Mathematical Statistics

Mathematical statistics
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Mathematical statistics
Inferential statistics
Variables are usually of different kinds. There are categorical variables and numerical variables
(Cho and Abe, 2013). The numerical variables can be classified as discrete and continuous
variables. Different types of variables are measured using different methods. This implies that to
perform a statistical test, the method used for measuring categorical variables cannot be very
convenient in measuring continuous variables. Mostly categorical variables take on values that
are called dummy variables to represent them. Dummy variables mean the values that have been
coded by the user and assigned uniquely to the categorical variables, they are just meant to be
variable identifiers. Since numerical variables will only take on values that continuous or discrete
there will be no other measurement method. Since the categorical variable is a measurement
scale whose variable contains a set of categories different scale of measurement is used to
enhance statistical computation of the variable. The measurement methods that are used are the
nominal, ordinal, interval, and ratio measurements. These methods have been elaborated further
in the section below.
A nominal method is a measurement method used when the categorical variable contains
uncorded categories (Bianch et al. 2011). This means that the variable has not been ordered. For
instance, if you consider religion a person can be a Muslim, a Christian, a Hindu, or a pagan.
Such data there is no specific method in which the religion can be arranged say from the most
superior or less superior. This indicates that a person in any religion doesn’t feel that his/her
religion is better than that of another person since there is no order in which it can be measured.
Another example of a nominal measurement is gender. Gender cant is measured using any
quantitative values. For gender, you are either male or female and this no way a person can be

Mathematical statistics
assigned gender its just natural that you are either male or female. Since such kind of data cannot
give desirable information when computing, its usually coded dummy variable. The dummy
variables are usually coded using n-1 rule. The n-1 rule states that for any nominal variable you
are going to have dummy variables that are less than the nominal variables by one (Taranis et al,
2011). After coding the variable with dummy numbers, they are converted into factors a data
structure in which they are treated as variables with the levels that correspond to the number of a
dummy variable. For illustration if you have a nominal variable called gender it will be assigned
dummy variables 0 or 1, these variables will be assigned to the levels male and female.
Assigning a dummy variable to either male or female doesn’t have any order that is required.
The variable will have two levels, and statistical computing can be conveniently carried out
using various statistical software’s.
Ordinal measurement. This is a type of measurement that is used for ordered categorical
variables (Malhotra et al, 2012). This means that the categorical variable has a certain order
which has to be followed either in ascending or descending order. Such measurement is used for
measuring variables such as students performance. A student can score in the test as follows,
excellent, good, fair or poor. This order in which the variables have been arranged means that the
higher a students perform in a test the best he/she is and the converse is also true. Another
example of an ordinal measurement is the time of the day, it’s either morning, afternoon, or
night. This implies that you can’t move from morning to evening without going through the
afternoon. Ordinal measurement means that a certain order has to be followed that brings in
certain superiority of the highly ranked order.
Interval measurement. This measurement involves assigning values of variables into certain
intervals. The intervals can be of equal width or they can be unequal. Those intervals represent a