MIDTERM: BIOSTASTISTIC Nguyễn Tấn Phú Excel functions: Relationship: Percentile amd Quatile MIDTERM: BIOSTASTISTIC Nguyễn Tấn Phú Binomial Distribution: The binomial distribution applies in the following situation: MIDTERM: BIOSTASTISTIC Nguyễn Tấn Phú a) The outcome of any trial can only take on two possible values, say success and failure; b) There is a constant probability p of success on each trial; c) The experiment is repeated n times (i.e. n trials are conducted); d) The trials are statistically independent (i.e. the outcome of past trials does not P( x ) n! p x ( 1 p )n x x! ( n x )! affect subsequent trials); then if x equals the number of successes in the n trials, we have: for x = 0, 1, 2, …… n. EXCEL =binom.dist(x, n, p, condition), where x is the value of interest, n is the number of trials, p is the probability of success and condition is either “false” or “true”. If you specify the following command =binom.dist(3, 10, .50, false), then EXCEL will compute the probability that x = 3. If you use the command, =binom.dist(3, 10, .50, true), then Excel will compute the probability that x 3 . In other words EXCEL will accumulate the probabilities for x = 0, x = 1, x = 2, and x = 3 and report the total. Poisson Distribution MIDTERM: BIOSTASTISTIC Nguyễn Tấn Phú POISSON DISTRIBUTION where, just as in the case of the binomial distribution, a condition of ‘false’ gives us the probability of x , and a condition of ‘true’ gives us the probability of being less than or equal to x. In this case we want the probability of 3 or anything more extreme, that is the probability of three or more. We can find, P ( x 2 ) POISSON ( 2 ,1 , true ) .919699 P ( x 3 ) 1 P ( x 2 ) 1 .919699 .080311 so that, which is not rare by the usual standards of .05 or .01. MIDTERM: BIOSTASTISTIC Nguyễn Tấn Phú Normal distribution: