# chi-squared test

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## chi-squared test

a 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 (χ^{2})

*which is:*

The χ^{2} number is then converted to a probability value (P) using an χ^{2} 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 χ^{2}test 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 χ^{2}analysis 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 χ^{2} shows that, with one degree of freedom, a χ^{2} 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.