and they are, in fact we will allow data to be recorded and acted on that is in fact “broken” “ok” “erroreous”. This problem is similar to flipping a coin, that is, there should be a 50% probability of seeing the or higher. Thus we can express this situation in terms of flipping coins (since we can “A” “B” more easily visualize that). Just how surprising is it to see 15 when we expect p*n=10 “heads” What is the probability of seeing 15 heads? What is the probability of seeing at least 15 heads? Notice that what would surprise us is not seeing 15 H’s but seeing as 15 or more heads. If you were applying for a job and you were expecting a starting salary of around $55,000 and you were offered $42,000 or $88,888 are you surprised because of the (exact) number “specific” or the of the number (range of values)? “size” Therefore, we aren’t interested in P(x=15) = BINOMDIST(15,20,0.5,FALSE) = 0.014785767 but rather P(x>=15) = 1 P(x<14) = 1-BINOMDIST(14,20,0.5,TRUE) = 0.020694733 – Thus, we are rather surprised to see 15 or more H’s (or A’s>B’s) because by chance we should only see this happening 2% of the time. Thus, because we DID see it happen, we will believe we are seeing something because it happens less often than the 5% of the time it will happen “real” by chance. In words, suppose someone has just flipped a fair coin 20 times and they got 19 “claimed” heads. Do you think you just witnessed a once-in-a-lifetime occurrence that happened by random chance or do you think this is evidence that the coin is not fair and you aren’t seeing anything particularly rare at all? heads p(x>=H) 0 1.00000 1 1.00000 2 0.99998 3 0.99980 4 0.99871
“broken” and they are, in fact “ok” we will allow data to be recorded and acted on that is in fact “erroreous”. This problem is similar to flipping a coin, that is, there should be a 50% probability of seeing the “A” or “B” higher. Thus we can express this situation in terms of flipping coins (since we can more easily visualize that). Just how surprising is it to see 15 “heads” when we expect p*n=10 What is the probability of seeing 15 heads? What is the probability of seeing at least 15 heads? Notice that what would surprise us is not seeing 15 H’s but seeing as 15 or more heads. If you were applying for a job and you were expecting a starting salary of around $55,000 and you were offered $42,000 or $88,888 are you surprised because of the “specific” (exact) number or the “size” of the number (range of values)? Therefore, we aren’t interested in P(x=15) = BINOMDIST(15,20,0.5,FALSE) = 0.014785767 but rather P(x>=15) = 1 – P(x<14) = 1-BINOMDIST(14,20,0.5,TRUE) = 0.020694733 Thus, we are rather surprised to see 15 or more H’s (or A’s>B’s) because by chance we should only see this happening 2% of the time. Thus, because we DID see it happen, we will believe we are seeing something “real” because it happens less often than the 5% of the time it will happen by chance. In words, suppose someone has just flipped a “claimed” fair coin 20 times and they got 19 heads. Do you think you just witnessed a once-in-a-lifetime occurrence that happened by random chance or do you think this is evidence that the coin is not fair and you aren’t seeing anything particularly rare at all? heads p(x>=H) 0 1.00000 1 1.00000 2 0.99998 3 0.99980 4 0.99871
Notes10.docx