One Sample Chi-square Test

Chi-Square Goodness of Fit Test

When an analyst attempts to fit a statistical model to observed data, he or she may wonder how well the model actually reflects the data. How "close" are the observed values to those which would be expected under the fitted model?
One statistical test that addresses this issue is the chi-square goodness of fit test. This test is commonly used to test association of variables in two-way tables, where the assumed model of independence is evaluated against the observed data. In general, the chi-square test statistic is of the form

If the computed test statistic is large, then the observed and expected values are not close and the model is a poor fit to the data.
ですので、Chi-Square testは、上記の式を用いてΧの2乗を計算して、下記仮説を検証することになります。

Ho: The data are consistent with a specified distribution.
H1: The data are not consistent with a specified distribution.

計算したX2で、テーブルでαを求め、判断する。
※http://www.stat.yale.edu/Courses/1997-98/101/chigf.htm这里面有很不错的例子。
※And there is also a good lecture notes from University of New England:
https://webstat.une.edu.au/unit_materials/index.htm
Chi-Squareテストの例、及びRを使ってテストする方法はこちらに参照。