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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 alone is not enough, and we must look to other methods of determining a difference between the groups in the population.
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 middle 50%'s do not overlap
#1: The middle 50%'s do not overlap
In this scenario it shows one group tends to be larger than another.
#2: The middle 50%'s overlap, BUT one or both medians lie outside the other's middle 50%
#2: The middle 50%'s overlap, BUT one or both medians lie outside the other's middle 50%
In this scenario it show one group tends to be larger than another.
#3: The middle 50%'s overlap, and both medians lie inside the other's middle 50%
#3: The middle 50%'s overlap, and both medians lie inside the other's middle 50%
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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