< Probability and statistics definitions < *Homogeneity and heterogeneity*

## What are homogeneity and heterogeneity?

In the general sense, *homogeneity *refers to items that are alike, identical, and equal. On the other hand,* heterogeneity* refers to things that are different, distinct, unlike, and non-equivalent. Homogeneous items can be thought of as consistent, regular, and uniform — while heterogeneous items are assorted, diverse, and mixed.

For example, a heterogeneous sample of earth could be made up of a mixture of salt, sand, and gravel. On the other hand a sample made up of just sand would be a homogeneous sample. When it comes to human populations, homogeneity and heterogeneity have slightly more nuanced definitions [1]:

- A
*homogeneous population*has a uniform character, where all the set elements are believed to be the same or similar in nature — or can be altered to make those characteristics. Homogeneous populations can be combined or mixed together in different ways.. - A
*heterogeneous population*is diverse in nature, composed of different and dissimilar elements that are, and should be, separate.

For example, a homogeneous societal culture has a dominants set of cultural beliefs, where underlying values and beliefs are shared and

pervasive. A more heterogeneous societal culture would have many different values and beliefs are held by diverse population groups [2].

## Homogenous sampling

In **homogeneous sampling**, a purposive sampling technique, is where all items in the sample share similar or identical traits that are relevant to the research, such as age, location, or size. To illustrate, suppose you want to examine the impact of a new drug on a group of adults. In this case, you could use homogeneous sampling to create a sample of adults who share the same age, gender, and race. This ensures that the sample is representative of the entire population, thus minimizing bias in the study’s findings.

On the other hand, maximum variation sampling, where a researcher deliberately creates samples made up of items with a wide range of variation with regards to a specific characteristic such as age, income or size. For example, drug safety testing studies are often performed on adults who represent a wide range of ages, weights, and races. The FDA requires that drug safety testing studies include a diverse set of participants [3].

Homogeneous samples and are typically smaller and consist of similar cases, such as 20 people who are overweight. On the other hand, a heterogeneous sample is made up of diverse characteristics, such as a mixture of 18 to 80-year-olds of different heights, weights and races.

## Homogeneity and heterogeneity in data analysis

From a data analysis standpoint, a data set is homogeneous when it is made up of variables of the same type, such as all binary variables or all categorical variables. A mixed set, such as one comprised of binary *and *categorical variables is heterogeneous.

To determine whether or not a data set is homogeneous, data sets can be compared using boxplots or descriptive statistics such as variance, standard deviation, and interquartile range. Some statistical tests are specifically designed for homogeneity assessment. These tests are crucial for various data analyses, as many hypothesis tests assume some level of data homogeneity; for example, an ANOVA test assumes equal variances between populations.

One popular test for homogeneity is the chi-square test for homogeneity, which looks at whether two populations come from the same unknown distribution, determining whether they are homogeneous or not. The test follows the standard chi-square test procedure, where the Χ2 statistic is calculated and the null hypothesis — that the data come from the same distribution — is either accepted or rejected.

## Homogeneity of variance

Homogeneity of variance (also called *homoscedasticity*) is used to describe data with the same variance. On a scatter plot, homoscedastic data will have the same scatter. If data does not have the same variance, it will show a dissimilar scatter pattern.

## References

- Shim JK, Darling KW, Lappe MD, Thomson LK, Lee SS, Hiatt RA, Ackerman SL. Homogeneity and heterogeneity as situational properties: producing–and moving beyond?–race in post-genomic science. Soc Stud Sci. 2014 Aug;44(4):579-99. doi: 10.1177/0306312714531522. PMID: 25272613; PMCID: PMC4391627.
- Enz, C. NEW DIRECTIONS FOR CROSS- CULTURAL STUDIES: LINKING ORGANIZATIONAL AND SOCIETAL CULTURES
- FDA. Clinical Trial Diversity