Histograms of data in each group

When data are collected from two groups, a histogram can be used to graphically display the distribution of values in each group.

End-of-year bonuses paid to lower-level executives

A company has a generous but rather complicated policy on end-of-year bonuses for its lower-level managerial personnel. A key factor of the policy is a subjective judgement of 'contribution to corporate goals'. The diagram below shows the bonuses awarded to the 24 female and 36 male executives. The crosses have been jittered a little (randomly moved) to separate them in the scatterplot.

This diagram is 3-dimensional. Position the mouse in the middle of the diagram
and **drag towards the top left** of the screen to rotate the plot
(or click the 3D rotation button). The histogram within each group describes the
distribution of bonuses awarded to that gender.

Model for each group

A single batch of numerical values is usually modelled as a random sample from
some hypothetical infinite population -- often a normal distribution. In a similar
way, data sets that consist of measurements from two groups are often modelled
as **two** independent random samples from **two** underlying
hypothetical infinite populations. Normal distributions are again commonly used
as models.

(The assumption of normality should be checked from graphical displays of the sample data. If the data are noticably skew, a transformation may provide values that can be adequately modelled by normal distributions.)

End-of-year bonuses

The histograms of bonuses paid to male and female executives both seemed fairly symmetrical, so normal distributions are reasonable models within the two groups. The diagram below shows a possible model for the bonus data.

Click **Take Sample** to select a random sample from each of the
two normal distributions. The model claims that the **real** data
set consists of random samples from distributions like these.