N318b Winter 2002
Nursing Statistics
Lecture 9
Specific statistical tests:
Tests for means when there
are more than 2 groups
ANOVA
Today’s Class
 Discussion of mid-term exam
 Review of how to read a journal article
 Example of basic ANOVA
<< 10 min break >>
 Applying knowledge to assigned reading
 Arathuzik (1994)
Followed by small groups 12-2 PM
Focus on interpreting ANOVA results
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 9: page 2
Class Website
http://instruct.uwo.ca/nursing/318b
E-mail address: mkerr@uwo.ca
Lectures now online and can be printed
using web browser (e.g. MS Explorer)
Use the “Handout” and “pure black and
white” options for printing, at 3 per page as
this will allow you to put notes on them.
Exam questions and answers to be put online
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 9: page 3
“In Group” Session
Focuses on 1 assigned reading.
Q1. Chance to interpret ANOVA findings
Q2. Know when to use t-test or ANOVA
Key points about ANOVA relating to workshop
will be covered in the 2nd part of the lecture
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 9: page 4
Mid-term exam results
To be completed as time permits
4 parts (50 marks):
Section A: mean = ?/6
Section B: mean = ?/14
Section C: mean = ?/15
Section D: mean = ?/15
Class average = ?/50 = ??%
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 9: page 5
Statistical Tests – Review
How do you known when to use which test?
Helps to ask some basic questions:
1. What kind of data are used?
- ratio/interval or categorical (ordinal/nominal)
- dependent (e.g. follow-up) or independent
2. What kind of relationship is of interest?
- prediction, association or difference?
3. How many groups (samples) involved?
- one, two, or more than two
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 9: page 6
Analysis of Variance - ANOVA
How do you known when to use ANOVA?
Referring back to the 3 “basic questions”:
1. What kind of data are used?
- numeric/continuous (ratio/interval)
- independent OR dependent samples
2. What kind of relationship is of interest?
- differences between means (>2 means)
3. How many groups (samples) involved?
- more than two groups (although can be two
pre-post samples from multiple time points)
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 9: page 7
ANOVA assumptions
1. Three or more “groups”, independent (i.e.
mutually exclusive) or dependent (i.e. follow-up)
2. Used only for comparing means
3. Data are (approximately) normally distributed
4. Data in the groups come from same
underlying population (i.e. equal variances)
Some flexibility on points #3 & #4 but not #1 & #2
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 9: page 8
ANOVA
Why is the ANOVA a parametric statistical test?
1) assumes data are normally distributed
(this should be checked before using it)
2) continuous (ratio/interval) data are used
3) involves a population characteristic
(i.e. a parameter, the mean)
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 9: page 9
Non-Parametric Equivalent
for ANOVA
For situations where there are more than
two independent groups with ordinal data
e.g. Pain score (extreme  no pain)
Kruskal-Wallis test is used, which assigns
ranks to ordinal levels and then compares
overall rank scores between the groups
Note: also tests for dependent data sets
e.g. Friedman test
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 9: page 10
ANOVA – cont’d
Why not just use multiple t-tests?
ANOVA allows you to compare overall
differences between all groups involved in
study, not just one pair at a time
Individual t-tests can be time consuming and
if there are several groups then the number
of tests and calculations becomes unwieldy
ANOVA tells you only if a difference exists
between means, not which means are different
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 9: page 11
T-test versus ANOVA
Very similar to one another with respect to
underlying assumptions and mathematical
basis for calculating relevant test-statistic
Independent t-test ~ One-way ANOVA
e.g. 3 distinct groups, one variable examined
Paired t-test ~ Repeated measures ANOVA
e.g. 3 related groups, one variable examined
Remember: “T” for “two” !
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 9: page 12
3 Types of ANOVA
One-way ANOVA - used when data come
from distinct samples (i.e. unrelated subjects)
and only one independent variable is used
Multifactor ANOVA (MANOVA) – e.g. twoway ANOVA uses two independent
variables, such as gender by drug groups
Repeated measures ANOVA (RANOVA) e.g. two groups of subjects (experimental
and control groups) compared at two
different time points (such as pre-post)
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 9: page 13
ANOVA – Sample scenario 1
Want to compare somatic health complaints
(using scores on the Physical Symptom Survey)
between 3 groups of unrelated subjects:
1. smokers
2. recent ex-smokers
3. non-smokers
What do we do here?
One-way ANOVA: data come from independent
samples (i.e. unrelated subjects) and only one
outcome and exposure variable used
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 9: page 14
ANOVA – Sample scenario 2
Want to examine the effect of gender and
education level on sexual knowledge with
respect to HIV transmission
1. No high school
2. High school
3. Post-secondary
AND
1. Male
2. Female
What do we do here?
Two-way ANOVA: data come from independent
samples (i.e. unrelated subjects) but now have
one outcome and TWO exposure variables
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 9: page 15
ANOVA – Sample scenario 3
Want to examine the effect of 3 forms of
psychiatric therapy over 1 year, using
endpoints of 1 wk, 1-, 3- 6- and 12-months
1. Therapy 1
AT
1 wk, 1-, 3- 62. Therapy 2
and 12-months
3. Therapy 3
What do we do here?
Repeated measures ANOVA: data come from 3
independent samples but also have repeat data
collections within the groups of same subjects
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 9: page 16
ANOVA – what is it?
What does “variance” mean again?
When you take a mean, you want some idea of
how much the individual subjects vary from
each other “on average” (i.e. the SD) while the
total amount of this variation is the “variance”
So what does ANOVA do?
ANOVA takes advantage of this notion of total
variation, comparing variation both within the
group samples AND between the group means
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 9: page 17
ANOVA – splitting the variance
Steps in calculating ANOVA:
1. Separate calculations are done to find:
i) the variation between the groups
ii) the variation within each group
2. Then the ratio of “between to within”
variation is calculated (the “F” test statistic)
Between-group variability
F=
Within-group variability
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 9: page 18
Where does variance come from?
1. variation between the groups
i) random sampling “error”
ii) effect of independent variable (e.g. drug)
2. variation within each group (“subject-to-subject”)
i) random sampling “error”
Thus can now interpret F-statistic as:
effect of independent variable + sampling “error”
F=
sampling “error”
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 9: page 19
Interpreting the F-statistic
- distributions for F-statistics known thus
tables used (again with df) to translate “F”
into a p-value for observing study means
- now have two types of df though since we
have variation from subjects AND groups
- like other test statistics (eg. Z, t ) the bigger
the value of F (for a given set of df), the larger
the difference between the groups examined
larger F-statistic = smaller p-value
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 9: page 20
Interpreting the F-statistic – cont’d
F-statistic typically written specifying group
and subject degrees of freedom, as these are
needed to obtain table values:
F (group df, subject df) = ratio (p-value)
Example:
F (2, 60) = 2.86 p > 0.05
(Where group df = k-1 and subject df = n-k)
k = number of groups; n = number of subjects
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 9: page 21
Interpreting the F-statistic – cont’d
What does P-value from F-statistic tell you?
Only that the group means are NOT the same
What do you do next if F is significant?
Need to do post-hoc analysis of means to see
where differences are greatest or actually
significantly different from one another
Example – Duncan’s test for pairwise comparisons
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 9: page 22
10 minute break !
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 9: page 23
Reading research – First steps
Start with the overall structure and work in …
1. Read abstract – is study relevant to me?
2. What was the hypothesis/research question?
3. Scan tables – what do they show?
4. Were the methods appropriate?
5. What were the conclusions?
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 9: page 24
Tips on reading research results
Before you can interpret the results …
Some questions to ask yourself …
1. Who is in the table – e.g. groups explicit?
2. What is being tested – e.g. dep/indep?
3. How is it being tested – e.g. test used?
4. Was it statistically significant – e.g. p<0.05
5. Was it clinically important?
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 9: page 25
Reading research – cont’d
Some general points on research results …
1. Not all key results are in tables/graphs
4. Not all results in tables are significant !
2. Need to read text to be sure of results
3. “Discussion Section” interprets findings
Check footnotes for significance symbols !
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 9: page 26
Part 2:
Application to the
Assigned Readings
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 9: page 27
Arathuzik (1994)
Quick summary of the paper:
– a pilot study examining the effects of a
combination of interventions on pain
perception, pain control and mood in
metastatic breast cancer patients
– pre-test / post-test experimental design
– 3 groups enrolled with 24 (convenience
sample) subjects randomly allocated to the
three (intervention) groups, only 8 per group
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 9: page 28
Main study hypothesis
“Breast cancer patients who received
relaxation, visualization, and cognitive coping
skills training would would perceive less pain
intensity [and distress] than breast cancer
patients who received relaxation and
visualization training and than a control group.”
Was this hypothesis [for intensity] supported?
- look for table that compares means
(i.e. an ANOVA is a good way to answer this)
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 9: page 29
Interpreting Table 3 …
See Table 3 page 26 of Arathuzik paper
Look at structure of the table …
1. Who is in the table – e.g. groups ?
- all 3 study groups (separately by pre/post)
2. What is being tested – e.g. dep/indep?
- mean scores (separately by pre/post)
3. How is it being tested – e.g. test used?
- ANOVA (one-way, separately by pre/post)
4. Was it statistically significant – e.g. p<0.05
- only fatigue in pre-, and ability to
decrease pain in post-period
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 9: page 30
Interpreting Table 3 - cont’d
Why does Table 3 test “pre” scores?
A check on whether groups are comparable
Does Table 3 make sense on its own?
NO !
What else must go together with Table 3?
- Table 2 shows you group means by key
variables by pre/post status, then Table 3
tests if any of these means are different
- Table 4 then tests where change occurred
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 9: page 31
For Table 1 in Good (1995)
When interpreting results for workshop
Some questions to ask yourself …
1. Any statistically significant differences?
3. Was it in the expected direction?
4. Was it in the expected pattern?
5. Was it clinically important?
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 9: page 32
Next Week:
Correlation
For next week’s class please review:
1. Page 17 (bottom) in syllabus
2. Textbook Chapter 10
3. Syllabus papers: Birenbaum et al.
(1996); Turk et al. (1995)
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 9: page 33