The sample values are grouped in C categories,
and the counts of the number of sample values occurring
in each category is recorded.
The hypothesized distribution is specified in advance,
so that the number of observations that should appear each category,
assuming the hypothesized distribution is the correct one,
can be calculated without reference to the sample values.
Guidance:
Ways to detect before performing the
chi-square goodness-of-fit test whether your data violate any
assumptions.
Ways to examine
chi-square goodness-of-fit test results to detect
assumption violations.
Possible alternatives if your data or
chi-square goodness-of-fit test results indicate assumption violations.
To properly analyze and interpret results
of the chi-square goodness-of-fit test, you should be familiar with the following terms
and concepts:
If you are not familiar with these terms and concepts, you are advised to
consult with a statistician. Failure to understand and properly apply
chi-square goodness-of-fit test may result in drawing erroneous conclusions from your
data. Additionally, you may want to consult the following references:
Agresti, A. 1990. Categorical Data Analysis.
New York: John Wiley & Sons.
Cochran, W. G. 1954.
Some methods of strengthening the common chi-square tests.
Biometrics10: 417-451.
Conover, W. J. 1980. Practical Nonparametric Statistics. 2nd ed.
New York: John Wiley & Sons.
D'Agostino, R. B. and Stephens, M. A., eds. 1986. Goodness-of-fit
Techniques. New York: Dekker.
Daniel, Wayne W. 1978. Applied Nonparametric Statistics.
Boston: Houghton Mifflin.
Daniel, Wayne W. 1995. Biostatistics. 6th ed.
New York: John Wiley & Sons.
Koehler, K. J. and Larntz, K. 1980.
An empirical investigation of goodness-of-fit statistics
for sparse multinomials.
Journal of the American Statistical Association75: 336-344.
Roscoe, J. T. and Byars, J. A. 1971.
An investigation of the restraints with respect to sample size
commonly imposed on the use of the chi-square statistic.
Journal of the American Statistical Association66: 755-759.
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