Lecture 8 guidelines_and_assignments

Introduction to Applied Statistics and Applied Statistical Methods Practical guidelines
Prof.Dr. Chang Zhu page 1
Table of Contents
LECTURE 8 ...............................................................................................................................................2
I. PARAMETRIC TESTS..............................................................................................................................2
1. ONE-WAY ANOVA (INDEPENDENT).................................................................................................2
PLANNED CONTRASTS.....................................................................................................................2
POST HOC TESTS .............................................................................................................................3
SPSS OUTPUT ..................................................................................................................................4
EFFECT SIZE .....................................................................................................................................6
REPORT THE RESULT .......................................................................................................................6
2. ONE-WAY ANOVA (REPEATED MEASURE) ......................................................................................7
SPSS OUTPUT ..................................................................................................................................8
CONTRAST.......................................................................................................................................9
POST HOC TESTS .............................................................................................................................9
REPORT THE RESULTS ...................................................................................................................10
3. MANOVA (Multivariate analysis of variance) ...............................................................................11
SPSS OUTPUT ................................................................................................................................12
REPORT THE RESULT .....................................................................................................................13
II. NON-PARAMETRIC TESTS..................................................................................................................13
1. THE KRUSKAL WALLIS TEST...........................................................................................................13
SPSS OUTPUT ................................................................................................................................14
2. FRIEDMAN’S ANOVA.....................................................................................................................15
SPSS OUTPUT ................................................................................................................................15
POST HOC TESTS ...........................................................................................................................16
ASSIGNMENT 8......................................................................................................................................16

LECTURE 8
I. PARAMETRIC TESTS
1. ONE-WAY ANOVA (INDEPENDENT)
Imagine that I was interested in how different teaching methods affected students’ knowledge. I
noticed that some lecturers were aloof and arrogant in their teaching style and humiliated anyone
who asked them a question, while others were encouraging and supporting of questions and
comments. I took three statistics courses where I taught the same material. For one group of
students I wandered around with a large cane and beat anyone who asked daft questions or got
questions wrong (punish). In the second group I used my normal teaching style, which is to
encourage students to discuss things that they find difficult and to give anyone working hard a nice
sweet (reward). The final group I remained indifferent to and neither punished nor rewarded
students’ efforts (indifferent). As the dependent measure I took the students’ exam marks
(percentage). Based on theories of operant conditioning, we expect punishment to be a very
unsuccessful way of reinforcing learning, but we expect reward to be very successful. Therefore, one
prediction is that reward will produce the best learning. A second hypothesis is that punishment
should actually retard learning such that it is worse than an indifferent approach to learning. The
data are in the file teach.sav.
(The example is from Field (2009))
Carry out a one-way ANOVA and use planned comparisons to test the hypotheses that
 H1: reward results in better exam results than either punishment or indifferent; and
 H2: indifferent will lead to significantly better exam results than punishment.
In SPSS, Analyze > Compare Means > One-way ANOVAs
Move the variable exam into the dependent List and group to the Factor box.
PLANNED CONTRASTS
Click on Contrasts to access the Contrasts dialog box.
The function Polynominal helps us to detect the trend in the data. We have 3 groups, so it’s
suggested to check this function, then choose quadratic in the dropdown list from the Degree tab.
The contrast section is where we will specify our planned comparisons to answer the hypotheses. To
assign the weights for the comparison, we need to follow the following rules:

 Rule 1: We should be careful in pair selection as if we exclude any group in one comparison,
it will be excluded in subsequent comparison as well.
 Rule 2: Groups coded with positive weights will be compared against groups coded with
negative weights.
 Rule 3: The sum of weights for a comparison should be zero.
 Rule 4: If a group is not involved in a comparison, automatically assign it a weight of 0.
 Rule 5: For a given contrast, the weights assigned to the group(s) not included in the
contrast should be equal to the number of groups included in the pair comparison.
(Field. 2009, p. 365)
*In addition to these rule, it should be noticed that the order in which we put the weights should be
parallel with the values assigned to each group in the data.
For hypothesis 1, we want to compare the reward condition with the punishment and indifferent
groups. In order to gain the sum of the weights to zero, we will assign the following weights for the
groups:
 1: punish
 1: indifference
 -2: reward
So in SPSS, we will enter 1; 1; -2 because punish is given a value of 1, indifference 2, and reward 3.
For hypothesis 2, we do not include the reward group in the comparison, so we will assign 0 for this
group. The weights in the second contrast will be as follows:
 1: punish
 -1: indifference
 0: reward
Click Continue to proceed, and access the Options dialog box. Then select the options as indicated
below.
POST HOC TESTS
In case we do not have a priori hypothesis (no assumption as to which group differs from others), we
can access the Post Hoc option to ask SPSS perform all the possible pairwise comparisons.
Click on the Post Hoc button to access the dialog box. There are a lot of different kinds of post hoc
tests we can choose from. When group sizes are equal, Tukey and R-E-G-W-Q (Ryan-Elinot-Gabriel-
Welsch Range) tests are suggested.
When we already know which is the group in the study is the one that we’d like to compare with the
others, we choose the Dunnett’s test and set the appropriate control category under this option.
According to H1, reward (value 3) is compared against the others, so we will select Last for the
Control Category.
The suggested equivalent test when Equal Variances Not Assumed is Games-Howell. So we will also
select this option.

Click Continue to return to the main dialog box, and OK to run the analysis.
SPSS OUTPUT
The first important table we should look at is the Test of Homogeneity of Variances, which shows the
result of the Levene’s test. The significance value p = .095 > .05, so the assumption of homogeneity
of variances between the groups is met. For this reason, we will next examine the ANOVA table.
However, if the assumption is violated, we should report and look at the result from the Robust Tests
of Equality of Means.
Test of Homogeneity of Variances
Exam Mark
Levene Statistic df1 df2 Sig.
2.569 2 27 .095
We should read the result in the row labeled Between Groups (Combined). The F statistic, which is
the ratio between systematic variation (due to the teaching condition) and unsystematic variation
within the data is significant: F = 21.008, p < .001, i.e. there is a significant difference in exam marks
among different teaching conditions.
The Trend analysis can be found in the two rows labeled Linear and Quadratic Term. The result
shows that the means across groups increase in a linear fashion, but not curvilinear.
ANOVA
Exam Mark
Sum of Squares df Mean Square F Sig.
Between Groups (Combined) 1205.067 (SSM) 2 (dfM) 602.533 21.008 .000
Linear Term Contrast 1185.800 1 1185.800 41.344 .000
Deviation 19.267 1 19.267 .672 .420
Quadratic Term Contrast 19.267 1 19.267 .672 .420
Within Groups 774.400 27 28.681 (MSR)
Total 1979.467 (SST) 29
Planned Contrast Results
The Contrast Coefficients table indicates the weights that we have assigned for each group in the
first and second comparisons or contrast.
Contrast Coefficients
Contrast
Type of Teaching Method
Punish Indifferent Reward
1 1 1 -2
2 1 -1 0

For contrast 1 (comparing punishment with indifference and reward), t (27) = -5.978, p < .001
(significant).
For contrast 2 (comparing indifference and reward), the t value is also significant, so we can
conclude that there is a difference in the exam marks in these two teaching conditions.
Contrast Tests
Contrast Value of Contrast Std. Error t df Sig. (2-tailed)
Exam Mark Assume equal variances 1 -24.8000 4.14836 -5.978 27 .000
2 -6.0000 2.39506 -2.505 27 .019
Does not assume equal variances 1 -24.8000 3.76180 -6.593 21.696 .000
2 -6.0000 2.59915 -2.308 14.476 .036
Post Hoc Results
As the assumption of homogeneity of variances is met, we will look only at the Tukey HSD and the
Dunnett tests in the Multiple Comparisons table.
According to the results, each pair of the teaching conditions has resulted in a significant difference
in the exam marks.
Multiple Comparisons
Dependent Variable: Exam Mark
(I) Type of Teaching
Method
(J) Type of Teaching
Method
Mean
Difference (I-J)
Std.
Error Sig.
95% Confidence
Interval
Lower
Bound
Upper
Bound
Tukey HSD Punish Indifferent -6.00000
*
2.39506 .047 -11.9383 -.0617
Reward -15.40000
*
2.39506 .000 -21.3383 -9.4617
Indifferent Punish 6.00000
*
2.39506 .047 .0617 11.9383
Reward -9.40000
*
2.39506 .002 -15.3383 -3.4617
Reward Punish 15.40000
*
2.39506 .000 9.4617 21.3383
Indifferent 9.40000
*
2.39506 .002 3.4617 15.3383
Games-Howell Punish Indifferent -6.00000 2.59915 .086 -12.7772 .7772
Reward -15.40000
*
1.88680 .000 -20.2160 -10.5840
Indifferent Punish 6.00000 2.59915 .086 -.7772 12.7772
Reward -9.40000
*
2.62552 .007 -16.2287 -2.5713
Reward Punish 15.40000
*
1.88680 .000 10.5840 20.2160
Indifferent 9.40000
*
2.62552 .007 2.5713 16.2287
Dunnett t (2-
sided)
b
Punish Reward -15.40000
*
2.39506 .000 -20.9887 -9.8113
Indifferent Reward -9.40000
*
2.39506 .001 -14.9887 -3.8113
*. The mean difference is significant at the 0.05 level.
b. Dunnett t-tests treat one group as a control, and compare all other groups against it.
The Exam Mark table presents the results of the Tukey’s test and the REGWR tests, which show
which subsets of groups have similar means. As can be seen, we have no such subsets and this is in
accordance with the above-mentioned results.

Exam Mark
Type of Teaching Method N
Subset for alpha = 0.05
1 2 3
Tukey HSD
a
Punish 10 50.0000
Indifferent 10 56.0000
Reward 10 65.4000
Sig. 1.000 1.000 1.000
Ryan-Einot-Gabriel-Welsch Range Punish 10 50.0000
Indifferent 10 56.0000
Reward 10 65.4000
Sig. 1.000 1.000 1.000
Means for groups in homogeneous subsets are displayed.
a. Uses Harmonic Mean Sample Size = 10.000.
EFFECT SIZE
ANOVAs are usually used in experimental research, so it’s also helpful to report the effect size. We
have 2 ways to calculate (Field, 2009):
If we substitute the respective values found from the ANOVA table, we will obtain an r2
=
1205.067/1979.467 = 0.609. After taking the square root, r = .78. Doing the same for ω (omega), we
will get ω = .76
In addition to the overall effect size, we are also interested in the effect sizes in the contrast. The
contrasts are simply the t-tests, so the effect size is calculated as:
The values of t and df can be found in the Contrasts Test table. For contrast 1, with t = -5.978, df =
27, r = .75. For contrast 2, with t = -2.505, df = 27, r = .43.
REPORT THE RESULT
We just need to answer the two hypotheses, so we can write:
There was a significant effect of teaching conditions on exam marks, F (2, 27) = 21.01, p < .001, ω =
.76. Planned contrasts revealed that reward produced significantly better exam grades than
punishment and indifference, t (27) = -5.978, p < .01, r = .75 and that punishment produced
significantly lower exam marks than indifference, t (27) = -2.51, p < .05, r = .43.
 r (or η: eta) , ω (omega) : effect size
 SSM: between-group effect
 SST: total amount of variance in the data
 MSR: within-subject effect
 dfM: degree of freedom, which is the number of the groups minus 1

2. ONE-WAY ANOVA (REPEATED MEASURE)
A group of students investigated the consistency of marking by submitting the same essays to four
different lecturers. The mark given by each lecturer was recorded for each of the eight essays. It was
important that the same essays were used for all lecturers because this eliminated any individual
differences in the standard of work that each lecturer marked. This design is repeated-measures
because every lecturer marked every essay. The independent variable was the lecturer who marked
the esays and the dependent variable was the percentage mark given.
The data file is TutorMarks.sav
In SPSS, Analyze > General Linear Model > Repeated Measures
In the Within-Subject Factor Name, the given name is factor1. We will type the new name which
matches our data, e.g. tutors. As we have 4 tutors, we will indicate 4 in the Number of Levels box.
Click on Add to confirm.
Then click Define to continue.
In the main dialog box, move the four variables to the Within-Subjects Variables
Click on the Contrasts button to access the dialog box. As there is no meaningful difference in the
order of the tutors, we will choose Repeated, which will conduct pairwise comparison between 2
adjacent tutors (e.g. 1 vs. 2, 2 vs. 3).
Click Change to confirm, and Continue to proceed. Then access the Options dialog box.
Move the repeated measures variable tutors to the Display Means for area and select Compare
mean effects.

Under the Confidence interval adjustment, select Bonferroni, which is the most suggested correction
method (Field, 2009).
Under the Display, select Descriptive Statistics and Transformation matrix.
Click Continue to return to the main dialog box, and OK to run the analysis.
SPSS OUTPUT
The Mauchly’s Test of Sphericity is significant (p < .05) so there are differences in variances across
levels of the tutor variable. In other words, the assumption of sphericity has been violated.
Mauchly's Test of Sphericity
a
Measure: MEASURE_1
Within Subjects Effect Mauchly's W Approx. Chi-Square df Sig.
Epsilon
b
Greenhouse-Geisser Huynh-Feldt Lower-bound
tutor .131 11.628 5 .043 .558 .712 .333
To know if there is a difference in the marking among the tutors, we should look at the Tests of
Within-Subjects Effects table. The F = 3.7, p = .028 < .05 means that there is a significant difference.
Tests of Within-Subjects Effects
Measure: MEASURE_1
Source
Type III Sum of
Squares df Mean Square F Sig.
tutor Sphericity Assumed 554.125 (SSM) 3 184.708 (MSM) 3.700 .028
Greenhouse-Geisser 554.125 1.673 331.245 3.700 .063
Huynh-Feldt 554.125 2.137 259.329 3.700 .047
Lower-bound 554.125 1.000 554.125 3.700 .096
Error(tutor) Sphericity Assumed 1048.375 (SSR) 21 49.923 (MSR)
Greenhouse-Geisser 1048.375 11.710 89.528
Huynh-Feldt 1048.375 14.957 70.091
Lower-bound 1048.375 7.000 149.768

However, as the assumption of sphericity is violated, we should look at the corrected F values. Of the
three, Greenhouse-Geisser applies stricter criteria (likely to make Type II error), and we can see that
the p is non-significant. Huynh-Feldt corrected F-statistic gives us a significant value, p = .047. As
Steven (2002) suggests, to be neutral, we can take the average of Greenhouse-Geisser and Huynh-
Feldt’s estimates. This will give us a p value of (.063 + .047)/2 = .055, which is still non-significant.
Before making decision, we should also consult the Multivariate Tests table (MANOVA). As this test
makes no assumption about sphericity, it serves as a good reference. Again, we find a non-significant
difference. Hence, the conclusion is that there is no difference among tutors regarding essay
marking.
Multivariate Tests
a
Effect Value F Hypothesis df Error df Sig.
tutor Pillai's Trace .741 4.760
b
3.000 5.000 .063
Wilks' Lambda .259 4.760
b
3.000 5.000 .063
Hotelling's Trace 2.856 4.760
b
3.000 5.000 .063
Roy's Largest Root 2.856 4.760
b
3.000 5.000 .063
In the following part, we will look closely into which tutor marks differently from others. As we
choose both Contrast and Post hoc test, we will look at them in turn.
CONTRAST
As we chose the Repeated contrast, SPSS will compare two tutors who are next to each other in
terms of the values assigned in the data, e.g. the tutor with value 1 (Dr. Field) is compared against
the tutor with value 2 (Dr. Smith).
tutor
a
Measure: MEASURE_1
Dependent Variable
tutor
Level 1 vs. Level 2 Level 2 vs. Level 3 Level 3 vs. Level 4
Dr. Field (1) 1 0 0
Dr. Smith (2) -1 1 0
Dr. Scrote (3) 0 -1 1
Dr. Death (4) 0 0 -1
According to the Tests of Within-Subjects Contrasts, Dr. Field and Dr. Smith significantly differ in
their marking.
Tests of Within-Subjects Contrasts
Measure: MEASURE_1
Source tutor Type III Sum of Squares df Mean Square F Sig. Partial Eta Squared
tutor Level 1 vs. Level 2
(Dr. Field and Dr. Smith)
171.125 1 171.125 18.184 .004 .722
Level 2 vs. Level 3 8.000 1 8.000 .152 .708 .021
Level 3 vs. Level 4 496.125 1 496.125 3.436 .106 .329
Error(tutor) Level 1 vs. Level 2 65.875 7 9.411
Level 2 vs. Level 3 368.000 7 52.571
Level 3 vs. Level 4 1010.875 7 144.411
POST HOC TESTS
When we have no priori hypothesis as to which tutor differs from the others, we go for post hoc
analysis.

The Transformation Coefficients table tells us how the comparison is organized: one tutor’s marking
will be compared with the other three tutors.
Transformation Coefficients (M Matrix)
Measure: MEASURE_1
Dependent Variable
tutor
1 2 3 4
Dr. Field 1 0 0 0
Dr. Smith 0 1 0 0
Dr. Scrote 0 0 1 0
Dr. Death 0 0 0 1
Looking at the Pairwise Comparisons table, there is only significant marking between tutor 1 and
tutor 2.
Pairwise Comparisons
Measure: MEASURE_1
(I) tutor (J) tutor Mean Difference (I-J) Std. Error Sig.
b
95% Confidence Interval for Difference
b
Lower Bound Upper Bound
1 (Dr. Filed) 2 (Dr. Smith) 4.625
*
1.085 .022 .682 8.568
3 (Dr. Scrote) 3.625 2.841 1.000 -6.703 13.953
4 (Dr. Death) 11.500 4.675 .261 -5.498 28.498
2 1 -4.625
*
1.085 .022 -8.568 -.682
3 -1.000 2.563 1.000 -10.320 8.320
4 6.875 4.377 .961 -9.039 22.789
3 1 -3.625 2.841 1.000 -13.953 6.703
2 1.000 2.563 1.000 -8.320 10.320
4 7.875 4.249 .637 -7.572 23.322
4 1 -11.500 4.675 .261 -28.498 5.498
2 -6.875 4.377 .961 -22.789 9.039
3 -7.875 4.249 .637 -23.322 7.572
Based on estimated marginal means
*. The mean difference is significant at the .05 level.
b. Adjustment for multiple comparisons: Bonferroni.
REPORT THE RESULTS
We can write:
Mauchly’s test indicated that the assumption of sphericity had been violated, χ² (5) = 11.63, p < .05,
therefore degrees of freedom were corrected using Greenhouse-Geisser estimates of sphericity (ε
= .556). The results show that there was no significant difference in essay marking among the tutors,
F (1.67, 11.71) = 3.7, p > .05
As the main ANOVA is non-significant, hence the results of contrast or post hoc tests are just for
reference. However, in case the main ANOVA is significant, we should also report the effect size as
the between-subject ANOVAs and the results of contrast or post hoc analysis.
The effect size for repeated measure ANOVAs is calculated differently from the between subject
ANOVAs. For more detail about the equations, you can refer pages 480-481 in the book Discovering
Statistics Using SPSS by Field (2009).

3. MANOVA (Multivariate analysis of variance)
A lecturer is interested to find out if students’ knowledge of different aspects of psychology
improved throughout their degree.
He administered 5 tests (scored out of 15) including:
 Exper (experimental psychology such as cognitive and neuropsychology etc.)
 Stats (statistics);
 Social (social psychology);
 Develop (developmental psychology);
 Person (personality).
on three cohorts of students: first, second, and third year.
Carry out the MANOVA to determine whether there are overall group differences along these five
measures.
The data file is psychology.sav.
In SPSS, Analyze > General Linear Model > Multivariate
Move the five variables (exper, stats, social, develop, and person) to the Dependent Variables area,
and group into the Fixed Factors (s) area.
Click on the Post Hoc option to access the dialog box. As we do not know if equal variances assumed
or not and the group sizes are not equal, we will choose the Hochberg’s GT2, Gabriel and the
Games–Howell.
Click Continue to proceed, then access the Option dialog box.
Move the group variable into the Display Means for to obtain means for the levels of group.
Under Display, select Descriptive Statistics, Estimates of effect size, and Homogeneity tests.
Click Continue to proceed, then click OK to run the analysis.

SPSS OUTPUT
The Box’s test of the assumption of equality of covariance matrices is non-significant indicating that
the covariance matrices are equal across groups
Also, the Levene’s Test of equality of variances for each of the dependent variables is non-significant,
therefore, the assumption of homogeneity of variance is met.
Box's Test of Equality of
Covariance Matrices
a
Box's M 54.241
F 1.435
df1 30
df2 3587.253
Sig. .059
The important table we should look at is Multivariate Tests. All of the 4 tests are significant, so at
this step, we can conclude that there is a significant difference across different cohorts in terms of
the five knowledge tests.
Multivariate Tests
a
Effect Value F Hypothesis df Error df Sig. Partial Eta Squared
Intercept Pillai's Trace .960 159.166
b
5.000 33.000 .000 .960
Wilks' Lambda .040 159.166
b
5.000 33.000 .000 .960
Hotelling's Trace 24.116 159.166
b
5.000 33.000 .000 .960
Roy's Largest Root 24.116 159.166
b
5.000 33.000 .000 .960
Group Pillai's Trace (V) .510 2.330 10.000 68.000 .020 .255
Wilks' Lambda (Λ) .522 2.534
b
10.000 66.000 .012 .277
Hotelling's Trace (T) .853 2.730 10.000 64.000 .007 .299
Roy's Largest Root (λ) .773 5.255
c
5.000 34.000 .001 .436
a. Design: Intercept + group
b. Exact statistic
c. The statistic is an upper bound on F that yields a lower bound on the significance level.
Levene's Test of Equality of Error Variances
a
F df1 df2 Sig.
Experimental Psychology 1.311 2 37 .282
Statistics .746 2 37 .481
Social Psychology 2.852 2 37 .071
Developmental 2.751 2 37 .077
Personality 2.440 2 37 .101
Tests the null hypothesis that the error variance of the dependent
variable is equal across groups.
a. Design: Intercept + group

The Tests of Between-Subjects Effects table presents the ANOVA tests for each of the 5 dependent
variable. As can be seen, all of these separate tests are non-significant. This highlights the advantage
of using MANOVA when we have many dependent variables, because MANOVA can reduce the error
rate in case many ANOVAs are carried out.
Tests of Between-Subjects Effects (ANOVAs)
Source Dependent Variable Type III Sum of Squares df Mean Square F Sig. Partial Eta Squared
group Experimental Psychology 18.430 2 9.215 2.461 .099 .117
Statistics 52.504 2 26.252 2.967 .064 .138
Social Psychology 23.584 2 11.792 1.941 .158 .095
Developmental 37.717 2 18.859 3.114 .056 .144
Personality 39.415 2 19.708 3.044 .060 .141
As the ANOVAs are non-significant, so we do not proceed with post hoc tests.
REPORT THE RESULT
We can choose one of the four tests to report the result of MANOVA:
Using Wilk’s Lamda, there was a significant difference in the scores on the five knowledge tests
among the first, second, and third year students, Λ = .52, F (10, 66) = 2.53, p < .05.
In case one of the ANOVAs is significant, we should also need to report the significant post hoc
tests.
II. NON-PARAMETRIC TESTS
1. THE KRUSKAL WALLIS TEST
Does physical exercise alleviate depression? We find some depressed people and check that they are
all equivalently depressed to begin with. Then we allocate each person randomly to one of three
groups:
 no exercise
 20 minutes of jogging perday
 or 60 minutes of jogging per day
At the end of a month, we ask the participant to complete a test that measures the degree of
depression (scores from 0 to 100).
(This example is adapted from http://www.sussex.ac.uk/Users/grahamh/RM1web/Kruskal-Wallis%20Handoout2011.pdf)
As the data are not normally distributed, we will choose the non-parametric test, i.e. Kruskal Wallis.
In SPSS, Analyze > Nonparametric Tests > Independent Samples
Click on Fields to access the Fields dialog box. Move the depression (score) to the Test Fields, and
group to the Groups area.
Click Run to conduct the analysis.

SPSS OUTPUT
The following tells us that the test is significant and we will reject the null hypothesis.
Hypothesis Test Summary
Null Hypothesis Test Sig. Decision
1
The distribution of score is the same
across categories of group.
Independent-Samples
Kruskal-Wallis Test
.026
Reject the null
hypothesis.
Asymptotic significances are displayed. The significance level is .05.
At the bottom of the screen, if we click on the View option and select Pairwise Comparisons, we can
identify which group has different level of depression than the other. The significance value should
be read from the Adj.Sig. column (Adjusted significance). As can be seen, none of these are smaller
than .05, but as the comparison between group 1 (no exercise) and group 3 (jogging for 60 minutes)

REPORT THE RESULT
We can write:
The Kruskal-Wallis test revealed there was a significant effect of exercise on depression levels, H (2)
= 7.29, p < .05). Subsequent pairwise comparisons indicated that there was a significant difference in
the scores of depression between group 1 (no-exercise) and group 3 (60-minute jogging), though the
p value is marginal p = .051.
2. FRIEDMAN’S ANOVA
A researcher was interested in whether the growing café society in the UK has led to a change in
preference for non-alcoholic beverages. She therefore asks a number of students to give their
ratings (on a scale of 1 to 5) for their enjoyment of coffee, tea and hot chocolate. A rating of 5
signifies a greater enjoyment of the drink.
The data file is drinks_rating.sav
In SPSS, Analyze > Nonparametric Tests > Legacy Dialogs > K Related Samples
Move all the three variables into the Test Variables area. Under the Test Type, select Friedman.
Click on the Exact option to access the Exact Tests dialog box. As our sample is small, it’s suggested
to select the Exact option.
Click Continue to return to the main dialog box, then click OK to run the analysis.
SPSS OUTPUT
The Friedman test is based on the ranks. The Ranks table shows the mean ranks for each type of
drinks rated by the students.
The result of the test is found in the Test Statistics table, which in this case is significant.
Ranks
Mean Rank
Tea 2.40
Coffee 1.65
HotChocolate 1.95
Test Statistics
a
N 20
Chi-Square 7.475
df 2
Asymp. Sig. .024
Exact Sig. .022
Point Probability .001
a. Friedman Test

REPORT THE RESULT
We can write:
The Friedman test revealed that the students varied significantly in their preference of the three
types on non-alcoholic beverages, χ²(2) = 7.48, p < .05.
POST HOC TESTS
Similar to ANOVAs, we can conduct post hoc tests to find out which groups are different by using the
Mann-Whitney and Wilcoxon signed-rank tests after the Kruskal and Friedman tests, respectively.
On word of notice is that we should re-set the critical value of significance. For example, if we do 3
comparison, the significance value should be .05/3 = .0167 for a test to be significant (Field, 2009).
ASSIGNMENT 8
(You can work alone or in group for this assignment. If you work in group, please stay in the same
group of previous assignments and indicate the group members in the submission document).
You can choose one of the following options:
Option 1
A psychologist who is interested in aggression has devised an experimental paradigm in which
participants play a computer game with an opponent. When the opponent makes an error the
participant is invited to punish their opponent by exposing him to a blast of loud noise. The duration
and volume of the noise blast are combined to give a measure of aggression. A total of 60
participants were tested using this procedure before being given feedback about their performance
in the game. One third of the participants received negative feedback, one third received positive
feedback and the remaining third received neutral feedback. Finally, the participants played the
game again and their level of aggression was measured as before. The data from this study can be
found in the file aggression.sav.
1. Conduct an ANOVA to determine whether there is a difference between levels of aggression
among the participants measured before and after the feedback session.
2. Participants were randomly assigned to each of the three feedback conditions, and as a result the
pre-test scores for these three groups should not differ. Test whether this is confirmed.
Option 2
Search for a research article that use one of the kinds of analysis of variances
(independent/repeated ANOVA; MANOVA, Kruskal-Wallis, and Friedman ANOVA)
Briefly summarized the following:
- The variables measured in the study
- The groups that the analysis were conducted for.
- The study hypotheses
- The tests that were used to test the hypotheses
- The study’s conclusion (What has been found?)

Lecture 8 guidelines_and_assignments

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Lecture 8 guidelines_and_assignments