Levels of Measurement: A Key Consideration when Deciding the Data your Nonprofit will Track
In a recent post, we talked about the measures of central tendency - mean, median, and mode. In that post, we explained how certain types of data are appropriate for each measure of central tendency.
We use “Levels of Measurement” as a way to describe some key characteristics of the data we collect. There are three levels of measurement: nominal, ordinal, interval/ratio. Each level of measurement is appropriate for one or more measure of central tendency. Yikes! That's a jargon-filled statement! Don't worry. In this post we will explain you understand you levels of measurement and how your nonprofit can use them with your data.
Nominal Level of Measurement
The nominal level of measurement is used to categorize data into groups. Those categories have no meaningful numeric value and cannot be rank ordered. Despite it's simplicity, nominal data is widely used and will help you learn a lot about your participants and programs.
We can use nominal data to describe our participants by identifying different categories in which they fit without saying that one category is “better/worse” or “more/less” than the others. Examples of nominal data include: political party, religion, Android or iPhone, favorite color, gender, veteran status, zip code, and countless others.
Imagine that you ask participants to pick their preferred incentive for completing an important task. The options might be:
$25 Grocery Gift Card
$25 Bus/Transit Pass
$25 Savings Account Deposit
This is nominal data.
Sure, the gift cards themselves have a dollar value attached, but the categories (Groceries, Transit, Savings Account) do not have a meaningful numeric value. We can't rank order them, and we can't say that the Grocery Gift Card is inherently better or worse than the Bus/Transit Pass. We can simply say they are different.
Central Tendency and Other Analysis with Nominal Data
We can only use the mode to determine the central tendency of nominal data. In this example, the incentives have no meaningful numeric value and can't be rank ordered, so it doesn't make sense to calculate a mean or median. For this data, we can say something like: "The modal choice is the $25 Gift Card for Groceries."
With nominal data, we can also calculate the count and percentage of choices that fall into each category, as shown in Table 1 below. As you can see, the Grocery Gift Card (the mode) was chosen 75 times, or 50% of all responses. The Bus/Transit Pass was selected 50 times for or 33% of responses, and the Savings Account Deposit was chose 25 times, or 17% of all responses.
Having this data might help you know that you need to purchase, say, 20 Grocery Gift cards and 10 Bus Passes every few months to have enough on hand. Or, if you want to encourage people to choose the savings account option more frequently, then you might increase the savings account deposit to $50 to see if that changes preferences.
Table 1: Count and Percentage of Preferred Incentives
Preferred Incentive | Count | Percent |
$25 Grocery Gift Card | 75 | 50% |
$25 Bus/Transit Pass | 50 | 33% |
$25 Savings Account Deposit | 25 | 17% |
Total | 150 | 100% |
Nominal Level of Measurement Summary
Key Characteristics Of Nominal Data
Uses Categories (i.e. categorical data)
Categories have no underlying or logical numerical value
Categories cannot be ranked or ordered
Measure(s) of Central Tendency for Nominal Data
Mode
Ordinal Level of Measurement
Ordinal data is another type of categorical data. There's likely not a meaningful underlying value of ordinal data, but the categories can be put in a logical order.
Self-rated health is a commonly used ordinal measure. As you might imagine, it allows a person to rate their health on an ordinal 1-5 scale.
Excellent
Very Good
Good
Fair
Poor
These responses have a logical ordering to them, generally going from good health to bad health, but the numbers assigned to them don't mean anything. The categories and their values are in a logical order, but we could just as easily have said Excellent = 5 and Poor = 1, or Excellent = 100 and Poor = 96.
[Note, an illogical order to the numbers we assign to the categories would be something like Excellent =1, Poor =2, Very Good=5, Fair=0, and Good =14]
Since the values we assign to the categories are made up, we can't determine the true "distance" between different categories. The example below should help you understand why there's no true "distance" between ordinal categories.
Example Ordinal Data
Vivian= Excellent Health
Helen= Very Good Health
Antonio = Good Health
Example Interval/Ratio Data (Explained Next)
Vivian= 50 Years Old
Helen = 45 Years Old
Antonio =40 Years Old
With the the interval/ratio Level age data, we can compare the ages of Vivian and Helen and say "Vivian is 5 years older than Helen" and we can know that's a meaningful gap between their ages. We can also compare Helen to Antonio and make that same claim (i.e. Helen is 5 years older than Antonio). Interval/Ratio level data allows us to make precise comparisons because their values are inherently meaningful. Of course, we could be even more precise and calculate each person's exact age in days, hours, & minutes and perform even more accurate calculations of their age differences.
With the ordinal self-rated health data, we can compare Vivian and Helen and say say "Vivian has higher self-rated health than Helen ". But, we can't make any type of assessment of how much healthier Vivian feels than Helen. We run into that same limitation when we compare Helen to Antonio. We can't know how much healthier Helen feels compared to Antonio. We just know she has higher self-rated health.
In this example, the self-rated health categories are imprecise or fuzzy. Excellent health can mean a lot of things, so we can't make perfect comparisons between categories. The fuzziness of categories means that you can't calculate the exact distance between them.
Central Tendency and Other Analysis with Ordinal Data
We can use mode with ordinal data. We can also use the median with ordinal data since we can rank order it. We can also use counts and percentages to analyze and summarize ordinal data. We can use Table 2 below to see how ordinal data can be analyzed.
First, we can see that "Very Good" is the modal value because it has the greatest number of of responses. Second, we can determine that the median value is "Good" because the middle point of our responses is the 138th value [(275+1)/2 = 138] which falls somewhere in the Good category. Third, we can see that most of our respondents are in the "Good" through "Excellent" categories, and a only about 27% (roughly 1 in 4) self-rate as fair or poor.
Table 2: Counts and Percentages of Self Rated Health
Self Rated Health | Count | Percent |
Excellent ( value = 1) | 25 | 9.1% |
Very Good (value = 2) | 100 | 36.3% |
Good (value = 3) | 75 | 27.3% |
Fair (value = 4) | 50 | 18.2% |
Poor (value = 5) | 25 | 9.1% |
Total | 275 | 100% |
Ordinal Level of Measurement Summary
Key Characteristics of Ordinal data
Uses Categories
Categories can be ranked or ordered
There is no true "distance" between categories
Measure(s) of Central Tendency for Ordinal Data
Mode
Median
Mean* - in special circumstances this is done. See our post on measures of central tendency and look for the discussion of Likert Scales
Interval/Ratio Level of Measurement
Important Note: Interval /Ratio are technically different levels of measurement, but we discuss them together because we rarely need to consider the distinction between them (i.e. ratio has a true zero value, interval does not).
The interval/ratio level of measurement allows you to rank data in order and to calculate the difference between the values. This level of measurement also allows you to calculate the ratio of the values. Interval/Ratio data is often continuous in nature, rather than categorical. With many metrics, you can measure it to a very high level of precision. Basically, think of interval/ratio data as numbers on a number line. Examples of interval/ratio data include: height, weight, annual income, years of education, number of children, years of experience, an etc.
Income is a great example of interval/ratio data. In Table 3 below, we can see some important aspects of interval/ratio data. For example, the continuous nature of the data is demonstrated by Ichiro making one (1) cent more than Felix. You can also make precise calculations about the difference (or distance on a number line) between incomes. Ken makes $50,000 more than Felix ($100,000 - $50,000 = $50,000). We can also see that Ken's income is exactly twice as much as Felix's income.
Table 3: Participants and Annual Incomes
Participant | Annual Income |
Felix | $50,000.00 |
Ichiro | $50,000.01 |
Edgar | $50,000.02 |
Ken | $100,000.00 |
Randy | $250,000.00 |
Central Tendency and Other Analysis with Ordinal Data
The mean and median are used to determine the central tendency of interval/ratio data. For example, in Table 3, we can calculate the mean salary ($100,000.01) and the median salary ($50,000.02).
You can use counts and percentages to analyze interval/ratio data, but it can be challenging when you have unlimited possibilities. If we collect the annual incomes of 100 people, we might get 100 different answers. In that case, it wouldn't be very helpful to have a table with 100 different income values, each representing 1% of the responses.
When you have a narrower set of possibilities, such as years of education completed (which might range from 0 to 20 years), then you could use counts & percentages with interval/ratio data. Even then, you'd probably need a lot of responses to be able to glean insight into your programs or participants.
Interval/Ratio Level of Measurement Summary
Key Characteristics of Interval/Ratio data
Allows you to rank data in order
Can calculate the difference between the values
Can calculate ratios of values
Data are continuous and can be very precise
Measure(s) of Central Tendency for Interval/Ratio Data
Mean
Median
You could use the mode in rare circumstances, but it's likely not the best choice.
Converting from One Level of Measurement to Another
When your nonprofit decides the level of measurement for a piece of data you will collect, remember you can always convert data from greater detail/precision to less detail/precision, but you can't go the other way.
Table 3 gives a quick guide to data conversions that you can make. Notably, interval/ratio data can be converted to either ordinal or nominal levels of measurement. Ordinal data can be converted to nominal data. Nominal data can't be converted to any other type of data.
Table 3: Level of Measurement Conversion Guide
Original Level of Measurement | New Level of Measurement | OK to Convert |
Interval/Ratio | Ordinal | Yes |
Interval/Ratio | Nominal | Yes |
Ordinal | Interval/Ratio | No |
Ordinal | Nominal | Yes |
Nominal | Interval/Ratio | No |
Nominal | Ordinal | No |
You have to convert down because you are limited by the information you have available. For Example, if I tell you that Jane is in poverty (Nominal), how would you guess her precise income (Interval/Ratio) with just that piece of information? If I told you that TJ did not graduate from high school (Nominal or Ordinal), how could you tell me the precise number of years of education they completed (Interval/Ratio)?
So what? Why would I care about converting the level of measurement of my data?
It happens all the time. You might collect data using a certain level of measurement, and it can be helpful to change the level of measurement to simplify the data for analysis or presentation.
For example, you might collect each participant's precise annual income down to the penny (Interval/Ratio). If you have 10,000 participants, you will probably get thousands of different values.
It would be nearly impossible to make a meaningful pie chart or bar chart out of thousands of incomes, and a table created with this data would be huge and unreadable. To simplify things, you decide to categorize each income in $5,000 increments up to $100,000.
$0 - $5,000
$5,001 - $10,000
$10,001 - $15,000
And so on.
You’ve converted your interval/ratio data about income into ordinal data about income. You have less detail, but you'll have more meaningful information that you can use to understand your participants.
Let's go one more level down, and convert our interval/ratio data to nominal data.
Your program will serve people with any income level, but your donors care the most about households that are below the poverty line. You can take your interval/ratio income data, calculate the poverty line for each household, and categorize participants as (1) Living in Poverty or (2) Not living in poverty. These categories are nominal data.
You can now tell your donors "Approximately 60% of our participants live in poverty"
Finally, I can't tell you how often I have converted the ordinal data in Likert Scale (1= Strongly Disagree , 2 = Disagree, 3=Agree, 4=Strongly Agree), to nominal data (Disagree and Agree) to simplify my analysis of a satisfaction survey or feedback on a conference topic.
In sum, it's great to collect data with as much detail and precision as you can manage, and sometimes it's very helpful to transform that data into something simpler and less precise to convert that data into usable information.
Important Note About Data Conversions: Always Work From A Copy of your data when you are converting from one level of measurement to another. You'll want to keep the original data as a reference that you can use over and over. If you change your only copy of interval/ratio income data to ordinal or nominal data, you can't go back. Why? You guessed it. You don't have enough information anymore. Always Work From A Copy when doing data conversions.
Conclusion
In the past few posts in our nonprofit data bootcamp series we have covered a lot of basic concepts, including:
levels of measurement (this post)
If you have a strong grasp on these concepts and how to use them together to tell clear stories about your programs and participants, then you are well on your way to being an excellent practitioner of nonprofit data management. Yo don't need to be a stats wiz, you just need some basic skills and practice.
Learn More About Nonprofit Data Management
This post is part of our nonprofit data bootcamp series. Check out the complete list of nonprofit data bootcamp topics with links to other published posts.
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