• ##### Inferential statistics

Inferential statistics are a group of methodologies that allow you to draw inferences about a population based on the behaviour of a sample.

When an appropriate benchmark is not available, you can use inferential statistics to identify whether or not there is a causal relationship between the behaviour being observed and your strategies.

They use sampling methodologies to identify target and control groups from within a specified population (see figure 6).

• Population - A group of taxpayers who share a common set of characteristics.
• Target group - A sub-group of taxpayers selected from the population and used as the focal point for your strategies.
• Control group - A sub-group of taxpayers selected from the population that is isolated from your strategies for the purposes of the study.

Figure 6 illustrates the relationship between the population, the target group and the control group.

Comparing target and control groups from the same population allows you to screen out the effects of unknown variables - both groups will theoretically be subject to the same environmental factors except for the compliance strategies. Any differences in behaviour can be attributed to your strategies.

Methods for comparing target and control groups include the following.

• Randomised control trials
Both the target and the control groups are randomly selected from within the population that is to be targeted by the strategies. The control group is then isolated from treatment.
• As the target group has been subjected to the treatment, and the control group has not, any observed behavioural differences between the two groups can be attributed to the compliance strategies.

Example: Randomised control trial

Taxpayers are randomly selected from the population and separated into a target group and a control group.

The target group is used to test the effectiveness of an advisory letter on their compliance behaviour.

The control group is isolated from the treatment.

The difference in behaviour between the groups is then used as an indicator of the effectiveness of the strategy.

Theoretically, random selection should result in the selection of samples that are representative of the population. However, where a population has identifiable sub-groups that are likely to behave differently, the accuracy of the study can be further enhanced by randomly selecting cases from each sub-group. This eliminates the possibility of a sub-group being over-represented within the sample.

You should seek expert assistance when setting up these types of comparisons to ensure that you don't build unintended flaws into your indicator analysis.

You should consider:

• appropriate sample sizes - having too small a sample will limit the confidence that can be attached to the results
• proper selection techniques for group membership.

When using a randomised control trial, you need to select your target and control groups before you implement your strategies to ensure that the control group can be isolated from the treatment.

End of example
• Matched groups
When it isn't possible to use a randomised control trial, you can use a matched group instead - this is a comparison group that is similar to the treatment group. Groups are matched according to similarities in their characteristics.
• While the results from a matched study are adversely affected by unknown differences between the groups, well-matched groups can approach the rigor of a randomised control trial.