Degrees of freedom
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Degrees of freedom in a contingency table
A contingency table shows the results from taking a sample where each individual object in the sample can have two or more properties. For clarity we concentrate on just two properties. For example athletes should be considered for their muscle fibre and their type of sporting event. Suppose, for simplicity, athletes can have either slow twitch or fast twitch muscle fibres and be entered for either explosive or endurance sports [Table goes here &- download the original to see it.] This is a [Equation goes here &- download the original to see it.] contingency table. Now imagine that 120 athletes are sampled, of which 53 have slow twitch and 56 participate in endurance sports. These values determine the other row and column totals. [Table goes here &- download the original to see it.] The circled values are constrained by the other value(s) and the sample size.This also means that filling in any one box in the contingency table determines al other values. [Table goes here &- download the original to see it.] If, for example, 5 athletes with slow twitch fibres participate in explosive sports then the other frequencies are determined by the constraints that the sum of the values in each row has to equal the row total, and likewise for the columns. So a [Equation goes here &- download the original to see it.] contingency table with n columns and m rows hasDegrees of freedom [Equation goes here &- download the original to see it.]
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Contents of
Degrees of freedom
1 Degrees of Freedom
2 Degrees of freedom in a contingency table
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