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Section 1:
2 x 2 Tables
Chi-Square
Degrees of Freedom
p-Value
Flip Coin 100 times
Breast Cancer Example

Null hypothesis

The null hypothesis is that there is no difference between coin A and coin B in the probability of tossing a heads (or tails). This hypothesis can be tested. The test on a 2 x 2 table may be carried out by a convenient formula.

The test is a two-step process

1. First, one calculates the so-called chi-square statistic (symbolized by and pronounced as kai-square) and the degrees of freedom for the table.
2. Second, one uses the statistic to look up (in a table or computer program) the probability–called the p-value–of an outcome as extreme or more extreme than the observed outcome occurring by chance.

We will reject the null hypothesis if the p-value is equal to or less than the conventional requirement for statistically significant results, which is set at the so-called significance level of 0.05, or 5%.

Step 1-A: calculate chi-square

To illustrate, if a, b, c, and d are the numbers in the cells of the 2 x 2 table (a, b in the first row and c, d in the second row), then may be calculated as follows:

=
Equation (1)

In this case, the calculation yields . . .

= = 0.8333