Overview of most used statistical test using SPSS. Used for Teaching course "Experimental Praktikum" University of Fribourg, Department of Psychology.

1. Analysing your data
Eva A.M. van Poppel, MSc
..with statistics
using SPSS

2. Overview
•Experimental design
•Checking assumptions
•Most used statistical tests overview
(t-test & ANOVA)
•Which test should I choose?
•Break
2

3. Overview
•Post Hoc tests
•Contrasts
•Interaction effects
•Performing the RM or Mixed ANOVA in
SPSS
•Interpreting SPSS Output
•How to make figures
•Overview writing a report
3

4. Experimental design
• Between subjects design: Different participants in
each group, e.g. males & females.
• Within subjects design: Same participants in each
group, meaning the same participants perform the
conditions in each of the groups. Also called
“Repeated Measures” design.
4

5. Checking assumptions
You are making assumptions (Annahmen) when you
are performing a statistical test. For a parametric
test your data needs to be:
• Normally distributed
• Homogeneity of variance
• Measured on interval niveau (data is continuous
and equal intervals on the scale represent equal
differences in the measurement) (Scale)
• Independent measurements (no influencements)
5

6. Normal distribution
• Shapiro-Wilk / Kolmogorov-Smirnov tests the
“Nullhypothese” that:
the variabele is normally distributed.
The moment the test is significant…
…your data is significantly not normally distributed.
• Test the normality of the score of each group (e.g. score
females & score males; multiple normality tests).
• If your analysis involves comparing groups, what’s
important is not the overall distribution but the
distribution in each group.
6

7. Normal distribution
• In a big sample size (N>30 per group), use Kolmogorov-
Smirnov. Because Shapiro-Wilk will get significant easy
with little deviations.
• In a small sample size, use Shapiro-Wilk.
In SPSS:
Analyze  Descriptive statistics  Explore
Variable = Dependent
Plots: Histogram & Normality plots with tests
7

8. Homogeneity of variance
• What is variance?
Variance is a measurement for dispersion
(verbreitung) i.e. how much values differ mutually.
The bigger the variance, the more values differ from
each other and from the mean.
4 – 5 – 6 Mean: 5 Variance: Small
1 - - - 4 - - - - - 10 Mean: 5 Variance: Big
• The sample variance S² is an estimation of the
population variance. The square root out of
sample variance is called standard deviation (SD),
auf Deutsch: “Standardabweichung”.
8

9. Homogeneity of variance
Levene’s tests the “Nullhypothese” that:
the variance (verbreitung) between groups is equal.
When Levene’s test is significant…
… the variances are significantly not equal.
In SPSS: Analyze  Descriptive statistics  Explore
Variable = Dependent value
Factor list: Predictor / Group
Plots: Spread vs level with Levene Test:
Untransformed
9

10. What if…
My data is not normally distributed and/or
the variances between groups are not
equal?
 Deal with
outliers
 Data
transformation
 N>30 per group,
parametric tests
are quite robust

11. Source:
Discovering
Statistics Using
SPSS, Andy Field,
3rd edition,
2009, SAGE
Publications Ltd.

12. Which test should I choose?
12
Source: Discovering Statistics Using SPSS, Andy Field, 3rd edition, 2009, SAGE Publications Ltd.

13. The t-test
• The t-test tests whether there is a difference
between the means of two groups
• The independent t-test test whether there is a
difference between two different groups of
participants (between subjects).
Asumptions: your data is normally distributed and
the variances between groups is equal.
• In SPSS: Analyze  Compare Means 
Independent samples t-test
13

14. The paired t-test
• The dependent t-test, also called paired t-test,
tests whether there is a difference between the
means of two groups with the same participants
(within subjects, repeated measures design).
• Assumption: your data is normally distributed.
You don’t need to check for homogeneity of
variance, since it’s the same group of people.
• In SPSS: Analyze  Compare Means  Paired
samples t-test
14

15. ANOVA
• What does ANOVA stand for?
ANalysis Of VAriance
Tests whether means of three or more groups differ
from each other.
15

16. One-Way Independent ANOVA
• Between subjects, different participants in each group.
• Asumptions: your data is normally distributed and the
variances between groups is equal.
• In SPSS: Analyze  Compare Means  One-Way ANOVA
Options: Descriptive, homogeneity of variance test &
means plot.
16

17. One-Way Repeated Measures
ANOVA
• Within subjects design, meaning the same participants
perform the conditions in each of the groups.
• Asumptions: your data is normally distributed and the
variances between groups is equal. However, since we have
the same participants in each group, this variance is now
called “Sphericity” (denoted by ε).
17

18. Factorial Mixed ANOVA
• When you have both a within and between subjects design,
this is called a Factorial Mixed ANOVA.
• For example, you want to test whether there is an blocked /
unblocked effect between subjects (different participants in
each group) AND you want to test whether there is an effect
on old/new/lure words within subjects (same participants in
each group).
• Then you perform an Factorial Mixed ANOVA.
• In SPSS: Add the group as a between-subjects factor
(Nominal) in the Repeated-Measures ANOVA.
Analyze  General Linear Model  Repeated Measures.
Number of levels = number of groups. Each group should be
it’s own variable. Click define. Between factor = groups.
18

19. Which test should I choose?
19

20. Which test should I choose?
20
• I want to test whether females get a higher grade than
males on the Expra exam.
• Outcome variable?
• 1, continous: grade (test score)
• Predictor variable?
• 1: Sex.
• Type & amount of predictor?
• 2 Categories: Male & Female.
• Same or different participants in each category?
• Different.
• Which test? Independent t-test.

21. Which test should I choose?
21
• I want to test whether new words are correctly recognized
as new more often compared to learned words.
• Outcome variable?
• 1, continous: amount pressed new (test score)
• Predictor variable?
• 1: Learning category
• Type & amount of predictor?
• 2 Categories: Learned & New.
• Same or different participants in each category?
• Same.
• Which test? Paired t-test.

22. Which test should I choose?
22
• I want to test whether students in the psychology
department sleep more than students in the medicin and
law department.
• Outcome variable?
• 1, continous: amount of sleep (in minutes)
• Predictor variable?
• 1: Department
• Type & amount of predictor?
• 3 Categories: Psychology, Medicin & Law.
• Same or different participants in each category?
• Different.
• Which test? One-way independent ANOVA.

23. Which test should I choose?
23
• I want to test whether lure words are more often recognized
as old compared to learned words and new words.
• Outcome variable?
• 1, continous: amount pressed old (test score)
• Predictor variable?
• 1: Learning category
• Type & amount of predictor?
• 3 Categories: Old, New & Lure.
• Same or different participants in each category?
• Same.
• Which test? One-Way Repeated Measures ANOVA.

24. Which test should I choose?
24
• I want to test whether lure words are more often recognized
as old compared to learned words and new words in the
blocked design.
• Outcome variable?
• 1, continous: amount pressed old (test score)
• Predictor variable?
• 2: Categorical, Learning category + Blocked group
• Type & amount of predictor?
• Within: 3 Categories: Old, New & Lure.
• Between: 2: Blocked and unblocked
• Same or different participants in each category?
• Both
• Which test? Factorial Mixed ANOVA.

25. Break
Sources: Discovering Statistics Using
SPSS, Andy Field, 3rd edition, 2009,
SAGE Publications Ltd.
Discovering Statistics Using R,
Andy Field, 1st edition, 2012, SAGE
Publications Ltd.

26. Analysing your data
Eva A.M. van Poppel, MSc
..with statistics
Part 2

27. Overview
•Post Hoc tests
•Contrasts
•Interaction effects
•Performing the RM or Mixed ANOVA in
SPSS
•Interpreting SPSS Output
•How to make figures
•Overview writing a report
27

28. Statistical errors
28effectsizefaq.com
A type 1
error is
also called
«Alpha-
Fehler».
A type 2
error is
also called
«Beta-
Fehler».

29. Post Hoc tests
• When can you perform a post hoc test and why
would you want to do one?
• When your ANOVA is significant, you can perform
a post hoc test (afterwards) to see between which
groups there is a significant difference.
• This post hoc test will perform multiple
comparisons (mc) (t-tests) between all
combinations of groups (with 3 groups, these are
1-2, 2-3 & 1-3).
29

30. Fisher’s LSD
• Fisher's least significant difference (LSD) computes
multiple t-tests between groups, using the pooled
standard deviation from all groups. This increases
statistical power.
• You only perform this test when the main effect is
significant. Otherwise, you could get significant
results in the post hoc without having an overall
effect.
• Fisher's LSD does not correct for multiple
comparisons (mc)!
30

31. The dead salmon effect
• In 2009, Bennett et al. placed a dead salmon in an
fMRI scanner and reported brain activity in the
hippocampus. What happened?
• Performing 100 t-tests without correction, using
the <0.05 significance threshold, 5 tests are
expected to falsely reported as significant. This is
called a type 1 error or «Alpha-Fehler» (False
Positive).
• To avoid this, you should correct for multiple
comparisons. There are loads of post hoc tests to
correct for those multiple comparisons.
31

32. Bonferroni
• Bonferroni is the most strict correction. It will lower
the significance level by deviding with the amount of
tests performed, for example α=0.05/3=0.017.
• This makes sure there is no false positive (type 1 error
/ α-Fehler) possible, thus you can say that a significant
difference found with Bonferroni is truely there.
• However, with Bonferroni there is a chance of a false
negative (type 2 error / β-Fehler): failing to find a
significant difference between groups when in fact
there is one.
32

33. Post Hoc in a One-Way
Independent ANOVA
• Click Post Hoc and then LSD, Bonferroni & Tukey.
• Bonferroni is the most strict correction. You can say
that a significant difference found with Bonferroni is
truely there.
• Fisher’s LSD is not correcting for multiple comparisons.
• To use a test correcting for both type 1 & 2 errors, you
can use the Tukey correction.
In this course we only use the Bonferroni correction.
• This Bonferroni correction is also the post hoc test for
Mixed & Factorial ANOVA’s
33

34. Contrasts
• Compares groups, using the variance and degrees of
freedom of all your data
• Therefore, the statistical power is higher than using a t-
test
• It is also more flexible,
you can compare more than
2 groups with each other
• Disadvantage: you can only perform contrasts in a One-
Way Repeated Measures ANOVA
34
0
0.5
1
1.5
2
2.5
3
3.5
0 1 2 3
Coffee

35. Contrasts
• Polynomial (default): Tests polynomial patterns in
data with more than two means.
• Simple contrast: Compares each experimental
group with the control. Default: control is the last
group. Change by clicking «First».
• Repeated: Levels of UV have a meaningful order, for
example from low to high.
• Contrasts are not Post Hoc and you can’t do a mc
correction to them. Contrast performs an F-test
between groups to compare the variation.
35

36. Interaction effects
• Only with ≥ 2 UV’s.
• Distance between task 1 & 2 in control condition is
significantly smaller than in the treatment
condition
36

37. Interaction effects
• Significant difference in distance between
expected main effect and real effect.
37
Main effect

38. Interaction effects
38

39. Performing the One-Way Repeated
Measures or Mixed ANOVA in SPSS
• In SPSS: Analyze  General Linear Model  Repeated
Measures. Number of levels = number of groups. Each
group should be it’s own variable. Click define. Put each
scale variable in the Within-Subjects variables (Alt – Kritisch
– Neu).
• To make this a Factorial Mixed ANOVA, add the grouping
variable (Nominal) in the Between-Subjects factor box.
• Options: display means for factor1, compare main effects,
adjustment Bonferroni, descriptive statistics, transformation
matrix
• Auf Deutsch: Analysieren  Allgemeines lineares Modell 
Messwiederholung. Anzahl der Stufen = Anzahl Gruppen /
Konditionen. RM: Innersubjektvariabeln (Within).
Mixed: Zwischensubjektfaktoren (Between) hinzufugen. 39

40. Interpreting SPSS Output
What is Mauchly doing in my output?
• Mauchly tests the sphericity. When Mauchly’s test is
significant, the variances of the differences between levels
are significantly unequal. Now, we need a correction to still
use the ANOVA.
• When the Greenhouse-Geisser estimate Epsilon (ε) > 0.75,
report the ANOVA values with Huyn-Feldt correction.
• Otherwise, use the ANOVA values with the Greenhouse-
Geisser correction.
• The Pairwise Comparisons table is your post hoc output.
40

41. Interpreting SPSS Output
41

42. Interpreting SPSS Output
Report as: F(dfM, dfR) = F, p; F(2, 22) = 77.16, p<0.00142

43. Interpreting SPSS Output
Report as: F(dfM, dfR) = F, p; ε(.73), F(1.46,16.06) = 77.16, p<0.00143

44. Interpreting SPSS Output
The polynomial contrast test whether there is
a linear or a quadratisch pattern in your data.
44

45. Interpreting SPSS Output
This is the output of your posthoc test.
These are t-tests between all possible
combinations of groups, corrected for
multiple comparisons with Bonferroni
correction (b).
45

46. Standard Error of the Mean (SEM)
• Standard Error of the Mean (SEM)
«Standardfehler» displays the standard
deviation (SD) of the sample mean.
• You use this to display error bars
«Fehlerbalken» in your plots.
• It is calculated as:
• Standard deviation sample / 𝑁
• In Excel: =Stdev.s(values) /
sqrt(count(values))
• Deutsch: =STABW.S(Datenzellen) /
WURZEL(ANZAHL(Datenzellen))
46

47. How to make figures
In SPSS:
• Your data (old/new/lure) should each be a seperate
variable (column) which is set to scale «metrisch»
• The blocked / unblocked group should be one
variable saying for each values to which group it
belongs. You should set this to «Nominal
messniveau».
• Go to Grafik  Diagrammerstellung  Gruppierte
balken  X-achse blocked group  Y-achse select
3 old/new/lure variables with shift
• Fehlerbalken anzeigen, Statistik: Mittelwert,
Standardfehler Multiplikator 1.
47

48. How to make figures
In Excel: make custom error bars.
Calculate SEM as standardeviavtion.sample /
𝑁
=Stdev.s / sqrt(count(values))
48

49. Overview writing a report
• Abstract
• Introduction
• Methods
• Results
• Discussion
49

50. Overview writing a report
• Abstract is a mini report. It has the most
important information on the introduction,
methods, results and discussion.
• You normally write this the last.
• It is the most important part, while most
persons only read the abstract.
50

51. Overview writing a report
• Introduction starts with giving an overview
on the literature, theoretical background.
What do we already know?
• State research question (RQ).
• Hypothesis, what do you expect the answer
on RQ is and why? Support with literature.
• Expectations: which direction do you think
the data results will be and why? (support
with literature).
• Very short (~3 sentences) how you are
going to test your RQ. This is a little bridge
to the methods.
51

52. Overview writing a report
• Methods has little subsections
• Subjects, amount m/f, mean age ± SD, for
the total and in between subjects also for
each group
• Procedure: Short overview of the
experiment
• Task: Detailed explanation of the learning
and recall task
• Statistics: How did you perform statistics,
what was AV/UV, which test did you use,
which significance level did you use
52

53. Overview writing a report
• Results
• All your results in graphs / tables
• Also in text! Without looking at the figures,
I should know your results.
53

54. Overview writing a report
• Discussion
• Interpret the results
• What does this mean for your RQ and
hypothesis?
• What does this mean to the literature? Use
sources!
• Conclusion
• Future Research proposal
• Last sentence should be strong summary,
make your point (take home message for
the reader)
• References: APA Style 54

55. Sources
Bennett, C. M., Miller, M. B., & Wolford, G. L. (2009). Neural
correlates of interspecies perspective taking in the post-mortem
Atlantic Salmon: An argument for multiple comparisons
correction. Neuroimage, 47, S125.
Discovering Statistics Using R, Andy Field, 1st edition, 2012,
SAGE Publications Ltd.
Discovering Statistics Using SPSS, Andy Field, 3rd edition, 2009,
SAGE Publications Ltd.
effectsizefaq.com, retrieved on 30.10.2017