Analysing a single binary variable
Impression of the data (frequency table)
(if you prefer to watch a video on this than read, click here)
To begin with analysing a single binary variable, a good starting point can be to generate a frequency table. A frequency table is defined as "a table showing (1) all of the values for a variable in a dataset, and (2) the frequency of each of those responses. Some frequency tables also show a cumulative frequency and proportions of responses" (Warne, 2017, p. 512). An example is shown in Table 1.
Frequency  Percent  Valid Percent  

Valid  Female  12 
22 
26 
Male  34 
62 
74 

Subtotal  46 
84 
100 

Missing  No response  9 
16 

Subtotal  9 
16 

Total  55 
100 
Click here to see how to create a frequency table with Excel, Python, R (Studio), or SPSS.
with Excel
Excel file from video available here.
with Python
Jupyter Notebook of video is available here.
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 column contains the various possible options, split into Valid and Missing. Valid are those who answered this question, missing are those who didn’t. If you made a typing error when entering the data, it would easily be visible here. If for example you typed 'fmale' once when entering the data (or a value that does not exist) it would appear here as well with a frequency of only 1.
The column Frequency shows how many respondents answered each option. We can tell that 34 people in this survey reported to be Male. This is also known as the absolute frequency and defined as “the number of occurrences of a particular phenomenon” (Zedeck, “Frequency”, 2014, p. 144).
The Percent column shows the percentages, based on the grand total, so including the missing values. The 22 indicates that 22% of all respondents were Female (you can check that 12 / 55 x 100 ˜ 22).
The Valid Percent shows the percentage, based on the valid total, so excluding the missing values. The 26 indicates that 26% of all of those who answered this question reported to be Female. Most often the ‘Percent’ shown in reports are actually Valid Percent, but the word ‘Valid’ is then simply left out.
Percentages can be defined as “a way of expressing ratios in terms of whole numbers. A ratio or fraction is converted to a percentage by multiplying by 100 and appending a "percentage sign" %” (Weisstein, 2002, p. 2200).
In the report the entire frequency table is often not done for binary variables, since the only information we are often after can simply be written in one or two lines of text:
In the survey, 12 students reported to be Female (26%), and 34 to be Male (76%).
With most other analysis we would also visualise the results, however since the results can simply be written in one line of text, I’d not recommend this, so the next thing to do is actually to skip the visualisation, center & dispersion, and go straight to the testing.
FAQ's
Q: What about 'relative frequencies'? (click for the answer)
A: Percentages are actually a type of relative frequencies. Relative frequencies are “[absolute frequency] expressed as a fraction of the total frequency” (Kenney & Keeping, 1954, p. 17). This means that they are the absolute frequency divided by the total frequency. When multiplied by 100 you would get the percentages.
Q: How many decimals should I round values to? (click for answer)
A: For the percentages one or no decimal values is usually recommended (Cole, 2015)
Single binary variable
Google adds