Scales of Measurment
Definition
Scales of measurement refer to the ways in which variables are defined and quantified for statistical analysis. Essentially, they describe the type of information a number provides. Not all numbers are created equal! Some numbers simply categorize, others tell us about relative order, and still others provide precise amounts with a true zero point. There are four main scales:
- Nominal: Categorical data with no inherent order. Think of colors, types of fruit, or gender. Numbers assigned to categories are just labels; 1 for red, 2 for blue doesn’t mean blue is ‘more’ than red.
- Ordinal: Categorical data with a meaningful order or ranking. Think of a race finishing position (1st, 2nd, 3rd), or a satisfaction survey with options like 'Very Dissatisfied', 'Dissatisfied', 'Neutral', 'Satisfied', 'Very Satisfied'. We know the order, but the difference between ranks isn’t necessarily equal.
- Interval: Numerical data where the difference between values is meaningful and equal. Temperature in Celsius or Fahrenheit is a good example. A 10-degree difference represents the same amount of temperature change whether it's from 20°C to 30°C or 50°C to 60°C. However, there's no true zero point. 0°C doesn't mean the absence of temperature.
- Ratio: Numerical data with equal intervals and a true zero point. This means zero truly represents the absence of the measured attribute. Examples include height, weight, age, and income. A person who is 2 meters tall is twice as tall as a person who is 1 meter tall.
Example
A researcher studying customer preferences for coffee collects the following data from 10 customers:
- Coffee Type: (1=Americano, 2=Latte, 3=Cappuccino, 4=Espresso). This is Nominal data. The numbers are just labels for different types of coffee; there’s no inherent order.
- Coffee Satisfaction: (1=Very Dissatisfied, 2=Dissatisfied, 3=Neutral, 4=Satisfied, 5=Very Satisfied). This is Ordinal data. We know that 'Very Satisfied' is better than 'Satisfied', but the difference in satisfaction between 'Dissatisfied' and 'Neutral' might not be the same as the difference between 'Satisfied' and 'Very Satisfied'.
- Number of Coffees Drunk Per Day: (e.g., 0, 1, 2, 3) - This is Ratio data. There's a true zero (meaning no coffee is consumed), and differences are meaningful. Someone who drinks 3 coffees drinks twice as many as someone who drinks 1.5 coffees.
- Temperature of Coffee (in Celsius): (e.g. 65°C, 70°C, 75°C). This is Interval data. The difference between 65°C and 70°C is the same as the difference between 70°C and 75°C, but 0°C doesn't mean the absence of heat.
Why it Matters
Understanding scales of measurement matters because it determines the types of statistical analyses that are appropriate. You can’t meaningfully calculate an average of nominal data (what’s the average color?). Attempting to do so will lead to meaningless results. Choosing the correct statistical test depends on knowing whether your data is simply classifying (nominal), ordered (ordinal), or representing a true quantity (interval/ratio). Incorrectly applying a statistical test can lead to inaccurate conclusions and flawed research. Furthermore, correctly identifying the scale of measurement allows you to communicate your data effectively and interpret the results of analyses correctly.