In fact, when k is 90 or greater, a normal distribution is a good approximation of the chi-square distribution.Ĭhi-square distributions start at zero and continue to infinity. When k is only a bit greater than two, the distribution is much longer on the right side of its peak than its left (i.e., it is strongly right-skewed).Īs k increases, the distribution looks more and more similar to a normal distribution. There is low probability that Χ² is very close to or very far from zero. The curve starts out low, increases, and then decreases again. When k is greater than two, the chi-square distribution is hump-shaped. When k is one or two, the chi-square distribution is a curve shaped like a backwards “J.” The curve starts out high and then drops off, meaning that there is a high probability that Χ² is close to zero. A probability density function is a function that describes a continuous probability distribution. We can see how the shape of a chi-square distribution changes as the degrees of freedom ( k) increase by looking at graphs of the chi-square probability density function. If you sample a population many times and calculate Pearson’s chi-square test statistic for each sample, the test statistic will follow a chi-square distribution if the null hypothesis is true.
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