Binomial distribution

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Information about Binomial distribution
Education

Published on October 7, 2008

Author: headlessprofessor

Source: authorstream.com

Binomial : Binomial headlessprofessor When to use? : When to use? Variable is measured on a binary nominal scale When to use? : When to use? Variable is measured on a binary nominal scale Success / Failure When to use? : When to use? Variable is measured on a binary nominal scale Success / Failure Number of successes X When to use? : When to use? Variable is measured on a binary nominal scale N identical trials When to use? : When to use? Variable is measured on a binary nominal scale N identical trials The total number of successes is a discrete ratio scale When to use? : When to use? Variable is measured on a binary nominal scale N identical trials Trials are independent When to use? : When to use? Variable is measured on a binary nominal scale N identical trials Trials are independent Probability p of success the same for each trial What we need to use the table : What we need to use the table N = number of trials (cases) X = number of successes P = probability of a success in each trial The binomial charts : The binomial charts A different chart for each N for N =2 through N = 20 The binomial charts : The binomial charts A different chart for each N Each row represents an X The binomial charts : The binomial charts A different chart for each N Each row represents an X Each column represents a P Example : Example The probability of a sales rep making a sale on a given day is p = .10. Example : Example The probability of a sales rep making a sale on a given day is p = .10. There are two sales reps, N = 2. Example : Example The probability of a sales rep making a sale on a given day is p = .10. There are two sales reps, N = 2. What is the probability that neither will make a sale? X = 0 Answer : Answer The probability of having zero successes from these two cases is .81. Example : Example The probability of a sales rep making a sale on a given day is p = .10. There are two sales reps, N = 2. What is the probability that at least one sale will be made? X > 0 Answer : Answer The probability of one success is .18 and two successes is .01 for a total of .19. Answer : Answer Or subtract the probability of zero successes from 1.00. 1.00 - .81 = .19 Example : Example The probability of a sales rep making a sale on a given day is p = .90. There are two sales reps, N = 2. What is the probability that neither will make a sale? X = 0 Answer : Answer The probability of having zero successes from these two cases is .01. By the way : By the way Many other statistical tests are derived from the binomial distribution By the way : By the way Many other statistical tests are derived from the binomial distribution The sign test for repeated measures By the way : By the way Many other statistical tests are derived from the binomial distribution The sign test for repeated measures The median test for sample vs. norms What does it prove? : What does it prove? If you get an extremely low probability, that merely means that your observed results are unlikely to conform to the frequencies expected by the binomial distribution. Alternatives : Alternatives If the sample size is larger than 20, consider using a test of proportions Z Alternatives : Alternatives If the sample size is larger than 20, consider using a test of proportions Z Chi square Alternatives : Alternatives If the sample size is larger than 20, consider using a test of proportions Z Chi square Kolmogorov-Smirnov Binomial : Binomial headlessprofessor

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