Types of DataTypes of Data

Types of data

• Categorical data• Measurement dataMeasurement data

Categorical Data

• The objects being studied are grouped into categories based on some qualitative trait.g q

• The resulting data are merely labels or categoriescategories.

Examples: Categorical Data

• Hair color– blonde, brown, red, black, etc.blonde, brown, red, black, etc.

• Opinion of students about riotsticked off neutral happy– ticked off, neutral, happy

• Smoking statusk k– smoker, non-smoker

Categorical data classified asCategorical data classified asNominal, Ordinal, and/or BinaryNominal, Ordinal, and/or Binary

Categorical data

OrdinalNominaldatadata

Not binaryBinary Binary Not binaryy y

Nominal Data

• A type of categorical data in which objects fall into unordered categories.g

Examples: Nominal Data

• Hair color– blonde, brown, red, black, etc.blonde, brown, red, black, etc.

• RaceCaucasian African American Asian etc– Caucasian, African-American, Asian, etc.

• Smoking statusk k– smoker, non-smoker

Ordinal Data

• A type of categorical data in which order is important.p

Examples: Ordinal Data

• Class– fresh, sophomore, junior, senior, super seniorfresh, sophomore, junior, senior, super senior

• Degree of illnessnone mild moderate severe going going– none, mild, moderate, severe, …, going, going, gone

• Opinion of students about riots• Opinion of students about riots– ticked off, neutral, happy

Binary Data

• A type of categorical data in which there are only two categories.y g

• Binary data can either be nominal or ordinalordinal.

Examples: Binary Data

• Smoking status– smoker, non-smokersmoker, non smoker

• Attendancepresent absent– present, absent

• Classl l l– lower classman, upper classman

Measurement Data

• The objects being studied are “measured” based on some quantitative trait.q

• The resulting data are set of numbers.

Examples: Measurement Data

• Cholesterol level• HeightHeight• Age

SAT• SAT score• Number of students late for class• Time to complete a homework assignment

Measurement data classified asMeasurement data classified asDiscrete or ContinuousDiscrete or Continuous

Measurementdata

ContinuousDiscrete

Discrete Measurement DataO l t i l ibl (thOnly certain values are possible (there are

gaps between the possible values).

Continuous Measurement DataTheoretically, any value within an interval is possible with a fine enough measuringis possible with a fine enough measuring

device.

Discrete data Gaps between possible valuesDiscrete data -- Gaps between possible values

0 1 2 3 4 5 6 7

Continuous data -- Theoretically,no gaps between possible valuesno gaps between possible values

0 1000

Examples:Examples: Discrete Measurement Data

• SAT scores• Number of students late for classNumber of students late for class• Number of crimes reported to SC police

N b f i h d b i d• Number of times the word number is used

Generally, discrete data are counts.

Examples:Examples:Continuous Measurement Data

• Cholesterol level• HeightHeight• Age

Ti l h k i• Time to complete a homework assignment

Generally, continuous data come from measurements.

Who Cares?

The type(s) of data collectedThe type(s) of data collected in a study determine the type of statistical analysis usedof statistical analysis used.

For example ...

• Categorical data are commonly summarized using “percentages” (or “proportions”).g p g ( p p )– 11% of students have a tattoo– 2%, 33%, 39%, and 26% of the students in2%, 33%, 39%, and 26% of the students in

class are, respectively, freshmen, sophomores, juniors, and seniors

And for example …

• Measurement data are typically summarized using “averages” (or “means”).g g ( )– Average number of siblings Fall 1998 Stat 250

students have is 1.9.– Average weight of male Fall 1998 Stat 250

students is 173 pounds.– Average weight of female Fall 1998 Stat 250

students is 138 pounds.