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# Difficulties with informal inference

Informal inference uses evidence collected from samples to make generalisations about underlying populations, acknowledging the degree of uncertainty associated with the generalisation.

In the early years, data collected by students may be treated as a population with no questions asked other than about the data collected.

However, students at year 6 should start to realise that the purpose of statistical investigations is to make claims outside of the data set they collected or are considering.

The following questions may help students to gain this understanding.

• How much difference in two plots of samples would suggest a difference in the underlying populations?
• With points on a scatter plot, how close to a straight line do they have to be for a strong association between the two variables?

With comparative box plots, what overlap would indicate that there is no difference in the underlying populations?

## Is there a difference?

Students need to judge if a difference in two samples suggests a difference in the two underlying populations.

## Meaningful differences

How much difference is required to claim a meaningful difference in two data sets and their underlying populations? Answering this question is not easy for beginners.

## Differences in heights

Differences in samples can suggest differences in populations. This activity has data sets with height measurements for children of different ages.

## Is there an association?

Students need to judge the association between two variables shown in a scatter plot as strong, weak or non-existent.

## Strength of associations

Students often find it difficult to judge the strength of an association from the appearance of scatter plots.

## Judging associations

The examples presented give students the opportunity to judge the strength of an association from the appearance of scatter plots.

## Examples of box plots

Box plots can be used to compare data sets.

## Features of box plots

Box plots provide a transition between a stacked dot plot (or histogram) and numerical statistics summarising the data. Often students have difficulty visualising the data from the plot.

## Interpreting box plots

With comparative box plots, the overlap can indicate that there are differences in the underlying populations.