of magnetic field exposure and leukemia, the null and alternative hypotheses would be

Again we can use a chi-squared statistic.

where O represents the observed frequencies and E represents the expected frequencies. Recall that the expected frequency of a given cell is calculated as the product of the row and column totals divided by the total sample size. For the magnetic field exposure and leukemia example, the expected values are shown below.

Observed and Expected Frequencies in the Leukemia Study Above


Observed Frequency

Expected Frequency

High Exposure, Leukemia


(674 x 2,355)/69,567 = 22.82

High Exposure, No Leukemia


(674 x 67,212)/69,567 = 651.18

Medium Exposure, Leukemia


(1469 x 2,355)/69,567 = 49.73

Medium Exposure, No Leukemia


(1,469 x 67,212)/69,567 = 1419.27

Low Exposure, Leukemia


(67,424 x 2,355)/69,587 = 2,282.46

Low Exposure, No Leukemia


(67,424 x 67,212)/69,567 = 65,141.55

  Using these values, we can now calculate the chi-square statistic:

Now that we have calculated the chi-square statistic, we need to determine if this value would lead us to reject or fail to reject the null hypothesis at an α-level of 0.05. To do this, we compare our calculated chi-square statistic to a critical value with (3-1) x (2-1) = 2 x 1 = 2 df in the 0.05 column. From the chi-square table referenced on page 4, we see that this value is 5.99. Since our calculated test statistic is less than the critical value of 5.99, we fail to reject the null and conclude that there is no association between magnetic field exposure and development of leukemia. This result would not be considered "statistically significant."