![]() ![]() They also get to flip coins where we look into the randomness of the coin flipping - the thing that I try to show is that randomness is more random than what we usually believe inspired by this Radiolab episode. In my class I recommend them the Khan academy statistics videos and I also use some of his explanations for certain concepts. The defining intervals of interest is a natural transition to probability density/mass function functions and their cumulative counterparts. When changing into 200 flips you get a natural way of explaining why the probability of getting exactly 100 flips starts to lack relevance. I also like to point out the resemblance between the binomial curve and the bell curve. This simple example also shows how dependent we are on the null hypothesis to calculate the p-value. Since we in medicine usually are interested in studying failures we need to include the opposite side of the probability even if our intent is to do good and to introduce a beneficial treatment. This means that you end up with a probability of $5.4.\%+5.4.\% \approx 10.9\%$ for a two-tailed test. Now if we would get only 2 heads, ie 8 heads (the other tail), we would probably be just as willing to question the fairness of the coin. By adding the values we get that the probability now is a little more than $\approx 5.5\%$ of getting 2 tails or less. Since we would question the fairness of the coin if we got 9 or 10 tails we have to include these possibilities, the tail of the test. From the graph you can see that the probability of getting 8 out of 10 flips with a fair coin is about about $\approx 4.4\%$. Now if you wonder what the probability of getting only 2 tails out of 10 flips with this fair coin you can calculate that probability as I've done in the bar graph. ![]() I start with a explaining that if we believe that we have a fair coin we know it should end up tails 50 % of the flips on average ($=H_0$). My way of explaining calculating p-values & the tails I've been teaching fellow orthopaedic surgeons statistics and therefore I tried to keep it as basic as possible since most of them haven't done any advanced math for 10-30 years. This is a great question and I'm looking forward to everyones version of explaining the p-value and the two-tailed v.s. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |