Statistical analyses in practice usually include two parts: statistical description and statistical inference. The statistical description is a kind of fundamental work for statistical inference, which describes the feature of the sample. The main forms for description are tables (such as frequency table), plots (such as block plot, histogram), and numerical indices (such as mean, standard deviation).
1.1 Variables and Data
1.1.1 Types of variables
Variables are used to describe the properties of individuals in statistics. Different types of variables have different types of distributions and hence the statistical methods being used might be different. It is important to identify the types of variables before dealing with the data.
1.1.1.1 Continuous variable
They are the variables whose values can be obtained through measurements such as height, weight, blood pressure, pulse, and blood count of the individuals. Limited by the precision of measurement, the variables such as height and weight can take some values of real number but not all indeed, and the variables such as pulse and blood count can take values of integral number only. However, for convenience in theoretical study, they are regarded as continuous variables taking values in a continuous interval on the axis of a real number. Sometimes, the observed values of such kinds of variables are called measurement data.
31.1.1.2 Discrete variable
Some properties can only be described qualitatively with several mutually excluded categories, such as gender, occupation and effect of medicine (positive or negative). The variable for gender can only take a “value” either “male” or “female”; the variable of occupation may take a “value” among several categories (worker, farmer, salesman and soldier etc.). This kind of variables is called categorical variables or nominal variables. Example 1.1 The variable for gender can be defined with a binary variable X .
X 0 Female,1 Male.
In general, the variables taking values in a set of countable numbers are called discrete variables. Binary variable is the simplest special case of it.
The number of individuals within a certain category is often counted, and it is called frequency so that the data of discrete variable is sometimes called count data.
Example 1.2 In the sample of 108 patients, there are 63 males and 45 females. If a binary variable X is defined for gender as in Example 1.1, the sum of X for the 108 patients is the number of males (63).In general, the frequency of a certain category is equivalent to the sum of a binary variable.
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