Often in a statistical inquiry, we need to analyse graphical output.
It can be difficult to know what to say.
When examining graphs, we look at four main things:
Within each of these,
the OSEM acronym can help.
OSEM stands for:
We will now illustrate this process with an example.
This is a dot plot - box plot combination for the number of shoes owned by male and female students.
You can find out more about this investigation in our video:
The statistical inquiry cycle.
Each dot in the dot plot represents a number of pairs of shoes one person says they own.
The box plot shows the range,
The lower quartile, median, and upper quartile
for the sample. Our investigative question is:
Note that even though our question is specifically about the median,
we are also interested in other differences between the two groups.
First we will look at position. As we are comparing two graphs we need to
comment on their relative positions,
sometimes called shift.
We state what we can see. It does not need to be tricky,
and can be quite... obvious!
We can see that:
we say more carefully what we have observed
We say it so someone else would understand what we mean
We could say:
Here we need to give values to support our observation
We may need to draw on summary values if they are difficult to read off the graph.
We could say:
Or we could say:
Meaning. This is where we link the evidence from a graph with the
context or story behind the data,
and the investigative question.
What does our finding tell us about the problem?
We can also say why this is relevant
and what else we could find out.
We could say
We have now gone through the OSEM process looking at position, or shift.
Note that as we are comparing two graphs, it is important to state
specifically the differences and similarities between them.
There may be more than one element to comment on for each aspect,
but we will not cover everything here or the video will be too long!
Now we will use OSEM
to analyze and report on the spread of the data in the two groups.
Next we move onto Shape. Do the shapes of the distributions differ, and how?
Our obvious statement does not have to be well framed. It's good to get the idea
down first before developing
And finally, we comment on any special aspects of the graph.
We have already commented on the three spikes in the female graph, and given a meaning for it.
Special aspects can include gaps, clusters, a tail (or skew),
spikes or unusual observations. Sometimes there are no special features for a graph.
Note that some people might call this a tail, or skewed to the right.
As there are only a few observations, particularly for the males,
I think these are more unusual observations than skew.
OSEM is a useful acronym for many forms of analysis.
It was invented by Jeremy Brocklehurst, a maths teacher at Lincoln High School,
New Zealand.
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