What is Data?

Data is information describing some phenomenon.

What is a Phenomenon?

Phenomenon: a fact or situation that is observed to exist or happen, especially one whose cause or explanation is in question.

  • A lightning strike
  • A coastline
  • A country
  • A dog on a kayak!
  • Anything and everything are phenomena!

Types of Phenomena

Discrete Objects

  • Distinct boundaries
    • Chat can be exactly measured
  • Finite
    • They are countable and cannot be infinitely subdivided

Continuous Fields

  • No distinct boundaries
    • Everywhere has a value
  • Infinitely divisible
    • They are not countable and can be infinitely subdivided

    Types of Phenomena

    When is a phenomenon discrete or continuous?

    • To an extent, it depends on our perspective and the scale of our analysis.
    • Many phenomenon are a bit of both.

    Lightning

    • A strike is a discrete object
    • What about a lighting bolt ...?
      • Doesn't really have clearly defined boundaries?
      • Sort of continuous
    • Strike frequency is a continuous field
      • Everywhere has a frequency of lighting strikes
      • Even the absence of lighting strikes, is still a frequency of strikes

    A Coastline

    • Continuous field at large scale
      • Tides & waves
      • Where is the exact boundary?
    • Discrete object at small scale
      • Zoom out and the tides/waves don't really matter
      • Its easy to draw a static boundary
    • Unless you change the time scale
      • Until you start thinking about the long term :(

    Types of Phenomena

    Most things don't fall perfectly into one category or the other.

    • That said, it is a helpful framework as long as we recognize the discrete vs. continuous dichotomy is not a perfect classification

    TopHat Question 1

    Discrete objects: (select all that apply)

    • Are countable
    • Do not have distinct boundaries
    • Are infinitely divisible
    • Have well defined boundaries

    Discrete Objects

    Buildings are a great example.

    • Concrete boundaries
    • Countable
    • Real physical object

    Discrete Objects

    Political Boundaries are also a great example.

    • Distinct boundaries
    • Countable
    • Not a physical object

    Continuous Fields

    Elevation is a great example.

    • Everywhere on Earth
    • No "number of elevations"
    • A physical property

    Continuous Fields

    Density of tweets is also a great example.

    • Everywhere has this too
    • Derived from something countable
      • But not countable itself
    • Not a physical property

    Working Together

    Frequently we'll end up working with both discrete objects and continuous fields.

    • In Module 1, you worked with:
      • Cholera deaths (Discrete objects)
      • Kernel density (continuous field)
    • We use spatial data models to represent information in a GIS
      • Vector Data Model = discrete objects
      • Raster Data Model = continuous fields

    Digital information

    We'll talk more about spatial data models later. For now, lets think about data more broadly. How do we represent data in a computer?

    • Digital information is represented as bits (0's and 1's)
    • We typically quantify data as bytes (8 bits):
      • Kilobyte (kB) = 1,000 bytes
      • Megabyte (MB) = 1,000,000 bytes
      • Gigabyte (GB) = 1,000,000,000 bytes

    Digital information

    There are numerous ways to translate human readable data to binary, such as ASCII.

    • Each character is represented as one byte
    • There are 28 = 256 unique combinations of 0's and 1's in a byte
    • Some examples:
      • "A" : 01000001
      • "CAT": 01000011 01000001 01010100
      • "31": 00110011 00110001

    Digital Information

    Modern computers use 64-bit "architecture". That is, the central processing unit (CPU) can handle 64 bits (8 bytes) of information at a time.

    • "Word" length is 64 bits
      • A "Word" is a unit of data
        • i.e., an individual piece of information
      • 264 possible unique values
        • >18 quintillion possible unique combinations of 1's and 0's to describe something
    • CPUs can be stacked in parallel to handle more information at one time

    Representing Phenomena in GIS

    Within the context of a GIS, every piece of information describing a phenomenon is referred to as an Attribute.

    • Broadly speaking each attribute can address one of three questions:
      • Where?
      • What?
      • When?

    Types of Attributes

    There are multiple ways to classify/think about attributes. One important distinction we must make

    • Non-Spatial Attributes: describe what or when
    • Spatial Attributes: describe where
      • Puts the Geographic in GIS
      • Requires some special considerations
        • We have already talked a bit about these consideration (map projections)
        • We'll discuss more considerations in the next module

    Types of Attributes

    All data (attributes), spatial and non-spatial, can be either qualitative or quantitative.

    • The types of analysis we can do with qualitative data are more limited
    • That does not make quantitative data “better”
    • Measurement scales: both qualitative and quantitative can be measured on different scales
      • Qualitative: Nominal or Ordinal Sales
      • Quantitative: Interval or Ratio Sales

    Qualitative Data

    Qualitative data is Categorical. It is strictly descriptive and lacks any meaningful numeric value.

    • Textual, coded numerals, pictures, sounds, etc
      • Typically working with textual & coded numerals most frequently in GIS
    • Limited number of computational options, often requires careful consideration when analyzing
    • Measured on either a Nominal or Ordinal scale.

    Nominal Scale

    Names or categories with no ranking or direction. Categories are not more/less, better/worse, they just different. Some examples include:

    • Flower Species
    • Zoning Categories
    • Land cover Classification

    Nominal Operations

    With nominal data we can:

    • Check equivalency
    • Count frequencies
    • Nothing else

    Ordinal Scale

    Names or categories with a ranking or direction. Categories are more/less, better/worse, etc. But the differences are relative, there is no way to say by "how much". Some examples include:

    • Spice levels
    • Relative heights
    • Compass Direction

    Ordinal Operations

    With ordinal data we can:

    • Check equivalency
    • Count frequencies
    • Check order/rank

    All the same operations as nominal data + more.

    Ordinal Operations

    Sometimes we can calculate the median.

    • Odd sets the median is the middle.
    • Even sets, average of the middle two.
    • One solution, arbitrarily assign a numeric score.

    All the same operations as nominal data + more.

    Graded Membership

    Exceptions that blur the lines.

    • Grade membership to assign categories
    • Where to draw the line between forest/alpine?
    • Winner take all: alpine meadow
      • 45% alpine meadow
      • 40% forest
      • 5% bare rock

    Graded Membership

    In practice, lots of qualitative data we work with, especially for natural phenomena, are actually graded membership.

    • The downside: variability within the area is lost.

    TopHat Question 2

    Which of the following would be examples of Nominal Data? (select all that apply)

    • Air temperature
    • Ice cream flavors
    • Tree height
    • Colors
    • Drink sizes

    Quantitative Data

    Quantitative data is Numeric. It describe the quantities associated with a phenomenon. Key properties include:

    • Values separated by a meaningful unit.
    • More arithmetic operations possible.
    • Can be Discrete or Continuous numbers.
    • Measured on either a Ratio or Interval scale.

    Kinds of Numbers

    Discrete

    • Whole numbers
    • Counts
    • Not infinitely divisible
    • Names in ArcGIS Pro:
      • Integer, Long, etc.

    Continuous

    • Decimals
    • Measurements
    • Infinitely divisible
    • Names in ArcGIS Pro:
      • Float, Double, etc.

    Kinds of Numbers

    Discrete

    • Countable
    • Examples:
      • Population
      • Year
      • "Age"

    Continuous

    • Non-countable
    • Examples:
      • Temperature
      • Height
      • Speed

    Quantitative Data

    Both Interval and Ratio data can consist of discrete or continuous numbers. These types of quantitative data are closely related, but have one important distinction.

    • Interval scales have an arbitrarily zero point, which means:
      • Can have negative values
      • Cannot multiply/divide ...
        • To compare the magnitude of one value to another
        • Can still multiply/divide for other calculations, i.e. calculating an average
    • Ratio scales have a fixed, absolute zero point, which means:
      • Cannot have negative values
        • Absolute zero point does not imply an end point, can still have infinitely many values
      • Can multiply/divide

    The Difference

    Celsius (interval) vs. Kelvin (ratio).

    • °C = K-273.15.
    • 0 °C: Freezing point of water
      • Drops below 0 °C all the time
    • 0 K: "Absolute Zero"
      • Physically cannot get any colder
    • 100 °C is not ∞% warmer than as 0 °C
      • It's actually ~ 36% warmer
      • (373.15 K - 273.15 K) ⁄ 273.15 K ~ 0.36

    Interval Scale

    Interval data has an arbitrarily zero point. Examples include:

    • Calendar years
      • Discrete interval data
    • Temperature (in celsius)
      • Continuous interval data
    • Other examples:
      • ph scale (continuous)
      • IQ scores (continuous)
      • Times (discrete-ish)

    Ratio Scale

    Ratio data has a fixed, absolute zero point. Examples include:

    • Population
      • Discrete ratio data
    • Tree height
      • Continuous ratio data
    • Other examples:
      • Precipitation (Continuous)
      • Area (Continuous)
      • Units of time (Continuous)
      • Popular Vote Totals (Discrete)

    TopHat Question 3

    Match the value to the type measurement scale and type of number:

    Length a hiking trail Interval (Discrete)
    Temperature in Fahrenheit Ratio (Discrete)
    Global Orca Population Ratio (Continuous)
    Change in Global Orca Population from 2000 to 2022 Interval (Continuous)

    Derived Ratio

    Sometimes called normalizing or standardizing, we calculate derived ratios to account for the influence of a confounding variable over a variable of interest. e.x. Housing affordability (Ha):

    • You need to account for income (I) to figure out how affordable rent (R) is:
        • $$ H_a = \frac{R}{I} $$
      • R: My rent $1,450/mo
      • I: I make ~$4600/mo
      • Ha: 31.5% of my income goes to rent
      • Income and rent ($) are both discrete, housing affordability (%) is continuous.

    Derived Ratio

    In Lab, you are going to work with two derived ratios:

    • Income and Food expenditures are correlated
      • Need to account for income if you analyze other factors
    • Population and Area are not highly correlated
      • But area definitely influences population
      • Need to account for area to analyze other factors

    TopHat Question 4

    Speed is another example of a derived ratio. If a line of thunderstorm takes 5 hours to travel from Brandon, MB to Winnipeg, MB (200 km), what is the storm's speed in km/hr?

    Summary: Types of Data

    Summary: Operations by Data Type

    Operation Nominal Ordinal Interval Ratio
    Equality x x x x
    Counts/Mode x x x x
    Rank/Order x x x
    Median ~ x x
    Add/Subtract x x
    Mean x x
    Multiply/Divide x