Paired samples and independent samples in statistical analysis
Hi I'm Dr Nic from Creative Maths, including Statistics Learning Centre.
In this video I'm going to explain the difference between paired samples and independent samples.
I will give examples of both.
I will also show how to graph paired samples
and explain why this is different from independent samples.
Paired samples are really just one sample
with two measurements taken on each of the subjects or observations.
Here is an example of paired samples
We want to compare a score in a statistics test before and after tutoring.
Each observation or line in the data refers to one person, for whom there are two scores,
taken before and after the tutoring.
We are interested to know about the differences
in the two measurements
Scoring the same people twice helps to account
for variation between people.
In an actual study we would have more than six people.
Another approach compares the mean scores
in a statistics test between people who have had face-to-face tutoring
and those who have learned through an online course.
In this instance there are two samples - one for each group of people.
The two samples are independent -
there is no relationship between the people in one group and the people in the other group.
When you enter the data for analysis each line will be a person,
and there will be one variable giving the score, and one variable for group membership.
Here is another example of paired data
We wish to test which of two cat food varieties is more appealing to cats.
We have a sample of 15 cats. On one day we offer each cat one variety, Nubbles,
and measure how much it eats.
The next day we offer the other variety, Yum,
and again measure how much each cat eats.
This is paired data as there is one sample of cats,
and the measurements are taken twice on each cat.
Another way to explore the cat food varieties is to randomly assign the cats into two groups.
We give a different variety of food to each cat, depending on which group they belong to.
This is an example of independent samples.
For the paired samples, the data will look like this, with two measurements for each cat.
For the independent samples the data will
look like this, with one line per cat, and a variable stating which food they were given.
In Excel, the data is put in two columns like this if you are going to use the data analysis toolpak.
But in statistical packages, the data needs
to be listed with one observation per line.
When we are comparing two independent samples,
we should plot the data using box and whisker plots.
Here are the plots for the cat food example independent samples
We CAN use box and whisker plots for paired samples and sometimes this is better than nothing
but it disregards the information we gained from pairing and reduces the power of our test.
For paired data, we can make an arrow plot showing the paired results.
This one was made on Excel.
Each line represents one cat.
A horizontal line means that it ate the same amount of each catfood.
These plots are only useful for small sets of data.
Rather than use the arrow plot, we can calculate
the difference for each observation, in this case a cat,
and plot those differences using a box and whisker plot.
When a cat eats the same amount of each variety the difference is zero.
We would look to see how close the mean difference is to zero.
To determine if there is evidence of difference
in the population from which the sample or samples are drawn
we will use a t-test for the difference of two means.
The tests are different for paired samples and independent samples.
Check in the description below for links to videos for each of these of these tests.
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