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Analysing a single binary variable

Impression of the data (frequency table)

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.

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

Single binary variable 

Introduction

Impression

Visualisation (na)

Center & Dispersion (na)

Test

Effect Size

Report

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