Biomedical Engineering Reference
In-Depth Information
independent of each other, but they must be either present or absent. Furthermore, the possible
outcomes must be mutually exclusive, and there can be only one outcome.
A basic assumption in many statistical analyses is that the sample mean tends to approach the
population mean, given a large enough sample size or enough smaller samples. Descriptive statistics
such as mean, mode, median, and variance—a measure of how dispersed the values are around the
distribution mean—are measures of this central tendency. For example, the Punnet Square accurately
predicts the expected probability of genotypes and phenotypes, but only for sufficiently large sample
sizes. A single, random sample of only four plants might reveal all wrinkled peas, despite the
expected result of one wrinkled to three smooth offspring.
Sampling and Distributions
Much of statistics deals with obtaining as much information as possible from small samples. The
question is how large a sample is large enough considering it's usually unrealistic to measure every
data element, even if they are generated by a sequence machine or other automatic device. We
estimate population mean and variance by sampling population data and drawing inferences from the
sample data, based in part on assumptions of how the data are distributed in the population.
Popular distributions used in statistical analysis of discrete random variables include the Binomial,
Hypergeometric, and Poisson distributions. The more well-known Normal distribution is used for
analysis of continuous random variables. A special case of the Normal distribution is the z-
distribution, which is normally distributed data with a mean of zero and a standard deviation of one
(see Figure 6-11 ). The distinction between distributions of continuous and discrete variables is
important because many statistical methods are valid only when used with data drawn from
populations with specific distributions. For example, the analysis of discrete random variables, such
as the position of a nucleotide on a given sequence, may use techniques based on a binomial
distribution, but may not use techniques that assume a normal distribution. If assumptions of
distribution aren't valid, then the relevance of the analysis should be downplayed accordingly.
Figure 6-11. The Z-Distribution. This distribution is a special case of the
Normal distribution, with mean of zero and a standard deviation of one.
Returning to the starring method of capturing fluorescence intensity data, the response
characteristics of the image-capture electronics results in a skewed distribution (see Figure 6-12 ).
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