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Data Types

Data can be broadly categorized into two types:

  1. Quantitative. Also known as Numeric, these data are used to count or measure something. Their values are stored in various numeric classes of MATLAB, including floating-point types (such as double and single) and integer types (such as uint8, uint16, int32, etc.).
  2. Qualitative. Also known as Categorical, these data are used to describe something using a label like Male or Female, or Good or Bad. In MATLAB, qualitative data can be stored as logical, string, or categorical arrays (see below), depending on the nature of the categories.
graph TD
    DATA:::data --> Num[Numbers];
    DATA --> Cat[Categories];
    Num --> Disc[Discrete];
    Num --> Cont[Continuous];
    Cat --> Nom[Nominal];
    Cat --> Ord[Ordinal];
    Cont --> Int(Interval)
    Cont --> Rat(Ratio)
    Rat --> RatX(speed, height, weight)
    Int --> IntX(Temp, 12-Hour Clocks)
    IntX --> MatFloat(datetime, single, double)
    RatX --> MatFloat
    Disc --> Whole(Whole Numbers)
    Whole --> WholX(Counts, Ratings,
     Images)
    WholX --> MatInt(uint8, uint16, etc.)
    Nom --> NomDesc(No Order)
    Ord --> OrdDesc(Ordered)
    NomDesc --> NomX1(Male, Female)
    NomDesc --> NomX2(Colors)
    OrdDesc --> OrdX(Beginner,
     Intermediate,
     Advanced)
    NomX1 --> MatCat[string, categorical]
    NomX2 --> MatCat
    OrdX --> MatCat
    class Num,Disc,Whole,WholX,Cont,Int,IntX,Rat,RatX nums
    classDef nums fill:#5DADE2  
    classDef data fill:#F39C12
    class MatFloat,MatInt,MatCat mats
    classDef mats fill:#48C9B0

Categorizing Data

Numeric Data can be classified into Discrete or Continuous classes.

  • Discrete numbers are whole numbers or integers.

  • Continuous numbers have an infinite number of possible values between whole numbers, like 1.2 or the value of \(\pi\). In statistics, Continuous numbers can be further classified into Interval and Ratio values, depending on whether they have a true absolute zero point (absence of value). The presence or absence of a true zero affects the types of mathematical operations you can perform and the conclusions you can draw from the data. For example, you can't say 20°C is twice as hot as 10°C (interval), but you can say 20kg is twice as heavy as 10kg (ratio).

    • Interval Numbers, like Temperature (1) or Time on a clock, do not have an absolute zero reference. For example, 0°C or 0°F does not mean no temperature; it is simply one value in a range of values. Similarly, 0:00 does not mean the absence of time, it just means midnight. In fact, to handle time values, MATLAB came up with the datetime data type.

    • Ratio Numbers, by comparison, do have an absolute zero reference. For example, a height of 0 means the absence of height and a weight of 0 means the absence of weight, so measurements like height, weight, and speed are all Ratio Numbers. By the way, time measured in seconds would also be a Ratio number, since in this scenario 0 seconds means the absence of seconds.

    1. unless you're dealing with Kelvin

Categorical Data can be further classified into Ordered (Ordinal) or Non-ordered (Nominal) categories. Ordinal categories are categories with an implied order, such as Beginner, Intermediate, or Advanced. Nominal categories do not have an implied order, e.g. Male and Female.

Categorical Arrays

To handle Qualitative Data, MATLAB created the categorical variable type. Categorical arrays operate similarly to string arrays, but they have built-in functions for statistical uses. They're also more memory-efficient than string arrays: instead of repeatedly storing the full text of a label like "Female" for every occurrence, MATLAB stores a compact integer code for each element and keeps a single copy of each category name.

Consider the following string array.

Create String array
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sex = ["Male" "Male" "Female" "Female" "Male" "Female"] % create string array

sex = 

  1×6 string array

    "Male"    "Male"    "Female"    "Female"    "Male"    "Female"

We can easily convert this string array into a categorical array using the function categorical

sex = categorical(sex) % typecast to categorical

…Here we just overwrite the string array with its categorical version.

sex = 

  1×6 categorical array

     Male      Male      Female      Female      Male      Female

And that's it. sex is now a categorical array. You can do a lot of the same things with a categorical array that you can do with a string array.

Create logical array from a categorical array
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la = sex == "Male" % logical array

la =

  1×6 logical array

   1   1   0   0   1   0

…Here we create a logical array from the relation operation "sex is equal to Male".

Categorical arrays also have a lot of built-in functions, designed to make data analysis easier. The function categories returns the categories (or group names) in a categorical array.

Get Categories
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categories(sex) % return categories

ans =

  2×1 cell array

    {'Female'}
    {'Male'  }

…There are two categories: Female and Male.

And you can use the function summary to report the count of each category in the array.

Summary
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summary(sex) % returns category count
sex: 1×6 categorical

     Female      Male      <undefined>
     3           3         0

…Notice the <undefined> category that shows up in the summary. This is the categorical equivalent of a missing value (similar to NaN for numeric data)—it represents elements that haven't been assigned to any category. Since every element in sex was already labeled "Male" or "Female," the <undefined> count here is 0.

Creating Ordinal Data

If you have ordinal data, you still use the categorical function, but with a couple of additional inputs.

Create Ordinal Categorical Array
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2
level = ["Advanced" "Advanced" "Beginner" "Intermediate" "Advanced" "Beginner"] % create string
level = categorical(level,{'Beginner','Intermediate','Advanced'},Ordinal=true) % typecast to ordinal

…Here, the second input into categorical is the category names in the order that you want. The third input sets Ordinal to true.

And we get an ordinal categorical array that looks very similar to just a categorical array.

level = 

  1×6 categorical array

     Advanced      Advanced      Beginner    Intermediate  Advanced      Beginner

The main difference is that when you call a function like summary…

summary(level)

level: 1×6 ordinal categorical

     Beginner      Intermediate      Advanced      <undefined>
     2             1                 3             0

Additional statistics:

    Min         Beginner  
    Median      Advanced  
    Max         Advanced

…the results are reported in the order of the ordinal categories (and not in alphabetical order).

Transforming Numeric Data into Qualitative Data

Sometimes the raw data comes in as numeric, when what you actually want is categorical.

Consider the following numeric array

ratings = [3 3 2 1 3 2 1 1 1 2]

These numbers actually represent three different categories:

  1. Terrible
  2. Meh
  3. Awesome

To replace the numbers with the category labels, you enter the following into categorical:

ratings = categorical(ratings,[1 2 3],{'Terrible','Meh','Awesome'},Ordinal=true)

…notice here that the second input is the rating categories as numbers, while the third input is the rating categories as labels. The fourth input turns Ordinal on.

And you get…

ratings = 

  1×10 categorical array

  Columns 1 through 5

     Awesome      Awesome      Meh      Terrible      Awesome 

  Columns 6 through 10

     Meh      Terrible      Terrible      Terrible      Meh

…a categorical array with all the correct categories included.

And these categories show up in the summary:

summary(ratings)
ratings: 1×10 ordinal categorical

     Terrible      Meh      Awesome      <undefined>
     4             3        3            0

Additional statistics:

    Min         Terrible  
    Median      Meh       
    Max         Awesome

Converting Back to Numeric

Since ordinal categories have an underlying order, MATLAB lets you convert them back into their original numeric codes using the function double:

Convert Ordinal Categorical back to Numeric
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double(ratings)
result
ans =

     3     3     2     1     3     2     1     1     1     2

…Notice that this returns ratings to its original numeric form: 1 for Terrible, 2 for Meh, and 3 for Awesome—the exact same values we started with before converting to categorical.

Challenge: Ordinal Categorical Data

Create an ordinal categorical array of shirt sizes and summarize it

Given the following numeric array representing shirt sizes:

sizes = [2 1 3 2 2 1 3 3 2 1]

where 1 = Small, 2 = Medium, and 3 = Large:

  1. Convert sizes into an ordinal categorical array with the labels "Small", "Medium", and "Large", in that order.
  2. Run summary on the result and identify the median size.
  3. Convert the categorical array back into its original numeric form.
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sizes = [2 1 3 2 2 1 3 3 2 1];
sizes = categorical(sizes,[1 2 3],{'Small','Medium','Large'},Ordinal=true)
summary(sizes)
double(sizes)

The median size is "Medium". And double(sizes) returns you right back to the original array: [2 1 3 2 2 1 3 3 2 1].