Observed and expected frequencies The results obtained from trials are rarely exactly the same as the results predicted by statistical theories. For example, if a coin is tossed 100 times, it is unlikely that the result will be exactly 50 heads and 50 tails. Let us assume that, say, 5 people each toss a coin 100 times and note the number of, say, heads obtained. Let the results obtained be as shown below. Person A B C D E Observed frequency 43 54 60 48 57 Expected frequency 50 50 50 50 50 A measure of the discrepancy existing between the observed frequencies shown in row 2 and the expected frequencies shown in row 3 can be determined by calculating the Chi-square value. The Chi-square value is defined as follows:

χ2 = ∑{ (o − e)2

e

}

,

where o and e are the observed and expected frequencies respectively.