# PROPHET StatGuide: Goodness of Fit (Chi-square) Test

### Assumptions:

The sample values are independent, and identically
distributed.

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:
- Cochran, W. G. 1954.
Some methods of strengthening the common chi-square tests.
*Biometrics* *10*: 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 Association*
*75*: 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 Association*
*66*: 755-759.
- Rosner, Bernard. 1995.
*Fundamentals of Biostatistics.*
4th ed. Belmont, California: Duxbury Press.
- Sokal, Robert R. and Rohlf, F. James. 1995.
*Biometry.* 3rd. ed.
New York: W. H. Freeman and Co.
- Zar, Jerrold H. 1996.
*Biostatistical Analysis.* 3rd ed. Upper Saddle River, NJ:
Prentice-Hall.

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##### Last modified: February 20, 1997

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