Informal Inference
The informal inference construct refers to students' emerging competence to make inferences by reasoning about distribution and variation. As inference inevitably involves comparison to a standard or expectation, we often use examples involving inferences about differences between two distributions.
Because both distributions are visible to students, this approach to inference is likely to be a more natural entrée for novices than the conventional approach of modeling population parameters of a single distribution.
Levels
1 Base reasoning on personal experience or belief instead of the data.
2 Believe that samples predict but use literal copy as the basis of prediction.
3 Particular cases or values, including sample statistics, guide inference without reference to the likely variability of these values.
4 Make inferences based on emerging understanding of distributional characteristics; expect the shape of the data to remain relatively stable.
5 Base reasoning on regions of distribution that are quantified via proportion or percentage.
6 Consider data in one observation set to comprise a sample distributionally related to other samples or a population.
7 Coordinate ideas about sample-to-sample stability and variation to reason about samples as representing sets from populations.