Male female math 10 20 English 20 10 History 15 15 What hypothesis might you be interested in here? The Physicians Health Study (1989) was a randomized, controlled, double-blinded experiment. Half of 22071 men over 40 took an aspirin every other day, while half took a placebo. Heart attack no heart attack aspirin 104 10933 placebo 189 10845 The question is whether memebership in the aspirin group affects (lowers) the heart attack rate. Why is the question here different from the previous question? What would we expect to see if the two categories are independent? Of course, random chance will cause some variation. What would we expect to see if the two categories are perfectly dependent? For example, if you toss a coin to determine who gets a heart attack and who does not, then aspirin use is clearly unrelated to heart attack. But we know that one is unlikely to get exactly equal numbers of heads for both groups. By chance, one or the other will have a slight excess of heart.