# Can nominal scale data be analyzed using regression analysis?

Regression analysis is commonly used to examine the influence of independent variables on dependent variables observed in a study. However, regression analysis is more suitable for data with interval or ratio scales. How about data with nominal scales, can regression still be used?

Nominal scale is a type of scale that provides labels or categories without any order or ranking among categories. Regression analysis typically requires independent and dependent variables with higher measurement properties, such as interval or ratio scales. This prompted me to explain in an article on the Kanda Data website.

## Measurement scales in statistics

In statistics, measurement scales refer to the properties of variables we measure. There are four types of measurement scales in statistics: nominal, ordinal, interval, and ratio scales.

Variables measured using nominal scales are categorized, but there is no order or ranking among categories. Examples: gender, occupation, and others.

Ordinal scales involve categorizing data with a known order or rank. However, in ordinal scales, the distance between values is unknown or inconsistent. Examples: educational variables and variables like motivation, attitude, and customer satisfaction measured using a Likert scale.

For variables measured using interval scales, there is a consistent order, rank, and consistent distance between values. However, there is no absolute zero in interval scale data, such as temperature, student grades, and others.

Ratio scale variables have characteristics similar to interval scale data but include an absolute zero. Examples: weight, production, consumption, profit, and others.

## Nominal scale falls under non-parametric statistics

In terms of analysis methods, statistics can be divided into parametric and non-parametric statistics. Nominal scales are often associated with non-parametric statistical methods.

Nominal scales, due to their categorical nature without order or rank, are more suited to non-parametric methods. Non-parametric statistical analysis is often used when data does not meet certain distribution assumptions.

In non-parametric statistics, nominal or ordinal scale data is more appropriate. However, sample size, analysis goals, and other assumptions also influence the choice of non-parametric statistics in research.

## Assumptions of Ordinary Least Squares (OLS) linear regression analysis

Linear regression analysis using the Ordinary Least Squares (OLS) method has several assumptions that need to be met to obtain the Best Linear Unbiased Estimator. Some assumptions include linearity, non-multicollinearity, non-heteroskedasticity, and normally distributed residuals.

Both cross-sectional and time series data need to undergo tests for these assumptions. For research using time series data, autocorrelation tests are necessary.

If the assumption tests do not meet the requirements of OLS linear regression, researchers do not need to force the use of these tests. Researchers can choose alternative tests based on data characteristics and research goals.

## Nominal scale data does not meet the normality of residuals assumption

Nominal scale data tends not to meet the assumption of normality of residuals in the context of linear regression. The assumption of normality of residuals assumes that the distribution of the residuals in the regression model should approximate a normal distribution.

OLS linear regression is more suitable for dependent variables with interval or ratio scales. So, what if the data we have is on a nominal scale? Can we still analyze the influence using regression?

## Analyzing nominal scale data

When you have data with a nominal scale dependent variable, there are several approaches for data analysis:

1. Binary logistic regression analysis

Binary logistic regression is a common choice for analyzing the influence of one or more independent variables on a nominal scale dependent variable (two categories). Binary logistic regression is suitable for modeling the probability of an event or non-event.

2. Binary dummy variables in regression analysis

If you choose to continue using linear regression, you can convert nominal category variables into binary dummy variables and use them as one of the independent variables in the regression equation. Each category is transformed into a dummy variable with a value of 0 or 1, and one category is considered the baseline for comparison.

In addition to these two analyses, nominal scale data can also be analyzed using the chi-square test to examine the relationship between variables. Furthermore, if the dependent variable has more than two categories, multinomial logistic analysis can be employed.

Alright, this concludes the article for now. I hope it proves helpful and adds value to the knowledge of those in need. Stay tuned for the next Kanda Data article next week. Thank you.