Multilevel Data Issues
What is Appropriate Unit of Analysis?
The individual student?
the class?
the school?
the school district?
the state?
Comments & Opinions
Sherif, 1963 - Even within a given discipline, researchers use different units of analysis depending, among other things, on the theoretical orientation and the type of variables and measures they use.
Hannan & Young, 1976 - "Despite the long history of concern and the recent upsurge of interest in the problem, a great deal of current research practice appears virtually unaffected."
Cronbach, 1976 - "The majority of studies of educational effects - whether classroom experiments, or evaluations of programs, or surveys - have collected and analyzed data in ways that have concealed more than they reveal. The established methods have generated false conclusions in many studies."
Cross-level inferences
When findings obtained from data collected using one unit of analysis are used to make
inferences about another unit of analysis.
Example: correlations between IQ & achievement made at the school level used to draw conclusions
about correlations among individual students.
Most discussions of cross-level inference are concerned with inferences made from
aggregates to individuals.
A Question?
Why not study the relation between variables using the unit of interest?
It may not be feasible to collect data on individuals or to match data for individuals
across variables.
Some Examples
(Thorndike, 1939) - Correlation bewteen IQ and number of pupils per room for 12 districts.
Within each district r = 0. When districts were aggregated into one large group, r = .45.
When the averages for IQ and room size were used, r = .90
(Robinson, 1950) - Correlation between race and literacy, in individuals r = .203.
When aggregated at the state level, r = .773.
Three Partitions
Within Groups
Between Groups
Total
Partitioning Sums of Squares
Correlations
Regression Coefficients
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UCLA Department of Education
Phil Ender, 29Jan98