Analysis

Part 1: Describe your Data

Discuss the following features of each graph (in comparison with the other):

Centre
Where are the middles of each distribution in comparison with each other. (Often referred to as the "Shift")
Which group has the higher middle and by how much?
Spread
What are the relative sizes of each IQR (box) in comparison with each other?
Which group has a greater spread?
Shape
What are the shapes of the distributions of each group?
Overlap
How much do the boxes of each group overlap?
Unusual Values
Are there any outliers?
Will these outliers affect any of the analysis in this investigation?

Example

Part 2: Looking at the data for information.

What does the data tell us about the two groups back in the POPULATION?

There are two guides that we can use to help us see what is likely to occur back in the population.

The 1/2 - 3/4 rule

This is a quick test but only useful for small sample sizes (30 - 50).

Rule:
If 1/2 of one group is greater than 3/4 of the other group in the sample then, we can say that:
"It is likely that that group tends to be greater than the other group back in the population".

eg:
In the above sample, we can "make the call" that:
"Female kiwi birds tend to be heavier than male kiwi birds, back in the population of all kiwi birds in NZ".

Summary

The DBM-OVS rule

This rule works for any sample size (min of 30) but requires some calculations.

DBM = Difference Between Medians
DBM = Larger median - Smaller median

OVS = Overall Visible Spread
OVS = Larger upper quartile - Smaller lower quartile

For sample sizes around 30

For sample sizes around 100

For sample sizes around 1000

Examples

DBM = 3.07 - 2.157 = 0.917
OVS = 3.311 - 2.026 = 1.285

DBM/OVS = 0.917/1.285 = 0.71

The sample sizes in this sample are around 30.
For this sample size the ratio of DBM/OVS needs to be greater than 1/3 (0.33) for us to be able to "make the call".

0.71 is greater than 0.33 so, we can make the call that female kiwi birds tend to be heavier than male kiwi birds back in the population of all kiwi birds in NZ.

...in a report this would be split between the analysis and conclusion sections, as shown below:

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