Some reminders
CHAPTER 1
MEASUREMENT
Overview
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Preview of the four pillars of scientific reasoning
Scales of measurement (nominal, ordinal, interval/ratio)
Discrete vs. continuous variables
Choosing a scale of measurement
Milgram’s shock generator measurements and Activity 1.1
The Four Pillars of Scientific Reasoning
Variables
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A variable is a quantity that can change (e.g., height, mood, hunger).
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How variables are measured determines which statistics we can use to analyze the data.
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For each variable you need to:
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Identify the scale of measurement as nominal, ordinal, or interval/ratio for each variable.
Determine if the measurement is discrete or continuous.
Types of Variables
•Quantitative (numeric) variables:
–It DOES make sense to say that someone with one level of the
variable has more of it than someone with another level
•Qualitative (categorical) variables: •Does NOT
make sense to say that someone with one level of the variable has
more of it than someone with another level
Scales of Measurement: Nominal
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Nominal
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Examples of Nominal Variables
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Sex Assigned at Birth (e.g. male, female, intersex)
Where students attend school (e.g. Valparaiso University, Saint Mary’s College, Indiana University)
Scales of Measurement: Ordinal
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Ordinal
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Examples of Ordinal Scales
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Year in school (freshman, sophomore, junior, senior)
Finishing place in a race (1st, 2nd, 3rd)
Scales of Measurement: Interval/Ratio
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Interval/Ratio
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Examples of Interval/Ratio Scales
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Time to run a mile in seconds
Height in inches
Example of difference between ordinal and
interval/ratio
Surveys and Scales of Measurement
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Researchers often ask people to respond to a series of questions where they give a
rating. For example:
I like statistics.
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Strongly disagree
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2
3
4
5
Strongly agree
Although there is some controversy about this, the vast majority of researchers treat
these data as interval and so we do the same in this course.
Discrete vs. Continuous Variables
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Discrete Variables
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There are no possible outcomes between any two categories (e.g., number of children)
Continuous Variables
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There are an infinite number of possible outcomes between any two categories (e.g., height in inches)
Scales of Measurement Examples
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Minutes to complete a math problem
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Preferred type of phone (apple, android, or other)
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Head circumference in cm
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Olympic medal winner (gold, silver, bronze)
Discrete/Continuous Examples
Ask yourself, do decimals or fractions make sense?
If yes, variable is continuous
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Minutes to complete a math problem
Number of phones a person owns
Head circumference in cm
Number of multiple choice test questions answered correctly
Number of baskets made in a basketball game
Political party (republican, democrat, independent, other)
Scales of Measurement and
Continuous/Discrete
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Nominal and Ordinal variables are always discrete
Interval/Ratio variables may be continuous or discrete
Choosing a Scale of Measurement
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Given the choice, try to measure variables using more precise measurement methods (e.g., interval
rather than ordinal)
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Avoid yes/no questions if other options exist.
More precise measures give you more statistical options.
For example, how would you ask if someone is right or left handed?.
Handedness Example
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Are you primarily right or left handed ?
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Use the following rating scale to indicate your preference for using your right or left hand for throwing
a ball.
1
2
Strongly prefer
my LEFT hand
3
4
5
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8
Strongly prefer
my RIGHT hand
Handedness Example
Try it Online
Quick Review of Milgram’s Experiment
Milgram’s Shock Generator
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The distance between each level is 15 volts
Slight--Moderate--Strong--Very Strong---Intense
LEARN-STATS.COM