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chi-square distribution

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distribution /dis·tri·bu·tion/ (dis″trĭ-bu´shun)
1. the specific location or arrangement of continuing or successive objects or events in space or time.
2. the extent of a ramifying structure such as an artery or nerve and its branches.
3. the geographical range of an organism or disease.

chi-square distribution  a distribution of sample differences using observations of a random sample drawn from a normal population.
normal distribution  a continuous probability density function roughly characterizing a random variable that is the sum of a large number of independent random events; usually represented by a smooth bell-shaped curve symmetric about the mean.
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Normal distribution. The approximate percentage of the area (or frequency) lying under the curve between standard deviations is indicated.

chi-square distribution
in statistical terms this is said of a variable with K degrees of freedom if it is distributed like the sum of the squares of K independent random variables each of which has a normal distribution with mean zero and variance of 1.


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Also, the empirical distribution function of D, found under the null composite hypothesis, follows the theoretical chi-square distribution function, if not as near.
Next, we evaluated the statistical significance of the change in chi-square to see whether the change in chi-square exceeded the critical value of chi-square given the change in degrees of freedom (the critical value is obtained from a standard chi-square distribution table).
Geared toward graduate students and professionals in statistics, engineering, social sciences and medical science but applicable to other fields as well, this text starts with the statistical decision principle and proceeds to normal distribution, chi-square distribution and properties, discrete distributions, and large sample theory.
 
 
 
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