1. Measurement
Measurement is the assignment of numbers (or other symbols) to characteristics (or objects) according to certain pre-specified rules.
One-to-one correspondence between the numbers and the characteristics being measured.
The rules for assigning numbers should be standardized and applied uniformly.
Rules must not change over objects or time.

2. Scales of Measurement
More simply, we can think of these as types of variables.
We can think of these as the degree to which measured variables conform to the usual abstract number system
Includes: identity, order, equal distance, and absolute zero
The reason this is important is because it determines the type of statistical analyses that are possible.

3. Scales of Measurement Categorical v. Quantitative
Categorical: Variable with values that are categories, groups, labels, etc.
Nominal: No natural order or ranking of values (only has identity)
Variable: Eye Colors  Values: Green, Blue, Brown, Gray, Hazel
Variable: Winter Olympic Sports  Values: Figure Skating, Curling, Ice Hockey, Skiing, etc.
Variable: Political Affiliation  Values: Democrat, Republican, Other
Assign numerical codes for values: Democrat = 1, Republican = 2, Other = 3
Still no order or ranking implied, as numbers stand for nominal values

4. Scales of Measurement Categorical v. Quantitative
Categorical: Variable with values that are categories, groups, labels, etc.
Ordinal: Natural order or ranking of values
Variable: Letter Grades  Values: A, B, C, D, F
Variable: Army Rank  Values: General, Colonel, Major, Captain, Sergeant, Private
Variable: Likert Ratings  Values: Strongly Disagree, Disagree, Neutral, Agree, Strongly Agree
Scale  Values:
Intervals or differences between adjacent values not necessarily meaningful or consistent

5. Scales of Measurement Categorical v. Quantitative
Quantitative: Variable with natural numerical values
Interval: Intervals (differences) meaningful or consistent, no absolute zero, ratios not meaningful.
Variable: Temperature (°C)  Values: -53, -10, 0, 5, 20, 65, 80, … (0°C not lowest temp)
 Difference of 10°C between values means same thing for all intervals
Is 20°C twice as hot as 10°C?  Is 68°F twice as hot as 50°F?
Variable: Birth Year  Values: 1985, 1989, 1992, 1994, … (Year 0 not beginning of time)
 1-year difference between years means same thing for all intervals
Logically doesn’t make sense to take ratio of two birth years

6. Scales of Measurement Categorical v. Quantitative
Quantitative: Variable with natural numerical values
Ratio: Absolute zero exists, ratios meaningful, intervals meaningful
Variable: Temperature (°K)  Values: 0, 45, 127, 450 … (0°K is absolute lowest temp)
Is 20°K twice as hot as 10°K? YES
Variable: Weight (lbs)  Values: 0, 20, 100, 4000 … (0 lbs is absolute lowest weight)
2000 lbs is 4 times as heavy as 500 lbs
Variable: Time (s)  Values: 0, 15, 60, 173 … (0 s is absolute shortest time)
60 seconds is half as long as 120 seconds

7. Scales of Measurement Variable Categorical Quantitative Nominal
Ordinal
Interval
Ratio
Lowest
Highest
Levels of Measurement

8. Types of Variables Quantitative: Discrete v. Continuous
Discrete: Integers (no decimal places, usually a count or number of something)
Variable: Number of Olympic Medals by Country  Values: 0, 1, 2, 3, …
Variable: Score for a Team in a Baseball Game  Values: 0, 1, 2, 3, …
Continuous: Real Numbers (any value from -∞ to ∞)
Variable: Distance from Home to School (miles)  Values: 0.5, 1.235, , 5.62, …
Variable: Hourly Wage  Values: $10.12, $15.98, $26.78, $83.12, …

9. Types of Variables
Quantitative: Discrete v. Continuous, Interval v. Ratio
Discrete Variable w/ Interval level of measurement
Calendar Year (1776, 1891, 1999, 2014, …)
Discrete Variable w/ Ratio level of measurement
Population of a City (1287, 20000, , )
Continuous Variable w/ Interval level of measurement
Temperature in Fahrenheit (-20.12, , 98.6, )
Continuous Variable w/ Ratio level of measurement
Height in Inches (43.7, 50.22, , )