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## Ordinal Categorical Arrays

### Order of Categories

`categorical` is a data type to store data with values from a finite set of discrete categories, which can have a natural order. You can specify and rearrange the order of categories in all categorical arrays. However, you only can treat ordinal categorical arrays as having a mathematical ordering to their categories. Use an ordinal categorical array if you want to use the functions `min`, `max`, or relational operations, such as greater than and less than.

The discrete set of pet categories `["dog" "cat" "bird"]` has no meaningful mathematical ordering. You are free to use any category order and the meaning of the associated data does not change. For example, ```pets = categorical(["bird" "cat" "dog" "dog" "cat"])``` creates a categorical array and the categories are listed in alphabetical order, `["bird" "cat" "dog"]`. You can choose to specify or change the order of the categories to `["dog" "cat" "bird"]` and the meaning of the data does not change.

Ordinal categorical arrays contain categories that have a meaningful mathematical ordering. For example, the discrete set of size categories ```["small" "medium" "large"]``` has the mathematical ordering ```small < medium < large```. The first category listed is the smallest and the last category is the largest. The order of the categories in an ordinal categorical array affects the result from relational comparisons of ordinal categorical arrays.

### How to Create Ordinal Categorical Arrays

This example shows how to create an ordinal categorical array by using the `categorical` function with the `Ordinal` name-value argument.

Ordinal Categorical Array from String Array

Create an ordinal categorical array. To make the array ordinal, set the `Ordinal` name-value argument to `true`.

```A = ["medium" "large";"small" "medium"; "large" "small"]; valueset = ["small" "medium" "large"]; sizes = categorical(A,valueset,Ordinal=true)```
```sizes = 3x2 categorical medium large small medium large small ```

Ordinal Categorical Array from Integers

Create an equivalent categorical array from an array of integers. Use the values `1`, `2`, and `3` to define the categories `small`, `medium`, and `large`, respectively.

```A2 = [2 3; 1 2; 3 1]; valueset = 1:3; catnames = ["small" "medium" "large"]; sizes2 = categorical(A2,valueset,catnames,Ordinal=true)```
```sizes2 = 3x2 categorical medium large small medium large small ```

Compare `sizes` and `sizes2`.

`isequal(sizes,sizes2)`
```ans = logical 1 ```

`sizes` and `sizes2` are equivalent categorical arrays with the same ordering of categories.

Convert a Categorical Array from Nonordinal to Ordinal

To convert an ordinal categorical array to a nonordinal array, use the `categorical` function without the `Ordinal` name-value argument.

`sizes3 = categorical(sizes)`
```sizes3 = 3x2 categorical medium large small medium large small ```

Determine if the categorical array is ordinal.

`isordinal(sizes3)`
```ans = logical 0 ```

Convert `sizes3` to an ordinal categorical array.

```sizes3 = categorical(sizes3,Ordinal=true); isordinal(sizes3)```
```ans = logical 1 ```

`sizes3` is now a 3-by-2 ordinal categorical array equivalent to `sizes` and `sizes2`.

### Working with Ordinal Categorical Arrays

In order to combine or compare two categorical arrays, the sets of categories for both input arrays must be identical, including their order. Furthermore, ordinal categorical arrays are always protected. Therefore, when you assign values to an ordinal categorical array, the values must belong to one of the existing categories. For more information see Work with Protected Categorical Arrays.