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.
Case 2: Formula
${P = \frac{DBM}{OVS} \times 100 }$
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
${P = \frac{DBM}{OVS} \times 100 \\[7pt] \ = \frac{4}{7} \times 100 \\[7pt] \ = 57.14 }$
As percentage is over 33% thus there is difference between Set A and Set B. It is likely that Set B is greater than Set A.
