observations causes
the actual
α
to be several times greater than the level of significance”
(p. 259).
5.2.6 SOLUTIONS TO VIOLATION OF INDEPENDENCE OF ERRORS
There is no easy-to-apply remedy for violating the independence of errors
assumption; rather, the goal is to prevent the situation from occurring in
the first place. The general maxim that is offered by writers (e.g., Cohen
et al., 2003; Keppel & Wickens, 2004) is to randomly sample cases from a
population, randomly assign the cases to treatment conditions, and ensure
that the treatment conditions are independent of each other. In this regard
Winer et al. (1991) have this to say:
Violating the assumption of random sampling of elements from a popula-
tion and random assignment of the elements to the treatments may totally
invalidate any study, since randomness provides the assurance that errors are
independently distributed within and between treatment conditions and is also
the mechanism by which bias is removed from treatment conditions. (p. 101)
