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˚ Temperature, does not mean no temperature, it 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 absence of any weight, so measurements like height, weight, 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 similar to string arrays, but they have built-in functions for statistical uses.

Consider the following string array.

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

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 also has 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

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(sex) % rturns category count
     Female      Male 
     3           3    

Creating Ordinal Data

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

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 differences is that when you call a function like summary…

summary(level)

     Beginner      Intermediate      Advanced 
     2             1                 3       

…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 ratings 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)
     Terrible      Meh      Awesome 
     4             3        3