Simple Probability Calculation from an Exemplary Survey Dataset, Statistical Note 45

Understanding the concept of simple or marginal probability and developing the skill to apply the concept to calculate from the given dataset is important in the real time.

An exemplary survey dataset constitutes one hundred records of randomly sampled respondents categorized as smokers or non-smokers. A part of the dataset in value label view of SPSS is shown in Table 1. Calculate the probability that a randomly sample respondent is a non-smokers.


Table 1: Part of dataset of smokers and non-smokers

Concept 

Simple or marginal probability of an event is the total number of favorable cases divided by total number of cases. Let ‘S’ be a simple event that a participant is a smoker and the simple or the marginal probability of ‘S’ represented by P(S) is the total number of smokers divided by total number of respondents. It is also referred to as the relative frequency.

Calculation 

The survey dataset can be summarized either in SPSS or Excel package upon the availability of the software.  In SPSS, using the function ‘Frequencies’ in Descriptive Statistics’ group of ‘Analyze’ tab, one can get the frequency table as in Table 2.
 

Table 2: Frequency table of smokers and non-smokers

In Excel, ‘Descriptive Statistics’ function in the ‘Data Analysis’ Add-In program can be used to generate frequency table.

The percent or valid percent column shows that 20 percent of respondents are non-smokers. It means that 20 out of 100 respondents are non-smokers.   Thus, the simple or marginal probability that a randomly sampled respondent is a non-smokers is calculated as 20 divided by 100 equal to 0.20. Similarly, the simple or marginal probability of smokers can be calculated to be 0.80.
 I hope this simple example will help create curiosity among the readers as to applying the concept in the real time data.