.
Comparing Groups using Box-plots
.
When comparing two groups a box-and-whisker plot is used
A Sample size of at least 30 is needed to generalize about a population
How can we tell if the groups are different?
"No overlap in spreads"
or "75% is below 75%"
so there IS a difference
between group 'A' & 'B'
(Achieve & Merit)
"Boxes overlap but
not both medians"
or "75% below 50%"
so there IS LIKELY to be
a difference between
group 'A' & 'B'
"Boxes overlap
with both
medians"
NO difference
can be claimed
B
B
B
A
“B is greater than A”
A
or
A
“It is likely that
B is greater than A”
A
B
We cannot tell if
there is a difference
.
More Comparing Groups using Box-plots
.
(Excellence) Using the 'Overall visible spread' to make a comparison when
the boxes overlap:
The Distance Between Medians (DBM) as a percentage of
Overall Visible Spread (OVS)
B
A
Overall Visible
Difference Between Spread (OVS)
Medians (BDM)
BDM
OVS
× 100 =
(see Excel demo)
For a sample size of 30 if this percentage is over 33% there tends to be a
difference between A and B
For a sample size of 100 if this percentage is over 20% there tends to be a
difference between A and B
For a sample size of 1000 if this percentage is over 10% there tends to be a
difference between A and B
.
Practice Comparing Groups using Box-plots
.
Describe the differences between these groups (Sample of 30)
1)
2)
3)
4)
Max
UQ
Median
LQ
Min
Set A
12
10
7
6
5
Set B
Set A
15
Max
14
13
UQ
12
10 Median
11
9
LQ
6
6
Min
5
Set A Set B
Set B
Set A Set B
Max
14
14
16
Max
14
16
UQ
12
13
13
UQ
12
14
11
9
10 Median
11
13 Median
LQ
8
7
9
LQ
8
9
Min
5
4
8
Min
5
8