Qualitative Data Analysis
6.1 Binomial Distribution
In many instances, microbiologists collect data that are binary. That is, data can occur in one of two possible outcomes, such as 0/1, +/–, growth/no growth, or pass/fail. The frequencies of each outcome are tabulated, relative to the number of trials, providing a data set ranging from 0 to 1.0. For example, let's take the number of trypticase soy broth tubes that are positive (+) for microbial growth over a 72-h incubation. Suppose ten tubes were used, and eight tubes were positive for growth. Then the proportion of positive growth is the number of positives ÷ total number = 8 ÷ 10 = 0.80. The value, “p,” is usually designated as the proportion of successes, in this case, positive (+) growth. The proportion of no-growth can also be calculated. The proportion of no-growth is q = 1 – p, or 1.0 – 0.80 = 0.20. Incidentally, what one terms “success” and “failure” is arbitrary.
There are many applications appropriate to using the binomial distribution, such as...