Week 3 - Parametric Assumptions, and how to test for them
Levene’s Test (Homogeneity of Variance) and Kolmogorov - Smirnov test
Before using a parametric test on your data (e.g. t-test or ANOVA), we have to make
sure the data meet the assumptions of parametric tests. There are various assumptions and
each parametric and non-parametric test may have a unique set of assumptions. Two most
frequently encountered assumptions of parametric tests are normality of data distribution
and homogeneity of variance. As you work through the activities, remember that your
screen may look a little different if you are using a MacBook or if you are using a different
version of SPSS (this is absolutely fine).
This handout will tell you:
1. What is parametric data?
2. How do we test for the properties of parametric data?
a. SPSS walkthrough for:
i. Kolmogorov-Smirnov Test (for normal distribution)
ii. Levenes Test (for homogeneity of variance)
3. Exercises
What is parametric data?
a. Data measured on a scale, like cm’s measured with a ruler (called ratio-level
data), or temperature which has scale but does not have a true 0 (called
interval-level data)
b. The data should be normally distributed:
c. If you have more than one sample, the variance in each sample should be
similar – this is called homogeneity of variance
How do we test for the properties of parametric data?
Data for the example shown underneath can be found on Canvas. The file containing the
data is called ‘Example data week 3.sav’. You can use this data set to investigate whether it
meets the assumptions of normality of data distribution and homogeneity of variance. Two
frequently used tests that investigate these assumptions respectively are the KolmogorovSmirnov Test and the Levene’s Test.
a. Interpreting the Kolmogorov-Smirnov Test for Normal Distribution
i. Tests the null hypothesis that the distribution is normal
ii. If significant then the data is NOT normally distributed – so we want
p to be above 0.05 for this test because it means our data is not
significantly different to a normal distribution. If p is below 0.05 this
means our data is not normally distributed.
b. Performing the Kolmogorov-Smirnov Test in SPSS:
1. Click on ANALYZE >
DESCRIPTIVE
STATISTICS > EXPLORE
2. Drag your dependent measure into
the DEPENDENT LIST. If you have
more than one group, drag your
grouping variable into the FACTOR
LIST. Make sure ‘Both’ is selected
3. Click on PLOTS
4. Check the boxes labelled:
HISTOGRAM and
NORMALITY PLOTS WITH
TESTS
5. Click CONTINUE
6. Back in the Explore box,
click ok
The SPSS software will now open a separate window which shows the output for the selected
procedure. The output should contain the following information:


Descriptive statistics: means, medians, standard deviations, range, minimum, maximum etc.
Histograms
Observe that the ‘No Cloak’ group data does
not APPEAR normal on the histogram.

Tests of Normality
To check whether the data is NORMALLY DISTRIBUTED, refer to
the Kolmogorov-Smirnov test (K-S)
1. Find the TESTS OF NORMALITY TABLE
2. The K-S test for the two groups is not significant
3. So, in both groups the data is normally distributed.
c. Interpreting the Levene’s Test for Homogeneity of Variance
i. Levene’s tests the null hypothesis that each sample has a similar
variance
ii. If the samples DO have a similar variance, and satisfy the
homogeneity of variance assumption, the Levene’s test will NOT BE
SIGNIFICANT! In other words, we want p to be above 0.05.
iii. If Levene’s test p value IS SIGNIFICANT, we CANNOT accept that the
data meets the homogeneity of variance assumption
d. Performing the Levene’s Test in SPSS
i. The Levene’s test can be performed in the Explore option
- Complete points from 1 to 3 as shown in point ‘b.’ (K-S)
Parametric tests use the
- Select ‘Untransformed’ in the ‘Plots’ option
Mean to calculate
- Press ‘Continue’ and ‘OK’
results. Therefore, we
will interpret the ‘Based
on Mean’ results.
Test of Homogeneity of Variance
Levene Statistic
Mischievous Acts
df1
df2
Sig.
Based on Mean
.545
1
22
.468
Based on Median
.270
1
22
.609
Based on Median and with
.270
1
21.754
.609
.440
1
22
.514
adjusted df
Based on trimmed mean
ii. The Levene’s test will also be performed whenever you carry out a
parametric test called the t-test in SPSS. Underneath is an example of
a t-test results (you don’t need to perform this analysis).
iii. Note that the numeric results of the K-S and the Levene’s tests are
typically not reported in a written format. However, it is typically
necessary to write whether the assumptions were met.
Exercises
Output 1:
Use Table 1 to answer the following questions:
1. Why do we perform a Kolmogorov-Smirnov test?
2. What is the significance level of the Kolmogorov-Smirnov test for:
a. The emotion recognition score of the ASD group?
b. The emotion recognition score of the Typical group?
c. Are either of these values significant?
3. Is the data for the ASD group normally distributed? Why?
4. Is the data for the Typical group normally distributed? Why?
Output 2:
Use Table 2 to answer the following questions:
5.
6.
7.
8.
9.
Why do we perform a Levene’s Test?
What is the significance value for Levene’s test?
Is the result of the Levene’s test significant?
What t-test values would we report based on the findings from Levene’s test?
Why would we report those values?
See the “answers” document on this week’s canvas page, for the answers.
Week 4 - Tests of Difference: Chi-Squared
This handout will tell you:
1. What is the Chi-square test and when should you use it?
2. How to perform a Chi-square test in SPSS?
a. Worked example: ‘Are males more likely to smoke than females?’
3. Exercises
What is the chi-square and when should you use it?
Chi-Square is a non-parametric test of difference.
Use this test if:
1. You want to know about differences between groups
a. Are there more females than males studying Psychology?
2. You want to know whether there is an association between two categorical variables
a. Is there an association between gender and smoking?
3. Your groups are independent – each observation only contributes to once cell of the
analysis (e.g. gender).
4. You have categorical data (otherwise known as on the nominal level of
measurement).
a. For example, frequency or number of observations in a number of categories
– e.g. 10 male versus 50 females enrolled in Psychology.
5. Your data violates parametric assumptions – i.e. your data is not normally
distributed.
How to perform a chi-square in SPSS?
Worked Example: Are males more likely to smoke than females?
The table underneath contains information about smoking status distributed by
gender. This information can be entered in to SPSS providing that appropriate variables are
constructed. In this example there are three variables, namely ‘smoking status’, ‘gender’,
and ‘frequency’. In Point 2 illustrates these variables in SPSS ‘Variable view’. Point 3
illustrates these variables and the associated data in SPSS ‘Data view’
Male
Female
Smokes
25
12
Does not smoke
128
85
1. To learn how to perform a Chi-square test you may open the example data in this
week’s Canvas folder and work through the steps detailed below.
2. Check that all relevant details are included in variable view (it should look like the
screen below). You should add your own labels here too. Also check that the values
are specified for ‘gender’ and ‘smokes’.
Remember to assign the correct
types of measures!
3. Click on data view and check that a row defines each cell of your frequency table (i.e.
you should have 1 row for females who smoke, 1 for females who do not smoke, 1
for males who smoke and 1 for males who do not smoke). The total observed
frequency of each category should be in the corresponding frequency column.
Remember you can change from numerical to written variable labels by pressing
4. Click on the menu Data > Weight Cases.
5. Select Weight cases by > transfer frequency to the corresponding box > click OK.
Note. In the output
window SPSS will
confirm whether the
procedure was
successful. From now
on the Weight cases
option will be on at all
times. Remember to
turn it off for a
different analysis!
6. Click on Analyze > Descriptive Statistics > Crosstabs
7. Add gender to the Rows box > add smokes to the Columns box > click on Statistics.
8. Select Chi-Square > Click continue.
9. Next, select the Cells button
Note that the Frequency variable is not
included. We have already weighted our
analysis by this variable in the earlier step so
SPSS already knows that Frequency is the
dependent variable we are interested in
10. Select Observed, Expected, Row, Column, Total and Standardized > Click continue.
11. Finally, click OK.
Results
Any large differences between
the expected counts (by
chance) and observed counts
would suggest there was an
association between gender
and smoking. In this case the
numbers are similar.
p > 0.05 therefore the
difference between
gender and smoking is
not statistically
significant. You must
report these results as
shown below.
How to report these results in APA format
A Pearson Chi-Square was used to identify whether gender influenced smoking frequency.
Results of the chi-square showed no significant difference in smoking frequency between
genders (χ² (1) = .742, p = .389).
Note: You can find the χ symbol on word by going to Insert > Symbol. You might need to
look under More Symbols if you haven’t used this symbol before.
Exercises
A chi-square analysis was carried out to investigate the relationship between gender and
smoking frequency, the SPSS output showing the results of the analysis is shown above.
1. What are the observed frequencies for men and women who did and did not smoke?
Put the frequencies into a table (see question 5 for a template).
2. How would you report the results of the chi-square analysis in APA format?
3. Are the results of the chi-square significant?
4. What do these results show?
5. The table underneath shows how often men and women play football. Enter this
data into SPSS following the same format as in the previous example.
Play football
Do not play football
Male
60
70
Female
45
80
a. Perform a chi-square analysis on this data in SPSS
b. What are the results of the chi-square?
c. Are the results significant?
d. What do these results mean? What can you conclude?
See the “answers” document on this week’s canvas page for the answers.
Week 5 - One Sample t-test
This handout will tell you:
1. What is the one sample t-test and when you should use it?
2. How to perform a one sample t-test in SPSS?
a. Worked example: ‘are first year Psychology students more intelligent than
the norm?’
3. Exercises
What is the one sample t-test and when should you use it?
The one sample t-test compares a population/sample mean to a known population (e.g. the
mean normal IQ of 100, or chance level on a given task).
Use this test if:
Your data meets the assumptions of parametric tests
a. Interval or ratio level data
b. Normally distributed
How to perform a one sample t-test in SPSS?
Worked Example: Are first-year Psychology students more intelligent than the general
population?
1. You should open the Example data in this week’s Canvas folder and work through
the following steps.
2. Check all of the relevant information is presented in variable view. IQ should be
defined and labelled.
3. Check that IQ scores have been added in one column in data view.
4. Click on Analyze > Compare Means > One-Sample T Test
5. Add IQ to the variable box > set the test value to 100 (population mean) > unselect
estimate effect size this time (this is an additional feature) > click OK. The Test Value
box is where you enter the known average you want to compare your data to. For
example, in this case we know (from exploring sources about IQ testing) that the
population mean for IQ is 100. In order to find out known averages/population
means, you will occasionally need to search online and/or published articles to find
this out.
SPSS Version 28 gives two p
values but don’t worry if your
version of SPSS only gives one.
If you need to calculate a onesided/one-tailed p value, it is
half the two-sided p value
(just divide it by 2). 0.001 is as
good as it gets though! Chose
the correct p value based on
what you have predicted. p <
0.001 therefore there is a
significant difference
between the mean of the
population (100) and the
sample mean (124).
How to report results of the one sample t-test:
The mean IQ of a sample of first year Psychology students was compared to the mean IQ of
the general population using a one sample t-test. Results of the t-test showed that the
mean IQ of the first year Psychology students was significantly higher than the mean IQ of
the general population (t (19) = 8.559, p < .001).
Addition point: Effect size tells you how strong the effect is and there are different measures for this.
This will be covered later in the course but you can do some additional reading on this now if you
would like to.
Exercises
You want to know whether people can do your new emotion recognition test. There are 21
videos and 3 possible responses, which means that chance level is 7/21, or 33%. You decide
that the best way of checking whether people can do this task is to see whether the mean
correct score on this new task is significantly higher than the chance score of 7. Therefore,
you decide to perform a one sample t-test, to compare the mean score on this new emotion
recognition task to chance (7 – this is the number that goes in the test value box).
1. Go to this week’s section on Canvas and find ‘Exercise week 5’
2. Check whether the data is normally distributed
3. Perform a one sample t-test comparing the mean emotion recognition score to
chance level (7)
4. Report the results of the one sample t-test in APA format
5. Are these results of the one-sample t-test significant?
6. What do these results mean?
See the “answers” document on this week’s canvas page for the answers.
Week 6 - Wilcoxon Rank Sum Test
This handout will tell you:
1. What is the Wilcoxon Rank Sum Test and when should I use it?
2. How do I perform a Wilcoxon Rank Sum Test in SPSS?
a. Worked example: ‘Do the glucose blood levels in a sample of patients differ
from the norm?’
3. Exercises
What is the Wilcoxon Rank Sum Test and when should I use it?
The Wilcoxon rank sum test can be used as the non-parametric equivalent of the one
sample t-test.
Unlike the one sample t-test which uses means, the Wilcoxon rank sum test compares a
sample median to a known population median (e.g. do the glucose blood levels in a sample
of patients differ from the norm?).
Use this test if:
You want to compare a population/sample to another known population AND
Your data DOES NOT MEET the assumptions of parametric tests:
a. E.g. if it is NOT normally distributed
How do I perform a Wilcoxon Rank Sum Test in SPSS?
Worked Example: do the glucose blood levels in a sample of patients differ from the
norm?
1. Open the example data file and work through the following steps.
2. Check that all relevant details are provided in variable view and add any aspects
which are not (e.g. you should add the label ‘blood glucose level’).
3. Click on Analyze > Non-Parametric Tests > One Sample
4. Select your objective from the options available. As you would like a Wilcoxon
Signed-Rank test chose Customized analysis. You will find additional information
about what the options permit in the description box. Next, click on Fields
5. Select Fields and make sure blood glucose is in the test fields box. Then select
Settings.
6. In Settings > Customize tests > Compare median to hypothesised (Wilcoxon SignedRank) > Enter the known median which in this case is 100) > Click Run
Note that SPSS displays which
types of measures are allowed
for the analysis.
Results
Our null hypothesis
states that there is no
difference between
our sample and the
hypothetical median.
The p < 0.05 so there
IS a significant
difference between
the sample and
population median.
How to report results of the Wilcoxon Rank Sum Test:
The median blood glucose of a group of patients was compared to the median blood glucose
of the general population using a one sample Wilcoxon Rank Sum test. Results of the
Wilcoxon Rank Sum test showed that the median blood glucose levels of the patient group
significantly differed from the blood glucose levels of the general population (T = 782.5, p =
.046).
Exercises
The distribution of hunter-gatherer population densities (N = 86) across all forest
ecosystems worldwide is skewed to the right and is non-normal. The median is therefore
the most reliable measure of central tendency. As such, the median population density (per
100 km) of forest hunter-gatherers is 7.38.
An interesting question that we may want to ask is whether this value is an accurate
estimate of the population density of forest hunter-gatherers on specific continents.
For this example, we will look at the hunter-gatherer groups of the northern Australian
forests (n = 13).
1. Go to this week’s section on Canvas and find ‘Exercise week 6’
2. Perform a one sample Wilcoxon rank sum test comparing the median density of
hunter gatherer groups in northern Australia to the median population density of
hunter gatherer groups in general.
3. Report the results of the one sample Wilcoxon rank sum test.
4. Are the results of the test significant?
5. What do these results mean?
See the “answers” document on this week’s canvas page for the answers.
Week 7 – Independent Samples t-test
This handout will tell you:
1. What is the independent samples t-test and when should I use it?
2. How do I perform an independent samples t-test in SPSS?
a. Worked example: ‘Do women score higher on verbal reasoning than men?’
3. Exercises
What is the independent samples t-test and when should I use it?
The independent samples t-test compares the means of two independent groups. For
example: the mean score of men to the mean score of women, or the mean memory score
of participants in one experimental condition (had coffee) to the mean memory score of
participants in the other experimental condition (did not have coffee).
Use this test if:
You want to draw inferences regarding group differences
Groups are independent of one another – participants only contribute to one data
sample
Your data meets the assumptions of parametric tests
a. Interval or ratio level data
b. Normally distributed
c. Homogeneity of Variance
How do I perform an independent samples t-test in SPSS?
Worked Example: Do women score higher on a verbal reasoning task than men?
1. If you are using this handout to practice your knowledge you will benefit from
opening the example data file in this week’s Canvas folder and work through the
following steps.
2. Check whether all relevant details are included in the variable view.
3. Check data is in the correct format in data view. Remember that your groups should
be coded as 1s and 2s, but you can alternate between seeing numerical data and
labels using the button below.
The box highlighted above is
checked so labels are displayed.
To switch back to numbers
simply click this button again
4. Click on Analyze > Compare Means > Independent Samples T Test
5. Add Verbal Reasoning to the Test Variable box and Gender to the Grouping Variable
box. Deselect estimate effect size unless you would like to include this. Then click on
‘Define Groups’.
You may want to explore
the various options that
SPSS provides in the
‘Options’ box.
For example, you can tell
SPSS how to treat missing
values in the Options box.
For this exercise you
don’t need to change any
options.
6. Define your groups based on the numbers you assigned to them. For example, in this
case Group 1 would be 1 (for female) and Group 2 would be 2 (for male). Different
numbers can be assigned for different data sets. Note that some datasets may have
more than two groups so you need to tell SPSS which two groups it should compare.
Then click ‘Continue’.
7. Finally, click OK.
The question
marks have been
replaced with your
group numbers
Results
Descriptives for the
two groups.
Levene’s test is not
significant so the data
is homogenous, we
can continue to use
this row.
SPSS Version 28 gives two p
values but don’t worry if
your version of SPSS only
gives the 2-sided. In most
cases you will use the two sided p value (when you
have predicted that there
will be a difference) rather
than the one-sided p value
(when you have predicted
what this difference will be)
How to report results of an independent samples t-test:
Male and female verbal reasoning was compared using an independent samples t-test. This
revealed that the mean verbal reasoning task score of females (M = 128.80, SD = 9.35) was
significantly (t (38) = 3.519, p = .001) higher than the mean for males (M = 115.80, SD =
13.62).
Exercises
You want to know whether people with a developmental disorder are impaired on an
emotion recognition task. You decide to compare the performance of those with autism to
typically developing individuals on this task using an independent samples t-test.
1. Go to this week’s section on Canvas and find ‘Exercise week 7’
2. Check whether the data for both groups is normally distributed
3. Perform an independent samples t-test comparing the mean emotion recognition
scores of people with autism to typically developing individuals
4. Is Levene’s test significant?
5. What do the results of Levene’s test mean?
6. Report the results of the independent samples t-test
7. Are these results of the independent samples t-test significant?
8. What do these results mean?
See “answers” document on this week’s canvas page for the answers.
Week 8 - Mann Whitney U Test
This handout will tell you:
1. What is the Mann Whitney U test and when should I use it?
2. How do I perform a Mann Whitney U test in SPSS?
a. Worked example: ‘Do women score higher on verbal reasoning than men?’
3. Exercises
What is the Mann Whitney U test and when should I use it?
The Mann Whitney U test is the non-parametric equivalent of the independent samples ttest.
The Mann Whitney U test compares the medians of two independent groups. For example:
the median heart rate of participants in one experimental condition (had sugar) to the
median heart rate of participants in the other experimental condition (did not have sugar).
Use this test if:
You want to draw inferences regarding group differences
Groups are independent of one another – participants only contribute to one data
sample
Your data is non-parametric
a. Violates the assumptions of parametric tests
i. Not normally distributed
ii. Does not have homogeneity of variance
b. Ordinal level data or above
How do I perform a Mann Whitney U test in SPSS?
Worked Example: Do women score higher on a verbal reasoning task than men?
1. You should open the example data in this week’s Canvas folder and work through
the following steps.
2. Check all of the relevant details are included in variable view.
3. Check data is in the correct format in data view. Remember that your groups should
be coded as 1s and 2s but you can alternate between seeing numerical data and
labels using the button below.
The box highlighted above is
checked so labels are displayed.
To switch back to numbers
simply click this button again
4. Click on Analyze > Non-Parametric Tests > Legacy Dialogs > 2 Independent Samples
5. Add verbal reasoning to the test variable list > add gender to the grouping variable
box > select Mann-Whitney U > click on define groups.
6. Define the groups you want to compare (e.g. 1 is the group number assigned to
females and 1 is the number assigned to males) > Click continue.
7. Finally, click OK.
Results
p < .05 means there is a
significant difference
between males and
females verbal reasoning
scores. Females had a
significantly higher mean
rank than males.
How to report results of a Mann Whitney U test:
The verbal reasoning ability of females and males was compared to data were analysed
using a Mann Whitney-U test. Results indicated that the median verbal reasoning score of
females was significantly higher than the median verbal reasoning score for males ( U =
91.000, Z = -2.954, p = .003).
Exercises
You want to know whether people with a developmental disorder are impaired on an
emotion recognition task. You decide to compare the performance of those with autism to
typically developing individuals on this task using a Mann Whitney-U test, as the data do not
meet the assumptions of parametric tests.
1. Go to this week’s section on Canvas and find ‘Exercise week 8’
2. Perform a Mann Whitney-U comparing the median emotion recognition scores of
people with autism to typically developing individuals
3. Report the results of the Mann Whitney-U test
4. Are these results of the Mann Whitney-U test significant?
5. What do these results mean?
See the “answers” document on this week’s canvas page for the answers.
Week 9 – Paired Samples t-test
This handout will tell you:
1. What is the paired samples t-test and when should I use it?
2. How do I perform a paired samples t-test in SPSS?
a. Worked example: ‘Does recall improve after attending “Hypnotic Memory
Training” with Paul McKenna?’
3. Exercises
What is the paired samples t-test and when should I use it?
The paired samples t-test uses the mean as a measure of central tendency. This parametric
test is used when one sample of participants is tested twice on the same measure/s (e.g. the
memory score of participants before and after memory training).
Use this test if:
You want to draw inferences regarding group differences
Groups are related – participants contribute to both data samples
Your data is parametric
a. Normally distributed
b. Interval or ratio level data
How do I perform a paired samples t-test in SPSS?
Worked Example: ‘Does recall improve after attending “Hypnotic Memory Training” with
Paul McKenna?’
1. You should open the example data file in this week’s Canvas folder and work through
the following steps.
2. Check all of the relevant information is included in variable view.
3. Check that data is arranged for a repeated measures analysis in data view. This
means that 1 row should equal 1 participants scores (1 column for before and 1 for
after).
Conditions should be
listed across the top.
Note the measure has
been changed to scale
1 row = 1 participants
scores. Each participant
has two scores
4. Click on Analyze > Compare Means > Paired-Samples T Test
5. Transfer before memory training to variable 1 > transfer after memory training to
variable 2 > click OK.
The correlation is sometimes useful in
helping to interpret the t-test result - the
higher the correlation, the more power
the t-test has.
p < .05 meaning that there does
appear to be a significant difference
between the two condition!
How to report results of a paired samples t-test:
Scores obtained before and after memory training were analysed using a paired samples ttest. This revealed that scores obtained after brain training (M = 7.60, SD = 1.43) were
significantly higher than those which were obtained before brain training (M = 6.80, SD =
1.28) (t (19) = -2.138, p = .046).
Exercises
You want to know whether people can achieve a significantly higher number of pull ups
after taking part in bootcamp sessions twice every week for four weeks. You decide to
perform a paired samples t-test comparing the number of pull ups attained before
undertaking the bootcamp training to the number of pull ups attained after four weeks of
training.
1. Go to this week’s section on Canvas and find ‘Exercise week 9’
2. Perform a paired samples t-test comparing the mean amount of pull ups before to
mean pull ups after the bootcamp.
3. Report the results of the t-test
4. Are these results of the t-test significant?
5. What do these results mean?
See “answers” document on this week’s canvas page for the answers.
Week 10 – Wilcoxon Signed Rank Test
This handout will tell you:
1. What is the Wilcoxon signed rank and when should I use it?
2. How do I perform a Wilcoxon signed rank in SPSS?
a. Worked example: ‘Does a drug lead to a significantly higher number of hours
of sleep compared to a placebo?’
3. Exercises
What is the Wilcoxon signed rank and when should I use it?
The Wilcoxon signed rank uses the median as a measure of central tendency. This nonparametric test is used when one sample of participants is tested twice on the same
measure/s (e.g. the memory score of participants before and after memory training).
Use this test if:
The same group of participants is tested twice;
You want to investigate group differences between the two times;
Your data does not meet the assumptions of parametric tests:
a. Not normally distributed
b. Ordinal level data or above.
How do I perform a Wilcoxon signed rank in SPSS?
Worked Example: ‘Does a drug lead to a significantly higher number of hours of sleep
compared to a placebo?’
1. You should open the example data in this week’s Canvas folder and work through
the following steps.
Question: Are these types of
2. Check that all relevant information is included in variable view.
measures assigned correctly?
3. Check that the data is arranged for a paired samples analysis in data view. This
means that 1 row should equal 1 participants scores (1 column for the number of
hours sleeping after being administered with the drug and 1 for the number of hours
sleeping after the placebo).
1 row = 1 participants
scores. Each participant
has two scores.
4. Click on Analyze > Non-Parametric Tests > Legacy Dialogs > 2 Related Samples
5. Transfer hours sleeping after the drug to the Variable 1 > Transfer hours sleeping
after the placebo to the Variable 2 box > Select Wilcoxon > click OK.
P < .001 meaning that there is a
significant difference between the
number of hours participants slept
after receiving a drug compared to
how long they slept after receiving
a placebo
How to report results of a Wilcoxon paired samples:
A Wilcoxon signed rank test was performed to investigate whether a drug would cause
participants to sleep for more time than when they received a placebo. Results indicated
that participants slept for significantly more hours after receiving the drug compared to
when they received a placebo (z = -3.648, p < .001)
Exercises
You want to know whether people are able to attain a significantly higher number of pull
ups after taking part in a bootcamp session every week for 4 weeks. You decide to perform
a Wilcoxon signed rank test comparing the number of pull ups attained before undertaking
bootcamp training to the number of pull ups attained after 4 weeks of bootcamp training, as
the data does not meet assumptions of parametric tests.
1. Go to this week’s section on Canvas and find ‘Exercise week 10’
2. Perform a Wilcoxon signed rank test comparing the mean pull ups attained before
bootcamp to the mean pull ups attained after bootcamp.
3. Report the results of the Wilcoxon signed rank test
4. Are these results of the Wilcoxon signed rank test significant?
5. What do these results mean?
See the “answers” document on this week’s canvas page for the answers.