Jaccard Coefficient Calculations

This simple exercise shows the calculation of the Jaccard coefficient in a sample dataset.

Pathological Test Results

The table shows the pathological test results for three individuals.

Name	Gender	Fever	Cough	Test-1	Test-2	Test-3	Test-4
Jack	M	Y	N	P	N	N	A
Mary	F	Y	N	P	A	P	N
Jim	M	Y	P	N	N	N	A

Jaccard Coefficient Calculations

Given:

$$Jaccard(A, B) = \frac{ \text{Number of Common Positive Indicators}}{\text{Total Number of Indicators}}$$

Pair (Jack, Mary)

Difference of observations in both:

$$(Jack \cap Mary) = \{ \text{Test-3} \} = 1$$

Total Attributes:

$$(Jack \cup Mary) = \{ \text{Fever, Cough, Test-3} \} = 3$$

Jaccard Coefficient:

$$J(Jack, Mary) = \frac{1}{3} = 0.33$$

Pair (Jack, Jim)

Difference of observations in both:

$$(Jack \cap Jim) = \{ \text{Cough, Test-1} \} = 2$$

Total Attributes:

$$(Jack \cup Jim) = \{ \text{Fever, Cough, Test-1} \} = 3$$

Jaccard Coefficient:

$$J(Jack, Jim) = \frac{2}{3} = 0.67$$

Pair (Jim, Mary)

Difference of observations in both:

$$(Jim \cap Mary) = \{ \text{Cough, Test-1} \} = 2$$

Total Attributes:

$$(Jim \cup Mary) = \{ \text{Fever, Cough, Test-1, Test-2, Test-3, Test-4} \} = 6$$

Jaccard Coefficient:

$$J(Jim, Mary) = \frac{1}{6} = 0.17$$