Analysing a single ordinal variable
1a: Sample results (frequency table and median)
To begin with analysing a single ordinal variable, a good starting point can be to generate a frequency table, such as the one shown in Table 1.
Frequency  Percent  Valid Percent  Cumulative Percent  

Valid  very scientific  100 
5.1 
10.5 
10.5 
pretty scientific  199 
10.1 
20.9 
31.3 

not too scientific  348 
17.6 
36.5 
67.8 

not scientific at all  307 
15.6 
32.2 
100 

Subtotal  954 
48.3 
100.0 

Missing  No answer  1020 
51.7 

Subtotal  1020 
51.7 

Total  1974 
100.0 
Click here to see how to create a frequency table with Excel, Python, R (Studio), or SPSS.
with Excel
File used in video: IM  Frequency Table (Ordinal).xlsm
with Python
File used in video: IM  Frequency Table.ipynb
Data file used in video and notebook GSS2012a.csv.
with SPSS
There are a three different ways to create a frequency table with SPSS.using Frequencies
watch the video below, or download the pdf instructions (via bitly, opens in new window/tab).
Datafile used in video: Holiday Fair.sav
using Custom Tables
watch the video below, or download the pdf instructions for versions before 24, or version 24 (via bitly, opens in new window/tab)
Datafile used in video: Holiday Fair.sav
using descriptive shortcut
watch the video below, or download the pdf instructions (via bitly, opens in new window/tab).
Datafile used in video: StudentStatistics.sav
The first few columns are the same as discussed for a single nominal variable (see there as well for more details). The first column contains the various possible options, split into Valid and Missing. Valid are those who answered this question, missing are those who didn’t.
The column Frequency shows how many respondents answered each option. We can tell that 100 people in this survey reported to find accounting very scientific.
The Percent column shows the percentages, based on the grand total, so including the missing values. The 5,1 indicates that 5.1% of all respondents answered 'very scientific' (you can check that 100 / 1974 x 100 = 5.1).
The Valid Percent shows the percentage, based on the valid total, so excluding the missing values. The 10.5 indicates that 10.5% of all of those who answered this question reported 'very scientific'. The Valid Percent is usually the one being reported, and then confusingly enough as simple Percent.
New are the two ‘cumulative’ columns. The word ‘cumulative’ simply means to add up. The cumulative frequency can be defined as: “the total (absolute) frequency up to the upper boundary of that class” (Kenney, 1939, p. 16). This would only be useful if there is an order to the categories, so we can say that for example 299 respondents found accounting pretty scientific or even more. Which is why these cumulative frequencies will not have a meaningful interpretation for a nominal variable (e.g. 28 students study business or less?).
The Cumulative Percent is the running total of the Valid Percent, it is the addition of all previous and the current category’s valid percentages. We can see that 31.3% of the respondents that answered this question though accounting is pretty or very scientific.
Instead of a frequency table, we might prefer to visualise the result. This is the topic for the next section.
Single ordinal variable
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