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This simple Minitab simulation exercise illustrates the concept of efficiency of estimators. Students compare the sampling distributions of the sample mean, median and mid-range from a normal distribution and from a uniform distribution. The striking differences observed give rise to much discussion. + INTRODUCTION +N UNBIASED estimator is one whose average is A equal to the parameter being estimated. To decide between competing unbiased estimators, we take the one that is the most efJicient. In other words, we choose the one with the smallest variance.These concepts are often omitted from service courses in statistics because they are perceived to be too theoretical. Unbiasedness and efficiency can be introduced in an intuitive way by using simulations with packages such as Minitab. This paper presents a dramatic illustration of the concept of efficiency.The first time our students meet a simulation activity we are careful to build up the concepts very slowly. Students should first simulate and look at small data sets, such as 10 rolls of a die, and perhaps even compare them with the results of rolling a real die. They should be given time to grasp the idea that when the computer fills for example 5 columns of 50 rows, it can be regarded as either 5 samples of size 50 or 50 samples of size 5. Students must feel ownership of their data, and not merely think it has come out of a "black box" . + PROCEDURE + Even the least mathematically able students are happy to accept that the sample mean, the sample median, and the mid-range (half way between the smallest and largest values) are all reasonable estimators for the centre of a symmetric distribution. By investigating the three estimators on a simulated set of data they can be convinced that all three are unbiased. The question of efficiency is then easily introduced in order to choose between them.We use a structured worksheet in which the students are given the Minitab commands as a series of steps, with questions requiring them to reflect upon what they are doing at each stage. Firstly, they look at the sampling distributions of the three estimators for the mean of the normal distribution. The following Minitab commands are provided for the students:Students attention is drawn to the spread of the dotplots in Figure 1 . Here the mean is seen to be slightly less variable than the median which is in turn less variable than the mid-range, and no one is surprised.The extract from the worksheet in Figure 2 illustrates how the students can be led through the necessary steps in order to focus on these characteristics. The complete worksheet may be found in Martin et a1 (1994).Students should note that the means are all approximately equal to ten, but that the standard deviations are not the same. If this is being done in a classroom situation, they should be encouraged to compare their results with those around them. This will highlight the fact that different simulations show the same pattern of results.The second part of the worksheet considers the same three estimato...

Variation in the song of the male Common Blackbird was investigated within and between two locations in 10 western Victoria. Each of 400 phrases (100 phrases per male) was characterised by 61 measurements relating to 13 aspects of each phrase. Principle component and stepwise discriminant analyses were undertaken on these measurements. Classification of blackbird song for location and individuality was based on timing within the phrase of the loudest elements. Evidence was found for within-phrase variability, with the greatest variation in the middle of the phrase. Within-and between-site comparison found that blackbird song exhibited both individual and site-specific characteristics consistent with earlier suggestions of phrase sharing within local populations. The study demonstrated that an objective statistical approach to song analysis was able to discriminant between individual birds from different locations.