(Including Cross Tabulation, Calculating Expected Values,

Goodness-Of-Fit Tests, Tests of Independence, Chi-Square,

Likelihood Ratio, Log-Linear, and Fisher's Exact Test)

`Analysis of Frequency Data` deals with data that has been tabulated;
that is, the number of sampled items that fall into different categories. The
categories can be based on 1 criteria ("1 way", for example, sex), 2 criteria
("2 way", for example, sex and race), or 3 criteria ("3 way", for example, sex,
race, and religion). For 2 way and 3 way tabulations, the process is often
called cross tabulation. The process of tabulation is also called binning, since
it analogous to sorting or categorizing items and putting them into bins.

This type of frequency analysis is quite different from an FFT which finds the component frequencies (as in Cycles Per Second) in a time series.

There are several procedures in CoStat related to frequency data:

`Cross Tabulation`- Tabulate the data if not tabulated already.`1 way, Calculate Expected Values`- For 1 way tabulations, calculate the expected values based on the normal, binomial, or Poisson distributions.- Print a table of observed and expected frequencies and descriptive statistics.

- Analysis -
`1 Way Tests`- Calculate descriptive statistics: the mean, standard deviation, skewness, and kurtosis of the data.
- Perform Kolmogorov-Smirnov test of goodness-of-fit (before pooling).
- Test goodness-of-fit (how closely the expected values match the observed values) with the Chi-Square and Likelihood Ratio tests.

`2 Way Tests`- Print margin totals.
- Test the independence (the lack of interaction) of the two factors with the Chi-Square test, the Likelihood Ratio test, and Fisher's Exact Test.

`3 Way Tests`- Print margin totals.
- Test the independence (the lack of interaction) of the three factors with Log-Linear models.

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