Ordinal data is classified into categories within a variable that have a natural rank order. However, the distances between the categories are uneven or unknown. Show For example, the variable “frequency of physical exercise” can be categorized into the following:
There is a clear order to these categories, but we cannot say that the difference between “never” and “rarely” is exactly the same as that between “sometimes” and “often”. Therefore, this scale is ordinal. Levels of measurementOrdinal is the second of 4 hierarchical levels of measurement: nominal, ordinal, interval, and ratio. The levels of measurement indicate how precisely data is recorded. While nominal and ordinal variables are categorical, interval and ratio variables are quantitative. Nominal data differs from ordinal data because it cannot be ranked in an order. Interval data differs from ordinal data because the differences between adjacent scores are equal. Examples of ordinal scalesIn social scientific research, ordinal variables often include ratings about opinions or perceptions, or demographic factors that are categorized into levels or brackets (such as social status or income).
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See editing example How to collect ordinal dataOrdinal variables are usually assessed using closed-ended survey questions that give participants several possible answers to choose from. These are user-friendly and let you easily compare data between participants. Examples of ordinal scale survey questions
Choosing the level of measurementSome types of data can be recorded at more than one level. For example, for the variable of age:
The more precise level is always preferable for collecting data because it allows you to perform more mathematical operations and statistical analyses. Likert scale dataIn the social sciences, ordinal data is often collected using Likert scales. Likert scales are made up of 4 or more Likert-type questions with continuums of response items for participants to choose from. Examples of Likert-type questions
Since these values have a natural order, they are sometimes coded into numerical values. For example, 1 = Never, 2 = Rarely, 3 = Sometimes, 4 = Often, and 5 = Always. But it’s important to note that not all mathematical operations can be performed on these numbers. Although you can say that two values in your data set are equal or unequal (= or ≠) or that one value is greater or less than another (< or >), you cannot meaningfully add or subtract the values from each other. This becomes relevant when gathering descriptive statistics about your data. How to analyze ordinal dataOrdinal data can be analyzed with both descriptive and inferential statistics. Descriptive statisticsYou can use these descriptive statistics with ordinal data: ExampleYou ask 30 survey participants to indicate their level of agreement with the statement below:
To get an overview of your data, you can create a frequency distribution table that tells you how many times each response was selected. Example: Frequency distribution table
To visualize your data, you can present it on a bar graph. Plot your categories on the x-axis and the frequencies on the y-axis. Unlike with nominal data, the order of categories matters when displaying ordinal data. Example: Bar graphCentral tendencyThe central tendency of your data set is where most of your values lie. The mode, mean, and median are three most commonly used measures of central tendency. While the mode can almost always be found for ordinal data, the median can only be found in some cases. The mean cannot be computed with ordinal data. Finding the mean requires you to perform arithmetic operations like addition and division on the values in the data set. Since the differences between adjacent scores are unknown with ordinal data, these operations cannot be performed for meaningful results. Example: Finding the modeThe mode of your data is the most frequently appearing value.In the current data set, the mode is Agree The medians for odd- and even-numbered data sets are found in different ways.
Since there are 30 values, there are 2 values in the middle at the 15th and 16th positions. Both of these values are the same, so the median is Agree. Now, suppose the two values in the middle were Agree and Strongly agree instead. How would you find the mean of these two values? Since addition or division isn’t possible, the mean can’t be found for these two values even if you coded them numerically. There is no median in this case. VariabilityTo assess the variability of your data set, you can find the minimum, maximum and range. You will need to numerically code your data for these. Example: Finding the rangeFirst, code your data by assigning a number to each response, in order from lowest to highest:
To find the minimum and maximum, look for the lowest and highest values that appear in your data set. The minimum is 1, and the maximum is 5. For the range, subtract the minimum from the maximum: Range = 5 – 1 = 4 The range gives you a general idea of how widely your scores differ from each other. From this information, you can conclude there was at least one answer on either end of the scale. Statistical testsInferential statistics help you test scientific hypotheses about your data. The most appropriate statistical tests for ordinal data focus on the rankings of your measurements. These are non-parametric tests. Parametric tests are used when your data fulfils certain criteria, like a normal distribution. While parametric tests assess means, non-parametric tests often assess medians or ranks. There are many possible statistical tests that you can use for ordinal data. Which one you choose depends on your aims and the number and type of samples.
Frequently asked questions about ordinal dataWhat is ordinal data?
Ordinal data has two characteristics:
However, unlike with interval data, the distances between the categories are uneven or unknown.
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