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A box plot is a graph that not only helps us to see the distribution (or the shape) of the data, but it can also be used to compare two different groups to see if one differs from one another. As you carry on with math in high school you will become very familiar with these plots.
A box plot (or box and whisker graph) is a graph based on a 5 number summary of:
minimum
lower quartile
median
upper quartile
maximum.
Box plots are not always the same shape, they take different shapes depending on the 5 statistics.
When plotting a box plot it is plotted on an axis.
Comparing Box Plots
Comparing Box Plots
Making the call if one is larger
Making the call if one is larger
Each time a sample is taken for the data of each group slightly different results are received. Therefore that means each time we will get a slightly different median.
This means comparing the medians along is not enough, and we must look to other methods of determining a difference between the groups.
Source: https://www.stat.auckland.ac.nz/~wild/WPRH/
To see if there is a difference between the groups we see if the median of one group is inside the median of the others middle 50% (box)
To see if there is a difference between the groups we see if the median of one group is inside the median of the others middle 50% (box)
There are three different situations that can arise when making a call.
The follow graphs are fictitious but are about comparing boys and girls height.
#1: The boxes do not overlap
#1: The boxes do not overlap
In this scenario it show one group tends to be larger than another.
#2: The boxes overlap, BUT one or both medians lie outside the other's box
#2: The boxes overlap, BUT one or both medians lie outside the other's box
In this scenario it show one group is likely to tend to be larger than another.
#3: The boxes overlap, and both medians lie inside the other's box
#3: The boxes overlap, and both medians lie inside the other's box
In this scenario we cannot tell the difference between the two groups.
As you can see in the animation above, for different samples we receive different results, and that's why when we draw conclusions we use the words 'tends to'. We also need to make sure that we are talking about the population that our sample was taken from.
For example:
"Back in the population, it is likely that boys height tends to be larger than girls height in NZ School Children"
Height of NZ School Children
Height of NZ School Children
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