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chi-squared testa statistical routine which is a test of SIGNIFICANCE, comparing the observed results of an experiment or sample against the numbers expected from a theory or prediction. The test produces a value called chi-squared (χ2) which is:
The χ2 number is then converted to a probability value (P) using an χ2 table. If the P value is larger than 5% we can conclude that there is ‘no significant difference’ between the observed results and those expected, any deviation being due to chance. If, however, the probability is less than 5%, it must be concluded that there is a ‘significant difference’ between the observed results and those expected from theory. Note that the χ2test can only be used with data that fall into discrete categories, e.g. heads or tails, long or short, yellow or orange. Take, for example, a sample of 100 plants arising from a cross between two hybrid red parents. Three quarters of the offspring are expected to be red-flowered, one quarter white. The χ2analysis is shown in the table below.
In this example, there are two classes of data (n = 2) so there is one ‘degree of freedom’ (n - 1). Using the Table of χ2 shows that, with one degree of freedom, a χ2 value of 2.61 indicates a greater than 5% chance that the deviation between observed and expected numbers was due to chance alone, i.e. there is no significant difference between the numbers observed and those expected.