Center for Analysis and Design of Intelligent Agents

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Scales & Display of Data

When measuring variables…	… we have to use some scale to do so. This applies to both independent and dependent variables.
Types of scales	Nominal Ordinal Interval Ratio
Different scales require different treatment	The main things that are affected are statistics and data display.

Nominal	Also called “classificatory”, because they classify. Example: Monkey, dog, human.
Ordinal	Also called “ranking”. Example: Tall, medium, short. It includes a “built-in” nominal scale PLUS the measurements can be compared and ordered, e.g. from shortest to longest.
Interval	A sequence of measurements, with equal spacing. Example: Degrees Celcius. It includes Nominal and Ordinal scales “built-in” PLUS a unit of measurement with an (arbitrary) starting and ending point.
Ratio	All the properties of an Interval scale PLUS a fixed starting point. Example: Height, salary, weight.

Dependent variable	The (main) variable we want to measure.
Independent variable	A non-dependent variable that enters into our measurements/experiment.
Active independent variable	Independent variable that we manipulate (for the purposes of the measurement).
Attribute variable	Independent variable that we cannot manipulate.
Continuous variable	A variable that has continuity in its measurement, e.g. minutes, hours, days.
Categorical variable	A variable that is not continuous.

Scatterplot	A.k.a. Scattergram. Distribution of measurement points in x dimensions (2 is most common).
Line diagram	Standard “x-y plot” where a line connects the points.
Bar Chart	A set of bars indicate the value of a variable for each value of another variable.
Pie Chart	For a total set of data (100%), the % distribution for a dependent variable over a fixed set of (categorical) variable values.
Histogram	A set of bars indicate frequency for each value of a (categorical) variable.
Cumulative graph	The cumulative frequency of a dependent variable over the values of another variable.

Scatterplot	Good for continuous variables, to show the relationship between two variables.
Line Chart	Drawing a line between the values indicates relationship between each successive measurement, which implies that the independent variable is Interval or Ordinal.
Bar Chart	When the independent variable is categorical; when we want to avoid implying that the order of measurements or independent variable values matters.
Pie Chart	Good for showing distribution among a fixed and low number of dependent variable values, e.g. voting for a small number of political parties.
Histogram	Can be used for both categorical and continuous variables.
Cumulative graph	Good for showing a relationship between counts/events and an Ordinal or Interval variable; e.g. displaying how events are distributed (collect) over time.

Scatterplot	http://en.wikipedia.org/wiki/Scatterplot
Line Chart	http://en.wikipedia.org/wiki/Line_chart
Bar Chart	http://en.wikipedia.org/wiki/Bar_chart
Pie Chart	http://en.wikipedia.org/wiki/Pie_chart
Histogram	http://en.wikipedia.org/wiki/Histogram
Cumulative Graph	www.abs.gov.au

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