Statistics 
Data measurement, probability
and statistical tests
Learning Aims
By the end of this
session you are going to
totally ‘get’ levels of
significance and why we
do statistical tests!
Levels of measurement


These are
quantitative
measures of data
which are of
extreme importance
when conducting
statistical tests
There are 4 levels of
measurement
Also known as levels of data


Nominal: Counting
into categories, e.g.
there are 4 men and
4 women in the room
Ordinal: Results are
put in order, they
are ranked. E.g. we
could rank the place
that each horse
came in a race
Levels of measurement


Interval: Data is defined as
being a specific measure, this
can be measured on an
instrument, there are equal
intervals between each piece
of data. E.g. We can record
the exact temperature using
a thermometer. (can be minus)
Ratio: This is like
interval data except the
scale has a meaningful
value of zero. E.g. time
and length.
Why do we need to conduct
statistical tests?


Statistical tests tell
us the significance
of a set of findingsdid the IV really
effect the DV or
were the findings a
fluke?!
The more significant
a finding is the more
effect the IV had on
the DV
Probability:





We need to use inferential statistics to tell us if the
result that we have found is due to chance or not.
To establish if our results are reliable we have to look
at the probability of a result being due to chance or
not.
The minimum accepted level of probability commonly
used in psychology is 5%, this is represented as 0.05.
If the level of significance achieved from a test is
equal to or less 0.05 than the results are said to be
significant.
This would mean that we are 95% sure that the IV
caused the change in the DV
Probability:

Can be expressed as:






A proportion: a 1 in 5 chance.
As a percentage: 20%
More commonly expressed as a decimal in psychology: 0.2.
In psychology: 10%=0.10, 5%=0.05, 1%=0.01 and
0.1%=0.001
To go from % to decimal divide by 100, move decimal
place 2 spaces to the left.
Remember the more stringent (lower) the level of
significance you set the more significant the results
are
Observed value:




Every time you perform a statistical test you
get an OBSERVED VALUE.
This observed value tells you the extent to
which your results are valid, you then have to
compare this observed value to a table of
CRITICAL VALUES to see of your results are
significant or not.
To be significant the observed value should
be greater or less than the critical value
depending on the type of test
Note that there will be a different table of
values for different statistical tests.
Interpreting results:
 Usually
in psychology if the results
are significant it means that the
probability of the result being due
to chance is 5% or less

P<0.05 means the results are
significant- so we would accept the
experimental hypothesis and reject the
null hypothesis
Interpreting results:

P is used to represent “the probability that is
due to chance”
 > =means greater than
 < =means less than
 ≥ means greater than or equal to.
 ≤ means less than or equal to.
SO………………
P<0.05 means that the probability that the
result is due to chance is less than 5%.
Type 1 and type 2 errors:
The 5% level of significance has been
accepted as it represents a reasonable
balance between the chances of making
a type 1 or type 2 error
 These can occur because:


Level of probability accepted is either too
lenient (too high) or too stringent (too low)
Type 1 and type 2 errors

Type 1 error:



Occurs when we
conclude that there
IS a significant
difference when
there is NOT
This can happen if
the accepted level of
probability is set
TOO LENIENT
Significance level set
at 20%

Type 2 error:



Occurs when we
reject the
experimental
hypothesis and
accept the null when
there IS a
difference
This can happen if
the probability level
is TOO STRINGENT
Significance level set
at 1%
Deciding on a statistical test
You must decide the following:
Are you trying to find out if your samples
are related (correlate) or different?
 What design you have used- related, non
related, matched pairs
 What level of measurement you have used.

You can use the following table to help
decide:
What test to use?
Design
Nominal
Ordinal,
interval, ratio
Correlation/
association
Chi-square
test of
association
Chi-squared
test of
independent
samples
Sign Test
Spearmans
Rank
Independent
measures
Repeated
Measures
Mann Whitney
U
Wilcoxon T
test
Test your understanding!
Using your newly found knowledge identify the test that would be suitable for the
following:
1.
2.
3.
4.
5.
6.
7.
An experiment with nominal data and an independent groups design
Ordinal data on both measures in a study to see if two measures
are associated
An experiment with and independent groups design in which the DV
is measured on a ratio scale
A study using a correlational technique in which one measure is
ordinal and the other is ratio.
A study testing an association using a nominal level of measurement
An experiment in which all participants were tested with alcohol
and without alcohol on a memory test
An experiment in which reaction time was tested using an
independent subject design
ANSWERS
1.
An experiment with nominal data and an independent groups design
chi-squared test
2.
Ordinal data on both measures in a study to see if two measures are associated
Spearman’s rank correlation
3.
An experiment with and independent groups design in which the DV is measured
on a ratio scale
Mann-Whitney U test
4.
A study using a correlation technique in which one measure is ordinal
and the other is ratio
Spearman’s rank
5.
A study testing an association using a nominal level of measurement =
Chi-Square test of association
6.
An experiment in which all participants were tested with alcohol and
without alcohol on a memory test
Wilcoxon’s T test
7.
An experiment in which reaction time was tested using an independent
subject design
Mann-Whitney U test
So…your data…
GX

For Spearmans Rho



The observed / calculated value must be equal to or
higher than the critical value for the result to be
significant
Observed / calculated = 0.685
Critical value = 0.456 (each test has a table of these – you do
not need to know this for the exam…. You need to be able to conclude
though so you need to be aware of what you need to do with these
numbers)

Is your data statistically significant?

So, your results should say something like….





Observed value = 0.685
Critical value for one-tailed test p<0.05 = 0.456
From this, we can say that the results are statistically significant at p<0.01
meaning that there is less than a 1% possibility that the results obtained were
due to chance
As the results are significant ….link to hypothesis
Also, link to your graph –positive correlation (not perfect…. Why??)
So…. Your data….
DX

For Spearmans Rho



The observed / calculated value must be equal to
or higher than the critical value for the result to be
significant
Observed / calculated = 0.378
Critical value = 0.4124 (each test has a table of these –
you do not need to know this for the exam…. You need to be able to
conclude though so you need to be aware of what you need to do
with these numbers)

So, your results should say something like….





Observed value = 0.378
Critical value for one-tailed test p<0.05 = 0.4124
From this, we can say that the results are not statistically significant at p<0.05
meaning that there is more than a 5% possibility that the results obtained were
due to chance
As the results are not significant ….link to hypothesis
Also, link to your graph – zero correlation

EX

For Spearmans Rho



The observed / calculated value must be equal to
or higher than the critical value for the result to be
significant
Observed / calculated = 0.525
Critical value = 0.4265 (each test has a table of these –
you do not need to know this for the exam…. You need to be able to
conclude though so you need to be aware of what you need to do
with these numbers)

So, your results should say something like….





Observed value = 0.525
Critical value for one-tailed test p<0.05 = 0.4265
From this, we can say that the results are statistically significant at p<0.05
meaning that there is less than a 5% possibility that the results obtained were
due to chance
As the results are significant ….link to hypothesis
Also, link to your graph –positive correlation
Remember…
The theory underpinning this report is??!!!
Freud! The psychodynamic approach specifically the
psychosexual stages of development
If we become fixated in these stages it can impact our
personality as an adult.
Anal stage important focus ~ if a parent is too strict with
toilet training, the child can become fixated and show
personality characteristics such as being obsessively tidy
(anal retentive). If a parent is too lenient with toilet training,
the child could grow up showing personality characteristics
such as being messy / untidy