In a computer, information is represented as bits (0's and 1's). We typically quantify data as bytes (8 bits): There are numerous ways to translate human readable data to binary, such as ASCII:

• Kilobyte (kB) = 1,000 bytes
• Megabyte (MB) = 1,000,000 bytes
• Gigabyte (GB) = 1,000,000,000 bytes

There are numerous ways to translate human readable data to binary, such as ASCII, where each character is represented as one byte. There are
2⁸ = 256 unique combinations of 0's and 1's in a byte.

• "A" : 01000001
• "CAT": 01000011 01000001 01010100
• "31": 00110011 00110001

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
• 2⁶⁴ (>18 quintillion) possible unique values
• CPUs can be stacked in parallel to handle more information at one time

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?

• Spatial Data: Attributes that describe where.
• Non-Spatial Data: Attributes that describe what or when.

All data, 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”.

Categorical: strictly descriptive and lack any meaningful numeric value.

• Textual or coded numerals.
• Measured on either a Nominal or Ordinal scale.

• Names or categories with no ranking or direction
• Categories are not more/less, better/worse, just different.

We can:

• Check equivalency
• Count frequencies
• Nothing else

• Names or categories
• Some ranking or directionality

We can:

• Check equivalency
• Count frequencies
• Check order/rank

Same operations as nominal data + more.

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.

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

The Downside: variability within the area is lost.

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

Numeric; describe the quantities associated with a phenomenon.

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

Discrete:
• Whole numbers
• Counts
• Not infinitely divisible
• Integer, Long

Continuous:
• Decimals
• Measurements
• Infinitely divisible
• Float, Double

Discrete:
• Countable
• Ex. Population

Continuous:
• Non-countable
• Ex. Temperature

Discrete and continuous data can be measured on an Interval or Ratio scale.

• These types of quantitative data are closely related, but have one important distinction.

Fixed, absolute zero point.

• Cannot take negative values
• Can multiply/divide

Population is a good example of discrete ratio data.

Tree height is a good example of continuous ratio data.

Other examples of ratio data include:

• Temperature in Kelvin (Continuous)
• Precipitation (Continuous)
• Units of time (Continuous)
• Rental cost (Discrete-ish)
• Popular Vote Totals (Discrete)

Arbitrary zero point

• Can take negative values
• Cannot multiply/divide

Celsius (interval) vs. Kelvin (ratio).

• °C = °K-273.15.
• 0 °K: "Absolute Zero"
• 0 °C: Freezing point of water

Other examples include:

• ph scale (continuous)
• Dates (discrete)
• Times (discrete-ish)

If we want to account for the influence of one variable when analyzing another. Referred to as Normalizing or Standardizing.

• Formula is C=A/B
• A is the variable of interest
• B is the "confounding" variable
• C is the Derived Ratio

There are many circumstances where we might need to do this. ie. Housing affordability.

• A: My rent $1,250/mo
• B: I make ~$4000/mo
• C: 31% my income goes to rent
• Income and rent (in $) are both discrete, housing affordability is continuous.

Another would be incident rates.