Section 1-2

Section 1-2

Variables and types of Data

Objective 3: Identify types of Data

• In this section we will detail the types of data and nature of variables.

1-2 Variables and Types of DataData

QualitativeCategorical

QuantitativeNumerical,

Can be ranked

DiscreteCountable

5, 29, 8000, etc.

ContinuousCan be decimals2.59, 312.1, etc.

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Data

Qualitative Quantitative

Discrete Continuous

Qualitative variables• Are variables that can be placed into

distinct categories, according to some characteristic or attribute such as:

Gender Political affiliation Grade level

Quantitative variables• Are numerical and can be ordered or

ranked. For example: Age height weight

Discrete variables• Assumes values that can be counted.

For example: Number of coffee shops in NoPo. Number of turkeys your mama is going

to cook on Thanksgiving. Number of unwanted hair on your

chin.

Continuous variables• Result from a measurement and can

take on infinite number of values, including decimal. For example:

Temperature of a fully cooked turkey.. Weigh of a turkey Ounces of gravy on mashed potatoes.

Rounding• Continuous data is rounded. • Continuous data is usually rounded to

the nearest given unit.• Raw data and boundaries

1-2 Recorded Values and Boundaries

Variable Recorded Value BoundariesLength 15 centimeters

(cm)Temperature 86 Fahrenheit

(F)Time 0.43 second

(sec)Mass 1.6 grams (g)

14.5-15.5 cm

85.5-86.5 F

0.425-0.435 sec1.55-1.65 g

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About Boundaries

• Boundaries always have one more decimal place than the data.

• Boundaries always end in a 5.• We will cover boundaries further in

chapter 2.

Levels of measure

Nominal Ordinal

Interval Ratio

Examples

Page 8

Nominal – categorical (names) When measuring using a nominal scale, one simply

names or categorizes responses. Gender, handedness, favorite color, and religion are examples of variables measured on a nominal scale.

The essential point about nominal scales is that they do not imply any ordering among the responses. For example, when classifying people according to their favorite color, there is no sense in which green is placed "ahead of" blue.

Responses are merely categorized. Nominal scales embody the lowest level of measurement.

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Ordinal – nominal, plus can be ranked (order)

A researcher wishing to measure consumers' satisfaction with their microwave ovens might ask them to specify their feelings as either "very dissatisfied," "somewhat dissatisfied," "somewhat satisfied," or "very satisfied." The items in this scale are ordered, ranging from least to most.

This is what distinguishes ordinal from nominal scales. Unlike nominal scales, ordinal scales allow comparisons, ranking or “ordering”

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Interval – ordinal, plus intervals are consistent

Interval scales are numerical scales in which intervals have the same interpretation throughout.

Interval scales are not perfect, however. In particular, they do not have a true zero point even if one of the scaled values happens to carry the name "zero."

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Ratio – interval, plus ratios are consistent, true zero

The ratio scale of measurement is the most informative scale. It is an interval scale with the additional property that its zero position indicates the absence of the quantity being measured.

You can think of a ratio scale as the three earlier scales rolled up in one. Like a nominal scale, it provides a name or category for each object (the numbers serve as labels). Like an ordinal scale, the objects are ordered (in terms of the ordering of the numbers). Like an interval scale, the same difference at two places on the scale has the same meaning. And in addition, the same ratio at two places on the scale also carries the same meaning.

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Consequences of level of measurementWhy are we so interested in the type of scale that measures a dependent variable?

The crux of the matter is the relationship between the variable's level of measurement and the statistics that can be meaningfully computed with that variable.

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Let's practice

The website above also some more examples and explanation of what we just covered.

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1-2 Variables and Types of Data

Determine the measurement level.Variable Nominal Ordinal Interval Ratio LevelHair Color Yes No NominalZip Code Yes No NominalLetter Grade Yes Yes No OrdinalACT Score Yes Yes Yes No IntervalHeight Yes Yes Yes Yes RatioAge Yes Yes Yes Yes RatioTemperature(F) Yes Yes Yes No Interval

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On your own

Study the examples listed on table 1-2 on page 8.

Do applying concepts on page 9

And answer questions 1-10 on page 26.

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