Association, Concepts, Meaning, Definitions, Nature, Types, Methods and Key Difference Between Association and Correlation

The concept of association arises when variables cannot be measured numerically but are expressed in terms of presence or absence of attributes. For example, literacy, employment, gender, smoking habit, or brand preference cannot be measured quantitatively but can be classified into categories. Association helps in examining whether the occurrence of one attribute affects the occurrence of another.

Meaning of Association

Association refers to the relationship between two or more attributes such that the presence or absence of one attribute is related to the presence or absence of another. It does not measure the degree of relationship but only indicates whether a relationship exists. Association is studied through frequency data and contingency tables.

Definitions of Association

• Definition by Yule

According to Yule, association refers to the relationship between attributes that cannot be measured numerically but can only be classified according to their presence or absence. This definition highlights the qualitative nature of association.

• Statistical Definition

In statistics, association is defined as the tendency of two attributes to occur together more or less frequently than expected under conditions of independence. This definition emphasizes comparison between actual and expected frequencies.

• General Definition

Association may be defined as a statistical relationship between two qualitative characteristics where the existence of one attribute influences the existence of another. It focuses on interdependence rather than numerical measurement.

Nature of Association

• Qualitative in Nature

Association deals exclusively with qualitative characteristics or attributes that cannot be measured numerically. Attributes such as gender, literacy, employment, brand preference, or habits are studied in terms of their presence or absence. Since numerical measurement is not possible, association focuses on frequency distribution and classification, making it different from correlation, which deals with quantitative data.

• Indicates Relationship but Not Degree

Association shows whether a relationship exists between two attributes but does not measure the degree or strength of that relationship. It only indicates whether attributes occur together more or less frequently than expected. Therefore, association is descriptive rather than quantitative and does not provide precise numerical measurement of the relationship.

• Based on Presence or Absence of Attributes

The nature of association is based on whether attributes are present or absent in a given set of observations. Symbols such as A and B are used to represent attributes, while α and β represent their absence. This symbolic representation helps in constructing contingency tables and analyzing relationships between attributes.

• Studied Through Contingency Tables

Association is generally studied using contingency tables that display the joint frequency distribution of attributes. These tables help compare observed frequencies with expected frequencies under conditions of independence. The analysis of contingency tables forms the foundation for determining whether association exists between attributes.

• May Be Positive, Negative, or Zero

Association can be positive, negative, or zero in nature. Positive association occurs when attributes tend to occur together, negative association occurs when the presence of one attribute excludes the other, and zero association indicates independence. This classification helps in understanding the direction of association between attributes.

• Commonly Used in Social and Business Studies

Association is widely used in social sciences, market research, psychology, and business studies. It helps analyze consumer behavior, employee characteristics, brand loyalty, and social trends. Since many real-world characteristics are qualitative, association becomes a practical and useful analytical tool.

• Does Not Establish Cause-and-Effect Relationship

Association does not establish a cause-and-effect relationship between attributes. It only shows that attributes are related in some manner. The presence of association does not imply that one attribute causes the other. Further analysis is required to determine causality.

• Supplemented by Coefficients of Association

Although association is qualitative, coefficients such as Yule’s coefficient are used to express the nature of association numerically. These coefficients provide a summarized indication of positive, negative, or zero association, enhancing interpretability while retaining the qualitative nature of analysis.

Types of Association

Association between attributes can be classified into different types based on the manner in which attributes occur together. These classifications help in understanding the nature of relationship between qualitative variables.

1. Positive Association

Positive association exists when two attributes tend to occur together more frequently than expected by chance. The presence of one attribute increases the likelihood of the presence of the other. For example, literacy and employment often show positive association. This type of association indicates a direct relationship between attributes and is commonly observed in social and business studies.

2. Negative Association

Negative association exists when the presence of one attribute reduces the likelihood of the presence of another. In such cases, attributes tend not to occur together. For example, smoking and good health may show negative association. This type of association reflects an inverse relationship between attributes and helps identify conflicting or mutually exclusive characteristics.

3. Zero Association (Independence)

Zero association occurs when the presence or absence of one attribute does not influence the presence or absence of another. The attributes are said to be independent of each other. For example, eye color and occupation may show zero association. In this case, the occurrence of attributes is purely by chance.

4. Complete Association

Complete association exists when two attributes always occur together or never occur together. If the presence of one attribute always implies the presence of another, the association is perfectly positive. If the presence of one always implies absence of the other, the association is perfectly negative. Such cases are rare in practical situations.

5. Partial Association

Partial association exists when attributes are related to some extent but not completely. The presence of one attribute increases or decreases the probability of the other, but not always. Most real-life situations show partial association, making it the most common type encountered in business and social research.

6. Positive but Imperfect Association

In positive but imperfect association, attributes generally occur together, but there are some exceptions. For example, higher education generally leads to higher income, but not in all cases. This type of association reflects real-world complexity where multiple factors influence outcomes.

7. Negative but Imperfect Association

Negative but imperfect association occurs when attributes generally do not occur together, but some overlap exists. For example, unhealthy habits and longevity may show negative association, but some individuals may still live long despite unhealthy habits. This type highlights the probabilistic nature of qualitative relationships.

8. Spurious Association

Spurious association refers to an apparent relationship between attributes that actually arises due to the influence of a third factor. The attributes appear related, but there is no direct association between them. Identifying spurious association is important to avoid incorrect conclusions in research and decision-making.

Methods of Studying Association

Association refers to the relationship between qualitative variables or attributes such as literacy and employment, smoking and disease, etc. Since attributes cannot be measured numerically like variables, special statistical methods are used to study their association. The main methods are explained below.

Method 1. Percentage Method

The percentage method is the simplest method of studying association between attributes. Under this method, percentages of one attribute are calculated in relation to another attribute and compared. If the percentage of occurrence of one attribute is higher when another attribute is present, a positive association is indicated. If the percentage is lower, it suggests a negative association. If percentages remain the same, there is no association. Though easy to understand and apply, this method lacks precision and does not provide a numerical measure of the degree of association.

Method 2. Contingency Table Method

A contingency table is a tabular presentation showing the frequency distribution of two or more attributes simultaneously. It classifies data into rows and columns based on the presence or absence of attributes. For example, a 2×2 table shows frequencies of two attributes and their combinations. By examining the distribution of frequencies in the table, one can infer whether attributes are positively associated, negatively associated, or independent. This method forms the basis for more advanced statistical measures like Yule’s coefficient and the Chi-square test.

Method 3. Yule’s Coefficient of Association

Yule’s coefficient of association provides a numerical measure of the degree and direction of association between two attributes. It is calculated using the frequencies from a 2×2 contingency table. The value of the coefficient ranges between –1 and +1. A value of +1 indicates perfect positive association, –1 indicates perfect negative association, and 0 indicates no association. This method is widely used because it is simple, precise, and gives a clear measure of association.

Method 4. Yule’s Coefficient of Colligation

The coefficient of colligation is another method proposed by Yule to study association between attributes. Unlike the coefficient of association, it measures the tendency of attributes to occur together without showing the direction of association. Its value lies between 0 and 1. A value closer to 1 indicates a strong association, while a value closer to 0 indicates weak association. This method is less popular in practice but is useful in theoretical analysis of association.

Method 5. Chi-Square (χ²) Test

The Chi-square test is a statistical test used to examine whether there is a significant association between attributes. It compares observed frequencies with expected frequencies under the assumption of independence. If the calculated Chi-square value exceeds the table value, the null hypothesis of independence is rejected, indicating the presence of association. This method is more scientific and reliable, especially for large samples, and is widely used in research and social sciences.

Method 6. Comparison of Observed and Expected Frequencies

This method involves comparing actual observed frequencies with theoretically expected frequencies assuming no association. If observed frequencies differ significantly from expected frequencies, it suggests the existence of association between attributes. This method forms the conceptual basis of the Chi-square test. While simple in concept, it requires careful calculation and interpretation to avoid incorrect conclusions.

Key Difference Between Association and Correlation