Need help with ordinal data??

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Ordinal data

classified into categories within a variable that has a natural rank order.

However, the distances between the categories are uneven or unknown.
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 the scale is ordinal.

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Ordinal is the second of four hierarchical levels of measurement

nominal, ordinal, interval, and ratio

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.

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Examples of Ordinal Scales:

In 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.

Language ability

beginner
intermediate
fluent

level of agreement

strongly disagree
disagree
neither agree nor disagree
agree strongly agree

Income level

lower level income
middle-level income

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How to Collect Ordinal Data

ordinal 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.

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Examples of Ordinal scale survey questions

what is your age

0 to 18
19 to 34
35 to 49
50 plus

what is your education level

primary school
high school
bachelors degree
master's degree
PhD

In the past three months, how many times did you buy groceries online

none
1 to 4 times
5 to 9 times
10-14 times
15 or more times

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Likert Scale Data

Ordinal data is often collected using Likert scales. Likert scales are made up of 4 or more Likert type questions with continuum of response items for participants to choose from

Example of Likert-type questions

How frequently do you buy energy-efficient products?

never
rarely
sometimes
often
always

How important do you think it is to reduce your carbon footprint?

not important
slightly important
important
moderately important
very important

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
you can say that one value is greater or less than another.
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 Data⏹️⏹️⏹️⏹️⏹️⏹️

Ordinal data can be analyzed with both descriptive and inferential statistics.

Descriptive Statistics⏹️⏹️⏹️⏹️⏹️

With Ordinal Data

the frequency distribution in numbers or percentages.
the mode or the median to find the central tendency
the range to indicate the variability

Example

You ask 30 survey participants to indicate their level of agreement with the statement below

Regular physical exercise is important for my mental health.

strongly disagree
disagree
neither disagree nor agree
agree
strongly agree

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To get an overview of your data, you an create a frequency distribution table that tells you how many times each response was selected

To visualize your data, you can use a bar graph

Plot your categories on the x-axis and the frequencies on the y-axis
Unlike nominal data,

the order of categories matters when displaying ordinal data.

Central Tendency⏹️⏹️⏹️⏹️⏹️⏹️⏹️⏹️

The central tendency of your data is where most of your values lie

The mode, mean, and median are the three most commonly used measures of central tendency.

the mode can almost always be found for ordinal data
the median can only be found in some cases.
The mean can not 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
the differences between adjacent scores are unknown with ordinal data, these operations can not be performed for meaningful results.
the mode of your data is the most frequently appearing value.

the mode of the data set is agree

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Medians

for odd and even numbered data sets are found in different ways

in an odd numbered data set the median is the value at the middle of your data set when it is ranked.
In an even-numbered data set, the median is the mean of the two values in the middle of your data set.

Order all data values and locate the middle of your data set to find the median

Since there are 30 values, there are 2 values in the middle at the 15th and 16th positions since both values are the same the median is Agree
If the two values in the middle were Agree and Strongly agree instead, then you could not find the mean since the mean of the two values can't be found even if you coded them numerically - so in this case there is no median.

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Variability

Find the minimum, maximum, and range of your data set

code your data by assigning a number to each of the responses in order from lowest to highest.

1 strongly disagree
2 disagree
3 neither disagree nor agree
4 agree
5 strongly agree

The minimum is 1 and the maximum is 5

The range gives you an 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.

From this information, you can conclude there was at least one answer on either end of the scale.

Statistical Tests

Inferential statistics will help you test scientific hypotheses about your data
The most appropriate statistical tests for ordinal data focus on the rankings of your measurements and these just happen to be non-parametric tests
Parametric tests are used when your data fulfills certain criteria like a normal distribution
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.
The one you choose depends on your aims and the number and type of samples