Question

Attached below is the 2-way frequency table for Season and SSI, also called the joint frequency table, from the Seasonal Effect data set. Use this data to answer question 6.

Seasonal Effect	No SSI	Yes SSI
Spring	0.280	0.022
Summer	0.223	0.020
Autumn	0.128	0.009
Winter	0.287	0.032

6. Calculate the following probabilities for a randomly selected patient from the study:

a. The patient’s surgery occurred in the Summer and they did not have an SSI (10%)

b. The patient had an SSI GIVEN that their surgery occurred in the winter (10%)

How do I approach this problem?

Answer 1

The joint frequency is given in terms of probabilities. So, we treat the given frequencies as probabilities.

a.

From the table, the probability for patient’s surgery occurred in the Summer and they did not have an SSI is 0.223.

(This is determined by finding the entry for Summer row and No SSI Column).

b.

From the table, the probability for patient’s surgery occurred in the winter and they did have an SSI is 0.032.

(This is determined by finding the entry for Summer row and No SSI Column).

Probability that patient’s surgery occurred in the winter = 0.287 + 0.032 = 0.319

(Summing all probabilities for row Winter)

Probability that patient had an SSI GIVEN that their surgery occurred in the winter =

Probability that patient had an SSI and that their surgery occurred in the winter / Probability that patient’s surgery occurred in the winter

= 0.032 / 0.319

= 0.1003