Chapter 15. Statistical Measures

Chapter 15. Statistical Measures
	Part I. Roulette

Table of Contents

Constructors
Methods

This section presents two ordinary statistical algorithms: mean and standard deviation. In one sense, this section could be treated as optional. Instead of having the simulator present useful summary statistics, raw data can be put into a spreadsheet for creating the statistics.

However, the process of designing these statistical processing classes is very interesting. This chapter examines some ways to add features to the built-in collection classes.

Overview

Currently, the Simulator class collects two Lists. One has the length of a session, the other has the maximum stake during a session. We need to create some descriptive statistics to summarize these stakes and session lengths.

On Statistics

In principle, we could apply basic probability theory to predict the statistics generated by this simulation. Indeed, some of the statistics we are gathering are almost matters of definition, rather than actual unknown data. We are, however, much more interested in the development of the software than we are in applying probability theory to a relatively simple casino game. As a consequence, the statistical analysis here is a little off-base.

In spite of our problems, we will build a relatively simple-minded set of descriptive statistics. We will average two metrics: the peak stake for a session and the duration of the session. Both of these values have some statistical problems. The peak stake, for instance, is already a summary number. We have to be cautious in our use of summarized numbers, since we have lost any sense of the frequency with which the peaks occured. For example, a player may last 250 cycles of play, with a peak stake of 130. We don't know if that peak occurred once or 100 times out of that 250. Additionally, the length of the session has an upper bound on the number of cycles. This forces the distribution of values to be skewed away from the predictable distribution.

We will design a Statistics class with responsibility to retain and summarize a list of numbers and produce the average (also known as the mean) and standard deviation. The Simulator can then use this this Statistics class to get an average of the maximum stakes from the list of session-level measures. The Simulator can also apply this Statistics class to the list of session durations to see an average length of game play before going broke.

We can encapsulate this statistical processing in two ways: we could extend an existing class or we could delegate the statistical functions to a separate class. If we extend the library java.util.List, we can add the needed statistical summary features; given this new class, we can replace the original List of sample values with a StatisticalList that both saves the values and computes descriptive statistics. In addition to delegation, we have two choices for implementation of this extended version of List, giving us three alternative designs.

Extend LinkedList. In this case, we are simply adding two new methods to the existing LinkedList implementation. However, our new methods would not apply to ArrayList or Vector.
Extend AbstractList. However, in doing this we would need to provide the implementation details of the list structure itself. In effect, we would reimplement LinkedList or ArrayList.
Create a separate class that computes statistics on a List given as an argument to the methods of the statistical class. In this case, our statistical methods will work with any subclass that implements the interface List. This can be applied to any of LinkedList, ArrayList or Vector.

Alternative three -- a separate statistical class -- has the most reuse potential. We'll create a simple class with two methods: mean and stdev to compute the mean and standard deviation of a List of Integer objects. This can be used in a variety of contexts, and allows us the freedom to switch List implementation classes without any other changes.

The detailed algorithms for mean and standard deviation are provided in Statistical Algorithms.

Since our processes are relative simple, stateless algorithms, we don't need any instance variables. Consequently, we'll never need to create an instance of this class. As with Java.lang.Math, all of these methods can be declared as static, making them features of the class itself.


Deliverables		Some Foundations