Statistics - Comparing Plots

Groups of population can be compared using box and whisker plots. Overall visible spread and difference between median is used to draw conclusion that there tends to be a difference between two groups or not.

Formula

${P = frac{DBM}{OVS} imes 100 }$

Where −

${P}$ = percentage difference

${DBM}$ = Difference Between Medians.

${OVS}$ = Overall Visible Spread.

Rules

For a sample size of 30 if this percentage is greater than 33% there tends to be a difference between two groups.

For a sample size of 100 if this percentage is greater than 20% there tends to be a difference between two groups.

For a sample size of 1000 if this percentage is greater than 10% there tends to be a difference between two groups.

Example

Problem Statement

Describe the difference between following sets of data.

Sr.No.	Name	Set A	Set B
1	Max	12	15
2	UQ	10	13
3	Median	7	10
4	LQ	6	9
5	Min	5	6

Solution

Consider the following diagram −

${OVS = 13 - 6 \[7pt] = 7 \[7pt] DBM = 10 -3 \[7pt] = 4 }$

Apply the formula

${P = frac{DBM}{OVS} imes 100 \[7pt] = frac{4}{7} imes 100 \[7pt] = 57.14 }$