RESEARCH METHOD COHEN ok

MEASURING ASSOCIATION 533
Box 24.26
APearsonproduct-momentcorrelation
The attention given to teaching and
learning at the school
How well students apply themselves
to learning
Discussion and review by educators
of the quality of teaching, learning and
classroom practice
Pearson correlation
Sig. (2-tailed)
N
Pearson correlation
Sig. (2-tailed)
N
Pearson correlation
Sig. (2-tailed)
N
Discussion
and review
by educators
The attention How well of the quality
given to students of teaching,
teaching and apply learning and
learning at the themselves classroom
school to learning practice
1.000
·
1000
0.060
0.058
1000
0.066*
0.036
1000
0.060
0.058
1000
1.000
·
1000
0.585**
0.000
1000
0.066*
0.036
1000
0.585**
0.000
1000
1.000
·
1000
Chapter 24
*Correlationissignificantatthe0.05level(2-tailed).
** Correlation is significant at the 0.01 level (2-tailed).
Curvilinearity
The correlations discussed so far have assumed
linearity, that is, the more we have of one property,
the more (or less) we have of another property, in a
direct positive or negative relationship. A straight
line can be drawn through the points on the
scatterplots (a regression line). However, linearity
cannot always be assumed. Consider the case, for
example, of stress: a little stress might enhance
performance (‘setting the adrenalin running’)
positively, whereas too much stress might lead to a
downturn in performance. Where stress enhances
performance there is a positive correlation, but
when stress debilitates performance there is a
negative correlation. The result is not a straight
line of correlation (indicating linearity) but a
curved line (indicating curvilinearity). This can be
shown graphically (Box 24.27). It is assumed here,
for the purposes of the example, that muscular
strength can be measured on a single scale. It
is clear from the graph that muscular strength
increases from birth until fifty years, and thereafter
it declines as muscles degenerate. There is a
positive correlation between age and muscular
Box 24.27
Alinediagramtoindicatecurvilinearity
Muscular strength
50
40
30
20
10
0
0 10 20 30 40 50 60 70 80 90
Age
strength on the left-hand side of the graph and
anegativecorrelationontheright-handsideof
the graph, i.e. a curvilinear correlation can be
observed.
Hopkins et al. (1996: 92) provide another
example of curvilinearity: room temperature and
comfort. Raising the temperature a little can make
for greater comfort – a positive correlation – while
raising it too greatly can make for discomfort – a
negative correlation. Many correlational statistics