6Variance of Evidence I

Let's next look at what happens when the coin is unbalanced and the chance of heads is more or less than 50%. As we'll see, a 50% coin will have more outcome variety than a 25% coin that, in turn, will have more outcome variety than a 10% coin. A coin with 0 or 100% chance of heads will have no outcome variety whatsoever. Variety decreases more and more as the chance of heads moves from 50% to 0% or 100% because variety becomes less and less likely. Let's look at three corresponding simulation histograms.

Figure 6.1 shows sample proportions with coins whose chance of heads is 50%.

A bar graphical representation for 1000 sample proportions when the chance of heads is 50%, where frequency is plotted on the y-axis on a scale of 0–400 and proportion of heads on the x-axis on a scale of 0–1.

Figure 6.1

Figure 6.2 is for coins whose chance of heads is 25%; its outcome variety is less; it is more bunched up.

A bar graphical representation for 1000 sample proportions when the chance of heads is 25%, where frequency is plotted on the y-axis on a scale of 0–400 and proportion of heads on the x-axis on a scale of 0–1.

Figure 6.2

And Figure 6.3 is for coins whose chance of heads is 10%; its outcome variety is even less; it is even more bunched up (it is also lopsided, which we'll consider in Chapter 9).

A bar graphical representation for 1000 sample proportions when the chance of heads is 10%, where frequency is plotted on the y-axis on a scale of 0–400 and proportion of heads on the x-axis on a scale of 0–1.

Figure 6.3

For coins whose chance of heads is 0%, all the sample proportions will be equal to 0. There will be no variety of outcomes.

The statistical ...

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