New Research Design =
‘Correlational’
(i.e. based on correlation/relationship)
• You are interested in knowing the relationship
between average daily calories consumed and
pounds lost in a 3 month period among clients
attending a new nutrition workshop. All
clients at this clinic are healthy adults (men
and women) between 20 – 40 years of age.
They are all enrolled in this weight loss clinic
as a part of a comprehensive weight loss
package which includes this workshop.
Continuous Variables
• Both ‘pounds lost’ and ‘calories consumed’
are continuous variables
– In nature, they exist on a continuum
0 ∞
– The measurement of these variables is bounded
only by our precision (i.e. scale)
Bivariate Linear Correlation
• Pearson’s r = the magnitude and direction of
relationship between two continuously
distributed variables
• Ranges from -1.0 to +1.0
• Negative numbers mean an ‘inverse’ (or
negative) relationship
• Positive numbers mean a ‘direct’ (or positive)
relationship
Positive Relationship
100
E
X 90 r = .86, p < .001
A
M 80
G 70
R
A 60
D
E 50
S
40
0 1 2 3 4 5
Hours studied
Scatterplot: calories consumed vs
pounds lost
r = -.68, p < .001
Assumptions (& limitations) of
correlation
• Linear relationship (eyeball it)
• ‘restriction of range’?? (think about it)
Population Distribution
Linearity?
Statistical Significance of r
Rho = 0.0
(the null hypothesis)
‘r’ = -.68
p < .001
• So, the larger ‘r’ is, the smaller the p value
associated with it!
• (can you sample, just by chance) a correlation
of .5 out of a population where there is NO
true relationship?
• Yes, but it’s very unlikely
Effect Size
• APA now says that all statistics have a
corresponding effct size measure noted.
• Why? Because ‘p’ ONLY tells you the
probabilty that your results could have
occurred by chance, right?
• Even if the probability the results are chance
results is really low, doesn’t mean the results
are BIG or important
PVE
• ‘Percent variance explained’
• It’s a possible ‘effect size’ measure, and the
one most often used for this kind of data
• Variance = standard deviation(squared)
• Also, its all the variability in the data.
• For example, is there variability in weight loss?
Lbs_lost
What ‘accounts for’ differences in how
much weight people lose?
– Health
– Genes
– Adherence to program/attendence at workshops
– Motivation
– Exercise
Calories variance
• Does calories consumed account for weight loss
amount?
• Actually, yes. R2’s worth of it!
• (-.68)2= .4624 ≈ 46% of ‘it’ (variance in weight
loss) is ‘accounted for’ for calories consumed.
Writing it up….
(the results section)
• “In 2010, we undertook a study to evaluate weight loss among
participants in a nutrition education program. Adult male and
female participants enrolled in a comprehensive wieght loss
program at a clinic took part in 6 1-hour nutrition education
classes over a period of 12 weeks. Mean weight loss among
participants was 22.60 lbs (SD = 7.16). Participants also self-
recorded their average daily caloric intake over that same
period. The relationship between calories consumed and
pounds lost was significant, r = -.68, p < .001. The percent of
variability in weight loss that was explained by calories
consumed was 46%. On the basis of these data we concluded
that ……….
Internal validity?
• Nope
External Validity?
• Adult men and women enrolled in a weight
loss program.
• Which community?
• If they are enrolled, it indicates resources and
motivation…..
• ??