N318b Winter 2002
Nursing Statistics
Lecture 10
Specific statistical tests:
Correlation
Today’s Class
 Brief discussion about issues related to
term paper and research paper
 Correlation lecture
<< 10 min break >>
 Applying knowledge to assigned reading
 Turk et al. (1995)
Followed by small groups 12-2 PM
Focus on interpreting correlation results
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 10: 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 10: page 3
“In Group” Session
Focuses on 1 assigned reading.
Q1. Chance to interpret correlation results
Q2. Know difference between “R2” and “r”
Key points about correlation workshop will
be covered in the 2nd part of the lecture
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 10: page 4
Term papers
Both are due by April 11th (not April 4)
If there are questions about how to
approach either type of paper don’t wait
until last minute – get it sorted out ASAP
Research experience – emphasis is on
describing experience and what YOU learned
Research Critique – emphasis is on showing
that YOU understand what has happened in
the paper, especially the results section
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 10: 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 10: page 6
Correlation (Pearson product)
How do you known when to use correlation?
Referring back to the 3 “basic questions”:
1. What kind of data are used?
- usually numeric/continuous (ratio/interval)
- two different variables from SAME subjects
2. What kind of relationship is of interest?
- direction and strength
3. How many groups (samples) involved?
- (usually) one sample, with  2 variables
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 10: page 7
Correlation - assumptions
1. The relationship under study is linear –
important non-linear relationships can be
overlooked with simple correlation analysis
e.g. see Figure 10-1 in textbook
2. Data are (approximately) normally distributed
3. Data in the two variables have roughly equal
range of variability (i.e. homoscedasticity)
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 10: page 8
Correlation
Why is correlation 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
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 10: page 9
Non-Parametric Equivalent
for correlation
For situations where there are non-normal
data or with ordinal data
e.g. Pain score (extreme  no pain)
with breast CA tumour grade (I-IV)
Kendall’s Tau or Spearman’s Rho – like
tests with ANOVA and t-test, assigns ranks
to ordinal levels and then compares
relationship between variables
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 10: page 10
Correlation – cont’d
Why not just use a scatter plot (e.g. Fig. 10-1)?
Plot is an important first step but correlation
takes next step and statistically quantifies
strength of relationship between variables
Test statistic is “r”, the correlation coefficient,
that ranges from –1.0 to +1.0, with larger
values indicating stronger relationship
Correlation does not equal causation !
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 10: page 11
Correlation – direction
Can be either positive or negative, as
coefficient “r” ranges from –1.0 to +1.0
What does a negative value of “r” mean?
As one variable increases the other decreases
What does a positive value of “r” mean?
As one variable increases the other increases
As “r”  0, strength of relationship  0
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 10: page 12
Correlation – strength
Value of “r”
Strength of
(either +’ve or –’ve) relationship
0 – 0.25
none
0.26 – 0.49
weak
0.50 – 0.69
moderate
0.70 – 0.89
strong
0.90 – 1.0
very strong
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 10: page 13
Correlation – p-values
“r” has a known distribution and thus probability
of a given “r” value arising by chance alone can
be determined (when assumptions are valid)
In general, larger “r” values have smaller p-values
BUT, statistical significance not as imprtant
here since large samples can generate small
p-values even for very weak correlations
e.g. see Tables 10-1 and 10-2 in textbook
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 10: page 14
Correlation – Sample scenario 1
We want to know if there is a relationship
between hours worked per week and
stress levels in nurses (i.e. burnout)
1. Hours worked
AND
2. burnout
Would you expect +’ve or –’ve correlation here?
How strong do you think it should be?
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 10: page 15
Correlation – Sample scenario 1
if stress levels did NOT correlate positively (as
expected) with hours worked we might be
worried about data errors or selection bias
Correlations provide useful background
information but no causal evidence
Especially useful for interpreting results of
more powerful analyses such as regression
that can be influenced by high correlations
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 10: page 16
10 minute break !
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 10: page 17
Part 2:
Application to the
Assigned Readings
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 10: page 18
Turk et al. (1995)
Quick summary of the paper:
– a cross-sectional study examining the
cognitive-behavioral mediation model of
depression in chronic pain patients
– 100 chronic pain subjects divided into
two groups: 73 randomly chosen younger
(<70); and 27 older (70 yrs) patients
– found a strong link between pain and
depression for older subjects but not for
younger ones (i.e. an age effect)
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 10: page 19
Some design issues?
Do you have any concerns with design of the
study – e.g. using a cross-sectional design to
examine chronic pain and depression?
Which came first (“chicken-and-egg”)?
Can a correlation analysis address this
problem adequately?
NO ! It looks only at relationship between
two variables (typically at one point in time)
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 10: page 20
Interpreting Correlations …
Correlation is rarely the main analytic tool for a
research paper, thus correlation results are
typically used to provide context or “help” with
interpreting other results (especially regression)
See Figure 2 page 98 of Turk et al. paper
What do these two diagrams illustrate?
Why did they split the old and “young” groups?
This was part of their main hypothesis !
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 10: page 21
Interpreting Correlations - cont’d
When interpreting results of Turk et al. paper
for workshop …
General questions to ask about correlations …
1. Any statistically significant correlations?
2. Were they in the expected direction?
3. How strong were the correlations?
4. How do the correlation results relate
back to the study hypothesis?
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 10: page 22
Next Week:
Regression
For next week’s class please review:
1. Page 18 (top) in syllabus
2. Textbook Chapter 11 (see syllabus)
3. Syllabus paper: Ferketich & Mercer
(1995)
School of
Nursing
Institute for Work & Health
Nur 318b 2002 Lecture 10: page 23