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Reply #38: I can refute them [View All]

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foo_bar Donating Member (1000+ posts) Send PM | Profile | Ignore Tue Jun-14-05 10:28 PM
Response to Reply #37
38. I can refute them
The binomial distribution describes the behavior of a count variable X if the following conditions apply:

1: The number of observations n is fixed.
2: Each observation is independent.
3: Each observation represents one of two outcomes ("success" or "failure").
4: The probability of "success" p is the same for each outcome.

http://www.stat.yale.edu/Courses/1997-98/101/binom.htm

The trials must meet the following requirements:

the total number of trials is fixed in advance;
there are just two outcomes of each trial; success and failure;
the outcomes of all the trials are statistically independent;
all the trials have the same probability of success.

http://www.stats.gla.ac.uk/steps/glossary/probability_d...

Your calculation fails three of the four conditions.

1) The number sampled N wasn't fixed in advance; they typed them in as fast as they came.
2) The outcomes aren't dichotomous; some of the "88" don't even describe one vote-switch, but series of vote-switches of indeterminate size, or rumors of vote-switches.
3) Unless the anecdotes were conducted with utter secrecy (and secrecy with respect to other volunteers), they can't be statistically independent. See: bandwagon effect, grapevine effect, halo effect.

Here's a fun webpage that explains it in terms of Hershey's Kisses:

5. Ask the students to argue that X is a binomial random variable:
a. The number sampled, n = 10, is fixed in advance.
b. There are two outcomes: approve or disapprove.
c. p = P(a Kiss approves) is unknown, but assumed to be 0.90, under the null hypothesis. If we sample with replacement, we have independent trials and p is constant. (Here, you can take an 'aside' to address "real" polls. The population is typically much larger, U.S. population is N=260,000,000, say, a typical sample is around n=1000, and sampling is without replacement. Hence, p=P(approve) changes, but is small enough to be ignorable.)
d. We let X = the number in the sample who approve of Clinton.

http://www.stat.psu.edu/~resources/InLarge/ljs_02.htm
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