The statistical treatment of count data is distinct from that of binary data, in which the observations can take only two values, usually represented by 0 and 1, and from ordinal data, which may also consist of integers but where the individual values fall on an arbitrary scale and only the relative ranking is important.
When such a variable is treated as a random variable, the Poisson, binomial and negative binomial distributions are commonly used to represent its distribution.
Statistical methods such as least squares and analysis of variance are designed to deal with continuous dependent variables.
These can be adapted to deal with count data by using data transformations such as the square root transformation, but such methods have several drawbacks; they are approximate at best and estimate parameters that are often hard to interpret.
This is a special case of the class of generalized linear models which also contains specific forms of model capable of using the binomial distribution (binomial regression, logistic regression) or the negative binomial distribution where the assumptions of the Poisson model are violated, in particular when the range of count values is limited or when overdispersion is present.