Table of Contents Levels of Measurement .............................................................................................. 2 Why does this matter? ..................................................................................................................... 2 What are the levels of measurement? ............................................................................................ 2 How to determine if you have any categorical data .................................................................... 2 How to determine if you have any quantitative data .................................................................. 4
Additional Resources.................................................................................................. 6
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Levels of Measurement This tutorial assumes that you know what a variable is and that you can identify the variables in your data set. If you are unsure, please see the relevant guide on Blackboard.
Why does this matter? The level of measurement of each variable will determine: 1. Which descriptive statistics you should use (both numbers and graphs) 2. Which statistical tests you can use to answer your research questions Using the wrong test will result in one or all of the following: 1. Incorrect results (e.g., you decide something is significant when it’s not or vice versa) 2. Incorrect or misleading conclusions 3. Unethical research (it is your responsibility to use, not misuse, statistics) 4. Poor research methodology
What are the levels of measurement? All variables can be described as either (see Figure 1): 1. Categorical (qualitative data), or 2. Quantitative (referred to as Scale in SPSS) *You may have used slightly different terminology in your stats background, and that’s okay – there are several different ways to describe levels of measurement. If this is you, keep reading and I will try and explain these differences. How to determine if you have any categorical data If the data for a variable are…
Words or text Groups or intervals (e.g., age groups, income brackets, experimental group, etc…) A likert scale (strongly disagree to strongly agree)
then the variable is categorical. *Even if you code your categorical data so that it is numeric (e.g., 1 = Male, 2 = Female) it is still categorical because the numbers do not represent a quantity or amount – they represent categories. There are two types of categorical data (see Figure 1): 1. Ordinal 2. Nominal Created by ASK (2012)
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Ordinal If the data have a meaningful order or rank then the variable is ordinal. Let’s consider a few examples (see Figure 1): Responses to a likert scale question on a questionnaire. The responses (strongly disagree, disagree, neutral, agree, strongly agree) have a meaningful order to them. Grouped income. This is not the exact income, but an income bracket (£0-£5000, £5001£10000, £10001-15000, etc…). These groupings have a meaningful order (i.e., £0-£5000 is less than £5001-£10000, etc…). Olympic medal. Say we had a list of every member of the GB team that earned a medal at the 2012 Olympics. The medal they each received (gold, silver and bronze) has a meaningful rank because gold represents 1st place, silver 2nd and bronze 3rd. Nominal If the data do not have a meaningful order or rank then the variable is nominal. Let’s consider a few examples (see Figure 1): Marital status. The possible responses (single, married, divorced, widowed, etc…) cannot be ordered or ranked in a meaningful way. That is, I can’t say that single is better than married, married is better than divorced and divorced is better than widowed. Likewise, although I can say that married comes after single, we cannot arrange divorced and widowed in a meaningful order as one does not follow the other. Gender. The typical responses of Male and Female do not have a meaningful rank or order as we cannot say that one is better than the other (regardless of your personal opinion).
Variables Categorical
Quantitative
Nominal
Ordinal
Scale
(unranked categories)
(ranked categories)
(not grouped)
Marital status Political party Eye colour Gender
Likert scale Grouped income Olympic medal
Height Weight Score on a test Duration (time)
Figure 1. Levels of measurement
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How to determine if you have any quantitative data If the data for a variable…
Are numbers (but not codes for categorical data) Represent a quantity or frequency Have a unit of measure (e.g., minutes, hours, £’s, kgs, kilometres, litres, etc…) Are at least at the interval level (I’ll explain this below)
then the variable is quantitative. This level of measurement is labelled as scale in SPSS. Sometimes, quantitative data is described as… 1. Interval or Ratio 2. Continuous or Discrete Interval vs. Ratio For most basic and intermediate statistics, you will not need to differentiate between the two. You just need to be able to identify that the variable is quantitative. However, it is good to at least understand what interval means so that you understand why ordinal variables cannot be treated in the same way as quantitative variables. INTERVAL. “Equal intervals also represent equal distances” (Field, 2009). This can be a difficult concept to grasp (and to teach). Say we are measuring a variable having to do with money (£’s). I know that £’s are at least at the interval level because the difference between £3 and £4 is the same as the difference between £5 and £6 – it’s £1. Similarly, I know that weight in kilograms is at least at the interval level because the difference between 10kg and 20kg is the same as the difference between 20kg and 30kg – it’s 10kg. This may seem obvious and you may think, “what isn’t interval?”. Let’s look at an example of something that isn’t interval to really get the idea. Consider a likert scale: Strongly Disagree
Disagree
Neutral
Agree
Strongly Agree
What is the distance between Strongly disagree and Disagree? How about the distance between Disagree and Neutral? Can they be measured? Are they the same? These distances/differences cannot really be quantified, nor can we determine if they are equal. In addition, in a questionnaire, it is likely that each respondent’s interpretation of this scale will be different. Thus, at most this data is ordinal, but it is not interval and thus, not quantitative. RATIO. Must satisfy the condition for being interval and have a meaningful zero. If you want more detail on ratio data, please get a good text, such as Field (2009).
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Continuous vs. Discrete CONTINUOUS. Quantitative data which can have meaningful decimal places. Here are some examples: Time: It is possible to count parts of a minute, hour, second, day, etc… E.g., 9.58 seconds, 1.5 hrs, etc… Even if you don’t measure time using a decimal place, you could and it would have meaning. Weight: It is possible to have parts of a kg, stone, gram, etc… E.g., 1.3kg, 10.6 stone, etc… Again, you don’t have to measure weight using a decimal place, but you could and it would have a meaning. DISCRETE. Quantitative data which do not have meaningful decimal places (i.e., whole numbers). Here are some examples: Number of students who attend a lecture: There will always be a whole number of students – you will never have part of a student. Number of working cars in the car park: There will always be a whole number of cars – you will never have half of a car. *Keep in mind that some statistics books use the word “Discrete” to refer to data that are simply whole numbers, but not necessarily quantitative data as we defined on the previous page (which is confusing!).
References Field, Andy. Discovering Statistics Using SPSS, 3rd Edition. SAGE Publications Ltd: London, 2009.
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Additional Resources In the SPSS resources section of Blackboard, you may be interested in the following: 1. How to identify variables in your dataset 2. Choosing the right descriptive statistics to summarise your data
Return to: 1.1 Why does this matter? 1.2 What are the levels of measurement? How to determine if you have any categorical data How to determine if you have any quantitative data
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