There are 4 people and their heights in inches are 55, 56, 72 and 74. Here height is a characteristic and the figures 55, 56, 72 and 74 are the values of a variable. These figures are the result of measurements. You know that the measurements generate a continuous variable. Thus the variable for heights is a continuous variable. Suppose we select 4 bulbs from a certain lot and inspect them. The lot contains good as well as defective bulbs. The sample may contain 0, 1, 2, 3, 4 defective bulbs. The values 0, 1, 2, 3 and 4 are the values of a discrete variable.
Out of 4 people whose heights are given above, 2 are tall with heights of 72 and 74 inches and 2 are short with heights of 55 and 56 inches. When we use the words tall and short, any variable is not under consideration. We do not make any measurements. We only see who is tall and who is short. Here level of height tall or short is not a variable, it is called an attribute. Out of 4 bulbs 2 are good and 2 are defective. Here also any variable is not under consideration. We only count the defective bulbs and good bulbs. We examine whether the quality of being defective is present in a bulb or not. The status of the bulb is an attribute with two outcomes, good and defective. Thus an attribute is a quality and the data is collected to see how many objects possess the quality of being defective and how many elements do not possess this quality. Other famous examples of attributes are level of education, level of smoking, level of social work, level of income, religion, etc. The data on the attribute is the result of recording the presence or absence of a certain quality (attribute) in the individuals. The data on the variables are called quantitative data whereas the data on the attributes are called qualitative data or count data. As the data on the variables is collected for the purpose of analyzing data and for inference about the population parameters, similarly the data on the attribute or attributes is collected for the purpose of analyzing data and for testing hypotheses about the attributes. We shall discuss hypothesis testing about attributes in the subsequent topic in this unit.
Notation for Attributes
For a single variable we use the symbol $$X$$, and if there are two variables we use the symbols $$X$$ and $$Y$$ for them. When there is a single attribute like height, the word, tall may be denoted by $$A$$ and short may be denoted by $$\alpha $$. If the tall and the short people are divided into intelligent and unintelligent people, then intelligent may be denoted by $$B$$ and $$\beta $$ may be used for the opposite attribute, unintelligent. It may be noted that the word attribute is used for the main group like intelligence, and the sub-groups intelligent and unintelligent are also called attributes.