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Additional information 11.4
Guide to working out descriptive and inferential statistics
Descriptive statistics
Measures of central tendency: Where is the middle of your data?
There are three typical ways to assess this. The first is the mode. This tells you what the most common
score is. To work it out, count how many times each value appears in your data. The most common is
your mode. If two values appear the same number of times, then you have two modes. The mode is
most useful when you have data that is categorical or ordinal, for example if your data is ‘yes/no’
questions.
The second is the median. To work this out, put your data in order, and count half way through. The
value right in the middle is your median. If two values are in the middle, work out what is half way
between them: that is your median. This is a particularly useful statistic if you have extreme scores.
The third is the average, or mean. To work this out, add up the data and divide it by the number of
values you have. For example, if ten participants gave you a speed estimate, add up the ten estimates
and divide this by ten. This is the most common way to describe the middle of your data set.
Measures of dispersion: How spread out are your data?
You can easily work out the range of your data by subtracting the bottom score from the top score. This
is a very basic way to describe the spread of your data.
Working out the standard deviation is usually more informative. You can do this online (e.g. at a
website like easycalculation.com) or using Microsoft Excel. The standard deviation is calculated based
on the average distance from the mean of your data: if you have a lot of extreme scores, you will get a
higher standard deviation; if your data are very stable and clustered closely around the mean, you will
get a lower standard deviation. What is most useful for you to look at is the difference between the
standard deviations of the groups in your study. If there is a big difference in the standard deviation,
this means one group has more variation in their scores. Try to explain why this is in your results
section.
Inferential statistics
If you are an HL student, you need to carry out a test to see if a difference between scores from the
groups in your study is significant or not. Obviously, you can see from your raw data or from a graph if
there is a difference or not, but at HL you do the test to see if the difference you have is big enough for
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you to say that the independent variable really had an effect.
The test you choose depends on the type of data you have and the design you used. Hugh Coolican’s
book (2004) is useful in helping you make the decision, as is Graham Hill’s (2001). For the majority of
Internal Assessments, you will use ordinal level tests, even if your data is ratio or interval level,
because the assumptions for the t-test are not usually met. Because you need to justify your choice of
test, you need to be careful that you can do so when using the t-test. The ordinal level test for repeated
measures designs is the Wilcoxon Signed Ranks test. For independent samples, it is the Mann–Whitney
U-test.
It is recommended that you use a website (for an example of one click here) as this makes the process
faster, but there is no substitute for working these tests out by hand as this increases your understanding
of what you have done. Coolican (2004) very clearly explains how to do the tests.
Whichever test you complete, you are transforming your data into a form that can be compared with
other data. Basically, you will be investigating what the probability is that you could get the results you
have obtained simply by chance. For example, when you do the Stroop test, there is usually a very big
difference in the time taken by participants to complete a difficult task with interference from more
than one visual stimulus. We know that if we just asked people to do any test twice there would be a
difference in their scores, but we know that there is a small probability that the difference will be very
big. This means that when we look at the scores from the two versions of the Stroop test, we can say
that it is not just by chance that we observed such big differences: it is because of interference.
In the same way, when conducting memory research with differences in the questions asked (e.g.
Additional information 11.1 and 11.2), it is possible that participants will provide a range of speed
estimates that just by chance are different for the two groups. But if you see a big difference, you know
that the probability of this happening is quite small, and you can assume that the reason for the
difference is not just chance, it is because of the verbs you used in the two different questions.
You will need to use statements like the following examples in your results section.

A Mann–Whitney U-test was carried out to determine if the difference between group A and group
B was significant. The U-test was chosen because my data were ordinal and I used independent
samples.

This tells us what test you used and why you chose it. ‘Significant’ means big enough to assume
the difference is not just due to chance.

The U-test showed that the difference was significant (U = 29, P <0.05).

Psychologists typically assume that differences are significant if the probability of it happening
just by chance is less than 5% (0.05). This sentence tells us what U-value you calculated, and how
likely it is that this U-value could occur by chance. In this case, the probability of obtaining this U© Pearson Education Ltd 2010. For more information about the Pearson Baccalaureate series please visit
www.pearsonbacc.com
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value by chance is less than 5%, so we can say the difference is significant.

Therefore, the null hypothesis was rejected.

This is the purpose of your experiment and the test: based on the inferential statistics test you have
chosen, you are able to say with confidence that the independent variable did or did not have the
effect you predicted in your hypotheses. If the result of your test is significant, reject the null
hypothesis. If not, reject the experimental or research hypothesis.
References
Coolican H. (2004). Research methods and statistics in psychology. Hodder and Stoughton
Hill G. (2001). A-level psychology through diagrams. Oxford: OUP
© Pearson Education Ltd 2010. For more information about the Pearson Baccalaureate series please visit
www.pearsonbacc.com
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