VARIABLES AND ORGANIZATION OF THE DATA [WEISS (1999), ANDERSON & SCLOVE (1974) AND FREUND (2001)]

VARIABLES AND ORGANIZATION OF THE DATA

[WEISS (1999), ANDERSON & SCLOVE (1974) AND FREUND (2001)]

 VARIABLES

A characteristic that varies from one person or thing to another is called a Variable  i.e, a variable is any characteristic that varies from one individual member of the population to another. Examples of variables for humans are height, weight, number of siblings, sex, marital status, and eye color. The first three of these variables yield numerical information (yield numerical measurements) and are examples of quantitative (or numerical) variables, last three yield non-numerical information (yield non-numerical  measurements) and are examples of qualitative (or categorical) variables. Quantitative variables can be classified as either discrete or continuous.

Discrete  variable:  Some variables, such as the numbers of children in family, the numbers of car accident on the certain road on different days, or the numbers of students taking basics of statistics course are the results of counting and thus these are discrete variables. Typically, a discrete variable is a variable whose possible values are some or all of the ordinary counting numbers like 0, 1, 2, 3, . . . . As a definition, we can say that a variable is discrete if it has only a countable number of distinct possible values. That is, a variable is is discrete if it can assume only a finite numbers of values or as many values as there are integers.

Continuous variables: Quantities such as length, weight, or temperature can in principle be measured arbitrarily accurately. There is no invisible unit. Weight may be measured to the nearest gram, but it could be measured more accurately, say to the tenth of a gram. Such a variable, called continuous, is intrinsically different from a discrete variable.

SCALES

Scales for Qualitative Variables Besides being classified as either qualitative

or quantitative, variables can be described according to the scale on which

they are defined. The scale of the variable gives certain structure to the variable and also defines the meaning of the variable.

The categories into which a qualitative variable falls may or may not have

a natural ordering. For example, occupational categories have no natural ordering. If the categories of a qualitative variable are unordered, then the qualitative variable is said to be defined on a nominal scale, the word nominal referring to the fact that the categories are merely names. If the categories can be put in order, the scale is called an ordinal scale. Based on what scale a qualitative variable is defined, the variable can be called as a nominal variable or an ordinal variable. Examples of ordinal variables are education (classified e.g. as low, high) and "strength of opinion" on some proposal (classified according to whether the individual favors the proposal, is indifferent towards it, or opposites it), and position at the end of race (first, second, etc.).

Scales for Quantitative Variables: Quantitative variables, whether discrete

or continuous, are defined either on an interval scale or on a ratio scale.

If one can compare the differences between measurements of the variable meaningfully, but not the ratio of the measurements, then the quantitative variable is defined on interval scale. If, on the other hand, one can compare both the differences between measurements of the variable and the ratio of  the measurements meaningfully, then the quantitative variable is defined on ratio scale. In order to the ratio of the measurements being meaningful, the variable must have natural meaningful absolute zero point, i.e, a ratio scale is an interval scale with a meaningful absolute zero point. For example, temperature measured on the Certigrade system is a interval variable and the height of person is a ratio variable.

ORGANIZATION OF THE DATA

Observing the values of the variables for one or more people or things yield

data. Each individual piece of data is called an observation and the collection

of all observations for particular variables is called a data set or data matrix. Data set are the values of variables recorded for a set of sampling units.

For ease in manipulating (recording and sorting) the values of the qualitative

variable, they are often coded by assigning numbers to the different categories, and thus converting the categorical data to numerical data in a trivial sense. For example, marital status might be coded by letting 1,2,3, and 4 denote a person’s being single, married, widowed, or divorced but still coded data still continues to be nominal data. Coded numerical data do not share any of the properties of the numbers we deal with ordinary arithmetic. With records to the codes for marital status,

 we cannot write 3 > 1 or 2 < 4, and

we cannot write 2 − 1 = 4 − 3 or 1 + 3 = 4.

 This illustrates how important  it is always check whether the mathematical treatment of statistical data is really pegmatite.

Data is presented in a matrix form (data matrix). All the values of particular

Variable is organized to the same column; the values of variable forms the

column in a data matrix, Observation, i.e. measurements collected from

Sampling unit, forms a row in a data matrix. Consider the situation where

there are k numbers of variables and n numbers of observations (sample size

is n). Then the data set should look like

Variables

x₁₁   x₁₂      x₁₃ . . . x_1k

x₂₁    x₂₂      x₂₃ . . . x_2k

x₃₁    x₃₂     x₃₃ . . . x_3k

.        .         .         .

.        .         .         .

.        .         .         .

x_n1     x_n2       x_n3 . . . x_nk

where xij is a value of the j :th variable collected from i:th observation, i=1, 2, . . . , n and

j = 1, 2, . . . , k.

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