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The huge denominators throw off one's intuition. Since the sample sizes are identical, and the proportions low, the problem can be recast: 13 events occurred, and were expected (by null hypothesis) to occur equally in both groups. In fact the split was 3 in one group and 10 in the other. How rare is that? The binomial test answers.

Enter this line into R: binom.test(3,13,0.5,alternative="two.sided")

The two-tail P value is 0.09229, identical to four digits, to the results of Fisher's test.

Looked at that way, the results are not surprising. The problem is equivalent to this one: If you flipped a coin 13 times, how surprising would it be to see three or fewer, or ten or more, heads. One of those outcomes would occur 9.23% of the time.

The huge denominators throw off one's intuition. Since the sample sizes are identical, and the proportions low, the problem can be recast: 13 events occurred, and were expected (by null hypothesis) to occur equally in both groups. In fact the split was 3 in one group and 10 in the other. How rare is that? The binomial test answers.

Enter this line into R: binom.test(3,13,0.5,alternative="two.sided")

The two-tail P value is 0.09229, identical to four digits to the results of Fisher's test.

Looked at that way, the results are not surprising. The problem is equivalent to this one: If you flipped a coin 13 times, how surprising would it be to see three or fewer, or ten or more, heads. One of those outcomes would occur 9.23% of the time.

The huge denominators through off one's intuition. Since the sample sizes are identical, and the proportions low, the problem can be recast: 13 events occurred, and were expected (by null hypothesis) to occur equally in both groups. In fact the split was 3 in one group and 10 in the other. How rare is that? The binomial test answers.

Enter this line into R: binom.test(3,13,0.5,alternative="two.sided")

The two-tail P value is 0.09229, identical to four digits, to the results of Fisher's test.

Looked at that way, the results are not surprising. The problem is equivalent to this one: If you flipped a coin 13 times, how surprising would it be to see three or fewer, or ten or more, heads. One of those outcomes would occur 9.23% of the time.

The huge denominators throw off one's intuition. Since the sample sizes are identical, and the proportions low, the problem can be recast: 13 events occurred, and were expected (by null hypothesis) to occur equally in both groups. In fact the split was 3 in one group and 10 in the other. How rare is that? The binomial test answers.

Enter this line into R: binom.test(3,13,0.5,alternative="two.sided")

The two-tail P value is 0.09229, identical to four digits, to the results of Fisher's test.

Looked at that way, the results are not surprising. The problem is equivalent to this one: If you flipped a coin 13 times, how surprising would it be to see three or fewer, or ten or more, heads. One of those outcomes would occur 9.23% of the time.

The huge denominators through off one's intuition. Since the sample sizes are identical, and the proportions low, the problem can be recast: 13 events occurred, and were expected (by null hypothesis) to occur equally in both groups. In fact the split was 3 in one group and 10 in the other. How rare is that? The binomial test answers.

Enter this line into R: binom.test(7,100,0.20,alternative="two.sided")

The two-tail P value is 0.09229, identical to four digits, to the results of Fisher's test.

Looked at that way, the results are not surprising. The problem is equivalent to this one: If you flipped a coin 13 times, how surprising would it be to see three or fewer, or ten or more, heads. One of those outcomes would occur 9.23% of the time.

The huge denominators through off one's intuition. Since the sample sizes are identical, and the proportions low, the problem can be recast: 13 events occurred, and were expected (by null hypothesis) to occur equally in both groups. In fact the split was 3 in one group and 10 in the other. How rare is that? The binomial test answers.

Enter this line into R: binom.test(3,13,0.5,alternative="two.sided")

The two-tail P value is 0.09229, identical to four digits, to the results of Fisher's test.

Looked at that way, the results are not surprising. The problem is equivalent to this one: If you flipped a coin 13 times, how surprising would it be to see three or fewer, or ten or more, heads. One of those outcomes would occur 9.23% of the time.