Statistics coin flip example

EXAMPLE 3.4 Why does energy exchange Consider the two systems, A and B, shown in Figure 3.9. Each system has ten particles and only two energy levels, f = 0 or f = 1 for each particle. The binomial statistics of coin flips applies to this simple model. 

The statistical test procedures that we use unfortunately are not perfect and from time to time we will be fooled by the data and draw incorrect conclusions. For example, we know that 17 heads and 3 tails can (and will) occur with 20 flips of a fair coin (the probability from Chapter 3 is 0.0011) however, that outcome would give a significant p-value and we would conclude incorrectly that the coin was not fair. Conversely we could construct a coin that was biased 60 per cent/40 per cent in favour of heads and in 20 flips see say 13 heads and 7 tails. That outcome would lead to a non-significant p-value (p = 0.224) and we would fail to pick up the bias. These two potential mistakes are termed type I and type II errors. 

As this book focuses on clinical trials our primary interest is in providing you with relevant examples of hypothesis testing in that arena. However, it is useful initially to lay some conceptual foundations with simpler examples. As for many other examples in statistics and probability, we illustrate these concepts first with flips of a coin. 

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