How to Use Crosstab Software for Probability

You may already know you can use crosstab software to dive deep into meaningful statistics that tell you a lot about an existing audience. But you can also use crosstabs to determine probabilities of something that does not yet exist. Here’s how. 

Understand what the table tells you. 

Your first goal is to fully understand the information provided by the crosstab software. We can use a simple eye color table as an example, one that shows the number of males and females with a given eye color. The table shows you the number of males and females with each eye color, along with the totals for males and females as well as the totals for each eye color.

Eye Color Black Brown Blue Green Grey Total
Male 25 15 12 20 10 82
Female 20 30 10 15 10 85
Total 45 45 22 35 20 167

 

Calculate for probability based on provided sample.

Once you understand what the crosstab software is telling you, you can move forward with any number of mathematical equations that calculate probability of a given occurrence based on the information in your table.

Probability Examples: One Trait

Let’s say you wanted to determine the probability of a randomly selected individual having black eyes. Basing your calculation on the data in the table, you would note that a total of 45 people have black eyes out of the 167 people that are part of the entire dataset.

Your calculation would thus divide the number of people with black eyes by the total number of people, or 45/167, giving you an answer of .27, or 27 percent.

  • Probability of person with black eyes: 45/167 = .27, or 27 percent

You could use the same method for calculating various probabilities based on the given data. Let’s say you wanted to determine the probability of a randomly selected female having black eyes, based on the information in the table.

Here you would divide the number of females with black eyes by the total number of females, or 20/85, giving you an answer of .235, or 23.5 percent.

  • Probability of female with black eyes: 20/85 = .235, or 23.5 percent

Probability Example: One Trait OR Another

You could take the calculations further, determining the probability of a randomly selected person’s gender or eye color.

For instance, let’s say you wanted to figure out the probability of a randomly selected individual being male OR having blue eyes.

  • Here you would first set up the equation determining the probability of being male: 82/167
  • Then you would set up the probability of having blue eyes: 22/167
  • Thirdly, you need to set up the probability of having blue eyes and being male: 12/167

You would then plug in the numbers into an equation used when determining the probability of one thing OR another. This equation is:

P(A or B) = P(A) + P(B) – P(A and B)

or

P(blue eyes or male) = P(blue eyes) + P(male) – P(blue eyes and male)

P(blue eyes or male) = (22/167) + (82/167) – (12/167)

P(blue eyes or male) = (22 + 82 – 12)/167 = 92/167 = .55, or 55 percent

Note the number of individuals who had blue eyes and were male had to be subtracted from the equation. This is because when you could all the males, and then count all the people with blue eyes, you end up counting the males with blue eyes twice. You need to subtract the number of males with blue eyes to get rid of the duplication.

Probability Example: Two Traits

In one final calculation, let’s say you wanted to determine the probability of a randomly selected individual being female and having grey eyes. Here you could embark in another lengthy equation, or you could go right to the chart to find the number of female with grey eyes and divide it by the total number of people.

The probability of a person being a female with grey eyes would be 10/167 = .059 = 5.9 percent

Using the same concepts, you can determine probability for any number of traits on any given data set, using the information to enhance your strategies and overall brand.

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