Inter-class correlation and intra-class correlation are two special cases of correlation analysis. Inter-class correlation shows the association among the groups and intra-class correlation shows the association within a group.
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| Intra class(a) vs Inter class(b) |
“Interclass” means among the groups.
“Intraclass” means within groups.
Inter-class correlation
Inter-class correlation refers to the degree of association or agreement between different groups or classes. It is often used to evaluate the consistency or similarity between multiple groups when measuring a particular characteristic. Inter-class correlation is commonly employed in studies comparing distinct entities, such as comparing scores between different schools, departments, or teams. More precisely, the interclass correlation means the relationship among the groups of data or between the groups of data.
Example: Suppose you are comparing the average test scores of students across different schools. Inter-class correlation would measure the level of similarity or consistency between these schools in terms of their test scores.
Mathematical Equation of InterClass correlation
![\[ InterClass Correlation (ICC) = \frac{\sigma^2_{\text{individual}}}{\sigma^2_{\text{total}}}\]](https://www.statisticalaid.com/wp-content/ql-cache/quicklatex.com-4cb4871d8f13303a0645b81e4402b858_l3.png "Rendered by QuickLaTeX.com")
Intra class correlation
Intra-class correlation, on the other hand, measures the level of consistency or agreement within a single group or class. It is used to assess how closely related individuals or items within the same group are with respect to a particular characteristic. Intra-class correlation is often used in reliability studies and assessing homogeneity within a group. More precisely, intra-class correlation means the relationship within data group.
Example: Suppose you are analyzing the consistency of test scores among students within the same classroom. Intra-class correlation would quantify the degree of similarity in scores within that group.
Mathematical Equation of Intra-Class correlation
![\[ Intra-Class Correlation (ICC) = \frac{\sigma^2_{\text{between}}}{\sigma^2_{\text{between}} + \sigma^2_{\text{within}}}\]](https://www.statisticalaid.com/wp-content/ql-cache/quicklatex.com-160cef1177a1653e5e0009a1ebd20fa5_l3.png "Rendered by QuickLaTeX.com")
Application of Intra class correlation
- How closely relatives resemble each other with regard to a certain characteristic or traits.
- Reproducibility of numerical measurements made by different people measuring the same thing.
From the above discussion now it is very clear about intra-class correlation and interclass correlation. I think there are no confusion about inter-class and intra-class correlation.
Comparison
| Feature | Inter-Class Correlation | Intra-Class Correlation |
|---|---|---|
| Definition | Measures correlation between groups. | Measures correlation within a single group. |
| Application | Used for comparing distinct groups or classes. | Used for assessing consistency within a single group. |
| Example | Comparing average scores of different schools. | Analyzing consistency of scores within a classroom. |
| Focus | Inter-group variability. | Intra-group similarity. |
Understanding the distinction between interclass and intra-class correlation helps in selecting the appropriate statistical tool depending on whether the focus is on groups or individuals within a group.
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