Chi-Square Goodness-of-Fit Test

Statistics has been an integral part of many economies in the
contemporary world. It is a study that is involved with the collection,
analysis, organization, as well as interpretation and subsequent
presentation of data. Whether as a branch of mathematics or a
distinctive body of mathematics, statistics comes in handy in explaining
data pertaining to populations through collecting representatives.
However, different techniques are used to determine how close the
observed values are to the expected values in the population, one of
which is the Chi-square goodness of fit test. The chi-square
goodness-of-fit test is used in determining whether the sample data is
in line or consistent with the hypothesized distribution. For instance,
in a case where a hypothetical company printing baseball cards claimed
that 10% of the cards were All-stars, 60% veterans and 30% rookies, a
random sample of the baseball cards may be gathered and a chi-test
goodness-of-fit test used to determine whether there was a significant
difference between the sample distribution and the distribution that the
company outlined.
The application of the chi-square goodness-of-fit test is subject to
the satisfaction of certain conditions. First, the sampling technique
used must be simple random sampling, with the population being 10 times
larger than the sample or more. In addition, the expected value for the
number of sample observations made for every level of variable must be
at least five. Lastly, the variables being studied must be categorical.
However, there exists a difference between the chi-square goodness of
fit test and other tests such as the independent samples t-test. The
independent samples t-test is used in instances where an individual
would like to make a comparison for the means of normally distributed
interval dependent variables pertaining to two independent groups.
Chance, B. L & Rossman, A. J. (2005). Investigating Statistical
Concepts, Applications, and Methods. New York: Duxbury Press.