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Friday, February 15, 2013

Chi Squared Research

Chi-squared test One independent variable
Background: The Students t-test and Analysis of section are used to analyze measurement data which, in theory, are incessantly variable. Between a measurement of, say, 1 mm and 2 mm there is a around-the-clock range from 1.0001 to 1.9999 mm.
But in some types of experiment we neediness to record how many individuals f completely into a particular category, much(prenominal) as blue eyes or brown eyes, mobile or non-motile cells, etc. These counts, or qualitative data, are noncontinuous (1, 2, 3 etc.) and must be treated differently from continuous data. Often the appropriate test is chi-squared (?2), which we use to test whether the turning of individuals in different categories fit a unprofitable hypothesis (an expectation of some sort).
Chi squared analysis is simple, and valuable for all sorts of things - not just Mendelian crosses! On this paginate we build from the simplest examples to more complex ones.
A simple example
count that the ratio of male to female students in the Science capacity is exactly 1:1, but in the Pharmacology Honors partition over the past ten years there put one over been 80 females and 40 males. Is this a significant departure from expectation? We proceed as follows.
Set out a set back as shown below, with the observed numbers and the expected numbers (i.e. our null hypothesis).

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Then subtract each expected value from the gibe observed value (O-E)
Square the O-E values, and divide each by the relevant expected value to give (O-E)2/E
Add all the (O-E)2/E values and call the total X2
|  |Female | phallic |Total |
|Observed numbers (O) |80 |40 | cxx |
|Expected numbers (E) |60*3 |60*3 |120 *1 |
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