Context and data played a role in eliciting some misconceptions. For example, consider the
results for the four main misconceptions. The use of chance cannot be measured mathematically
does not seem to depend on data or context. The compound approach is influenced by data but not
influenced by context. The approach was used more often when the compositions of bags/spinners
were quite different from each other than they are equal or close. Actually, when the compositions
were quite different from each other, the results from using the compound approach are in
agreement with those that could be deduced from probability calculations. The outcome approach is
influenced by context but may not be influenced by data (whether using a 50% chance elicits more
outcome approach responses is still unclear). Both context and data affect the equiprobability bias.
More equiprobable responses were observed in drawing names’ items than drawing marbles or
spinning arrowhead items, and also more equiprobable responses were observed when the
compositions were close than when they were far apart. It may be that students' familiarity with
drawing a name, where everyone has an equal chance (all names are equiprobable) leads to more
equiprobability misconceptions. When the data are close some students use the specific version of
equiprobability, namely that if the chances are close they are the same in practice, resulting in more
equiprobability responses.