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Descriptive and Inferential Statistics
When analysing data, such as the marks achieved by 100 students for a piece of coursework, it is
possible to use both descriptive and inferential statistics in your analysis of their marks.
inferential statistics? And what are their differences?
Descriptive Statistics
simply a way to describe our data.
describe data:
and standard deviation.
Inferential Statistics
perfectly represent the population. The methods of inferential statistics are (1) the estimation of
parameter(s) and (2) testing of statistical hypotheses.
We have provided some answers to common FAQs on the next page. Alternatively, why not now
read our guide on Types of Variable?
What are the similarities between descriptive and inferential
Both descriptive and inferential statistics rely on the same set of data. Descriptive statistics rely
solely on this set of data, whilst inferential statistics also rely on this data in order to make
generalisations about a larger population.
What are the strengths of using descriptive statistics to
examine a distribution of scores?
Other than the clarity with which descriptive statistics can clarify large volumes of data, there are
no uncertainties about the values you get (other than only measurement error, etc.).
What are the limitations of descriptive statistics?
Descriptive statistics are limited in so much that they only allow you to make summations about
the people or objects that you have actually measured. You cannot use the data you have
collected to generalize to other people or objects (i.e., using data from a sample to infer the
properties/parameters of a population). For example, if you tested a drug to beat cancer and it
worked in your patients, you cannot claim that it would work in other cancer patients only
relying on descriptive statistics (but inferential statistics would give you this opportunity).
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What are the limitations of inferential statistics?
There are two main limitations to the use of inferential statistics. The first, and most important
limitation, which is present in all inferential statistics, is that you are providing data about a
population that you have not fully measured, and therefore, cannot ever be completely sure that
the values/statistics you calculate are correct. Remember, inferential statistics are based on the
concept of using the values measured in a sample to estimate/infer the values that would be
measured in a population; there will always be a degree of uncertainty in doing this. The second
limitation is connected with the first limitation. Some, but not all, inferential tests require the
user (i.e., you) to make educated guesses (based on theory) to run the inferential tests. Again,
there will be some uncertainty in this process, which will have repercussions on the certainty of
the results of some inferential statistics.
Why not now read our guide on Types of Variable?
In statistics, mean simply means average score of the sample. This is where you add up all your
values and then divide by the number of participants. To expose you to some additional terms,
sum means simply to add up. Using sum may be new to you if you haven't taken many math
classes, but the term makes it easier to write and more educated sounding.
A quick example would be:
Number of bites it takes me to eat a fun-sized candy bar: 4, 2, 1, 1, 4, 1, 2, 1.
The sum total is 16, which makes the mean 2. Fairly simple, right?
Mean is useful for helping us understand the average participant's score in your study. It gives
us, the readers, a quick way to formulate what a typical or normal variable is in your study. This
is most often used to describe the average age of the participants but could also be used to
describe the average scores on a test or number of years involved in something.
With this in mind, we can take an individual score and compare it to an average. For example, if
I said the average height of the islanders is 5 feet tall and I'm 6 foot 3, then we know that in
comparison, I am much taller than the average islander.
Median is the middle score after the scores have been arranged in numerical order. For example,
if we looked at the candy bar eating numbers from before: 4, 1, 1, 1, 4, 2, 2, 1, we will need to
reorganize them into 4, 4, 2, 2, 1, 1, 1, 1. As you can see, I put the highest number first, but you
could put the lowest number first, and your median will be the same.
We have eight numbers, so we count halfway. Counting obviously works better with odd
numbers since you land on a single number. With even numbers, you will take the middle two
numbers and then average them. Our middle numbers are 2 and 1. This means our median is 1.5.
Median is useful for similar reasons to mean: It provides the reader with an understanding of an
average, or normal, participant or measured variable. Median, however, reduces the effect of
outliers, or a point of data that is distant from the others, either extremely high or extremely low.
In our candy-eating example, if it took me 15 bites to eat a really chewy and delicious candy bar,
then this would be an outlier. If you add 15 to the scores, our new mean would be 3.4, with our
median at 2. Which better describes the data?
Mode, defined as the most often occurring value, is by far the easiest to compute, particularly if
you have scores in numerical order. In our candy-chewing example, the most often occurring
number is 1. Another way of thinking about mode is what is the most common number.
But who cares? Well, you should. Why care? Because the candy bar example is not very good
when we're trying to make important decisions, but there are many studies out there where
individual descriptions matter.
For example, if we were looking at a school with financial issues, and the most common type of
staff is administration, what does that tell us? (That like almost everywhere in the world,
bureaucracy thrives so much so that it makes me crazy.) Or what if you were going to be a
senator, and you needed to know what ethnicity was most common in your district? So there are
a lot of ways that mode can help us describe the world we live in.
Range is simply a single number representing the spread of the data. This is where you take the
highest number you have - in our candy example it's 4 - and subtract the smallest number. In this
example, it's 1. This gives us a total range of candy bar bites at 3.
Range is kind of a funny thing. While it does tell us how spread out the data is, if you want a lot
of variability, then you want a high range. For example, if you're wondering if a new teaching
program educates both intellectually high and low children, you should have a wider range. If
you want little variability, like a study on people with severe depression, then you want the range
to be relatively small. It all depends on what you're looking at.
Standard Deviation and Variance
Standard deviation is a number corresponding to a bell curve describing how spread out the
data is. Variance is a numerical value indicating how spread out the data is. Why are these two
together? Because the standard deviation is the square root of the variance. Briefly, the math
involved for computing these involves comparing each score with the average and then summing
up the distance each score has from the average and comparing them to a standardized score,
which has more math involved than we can compute. It's
What Is Descriptive Statistics? - Examples & Concept - Video ...