A major challenge for the school research
lead is whether they are able to help colleagues develop the capacity and
capability to interpret research findings.
In particular, can school research help colleagues to correctly
interpret the statistical findings which are often found in research
reports. So this post, I will look at
the specific challenges of using the correlation coefficient(r ) when seeking
to interpreting Daniel Goleman’s work on
leadership and emotional intelligence (Goleman, 2000). To help us do this I will:
 Summarise Goleman’s work on leadership that gets results.
 Briefly explain what is meant by the term correlation coefficient and the implications for interpreting Goleman's work
 Consider some broader points about the challenge of using correlation in educational leadership research and the implications for practice
Daniel
Goleman and leadership that gets results
Goleman argues that leaders often mistakenly
assume that their leadership is a function of their personality, rather than is
something can be chosen to be meet the needs of a specific circumstance. Goleman claims that successful leaders have strengths
in six emotional intelligence competences* i.e.: self awareness, selfregulation, motivation, empathy, and social skill. Moreover, these components of emotional intelligence
can be combined in different ways and which reflect six basic styles of
leadership i.e. coercive, authoriative, affiliative, democratic, pacesetting
and coaching, which are summarised in Table 1 Moreover, the very best leaders
are not wedded to one particular approach and can change approaches depending
upon the demands of the situation.
Table 1 Six
approaches to leadership
Leadership style

Brief explanation

Coercive

‘Do
what I say’

Authoriative

‘Come
with me’

Affiliative

‘People
first’

Democratic

‘Let’s
decide together’

Pacesetting

‘Let’s
make this happen, and now.’

Coaching

‘People
development

The correlation coefficient and
leadership styles
Based on
research interviews with nearly 4000 executives out of a database of 20,000 executives
worldwide, Goleman goes onto to demonstrate
the impact that different leadership styles
have on the organisational climate (working atmosphere). Using
the correlation coefficient (r ), Goleman seeks to to
quantify both the strength and direction of a relationship between leadership
style and organisational climate . Now,
the correlation coefficient (r) can range from +1 – where there is perfectly
positive correlation to 1, where there is a perfectly negative correlation. On the other hand, a value of 0 would suggest
that there is no relationship between the two variables i.e. leadership style
and organisational climate.
Goleman’s research indicates that the relationship between leadership style and
organisational climate reflects a range of intermediate values between 1 and
+1.
Table 2 shows the relationship between different styles of leadership
and aspects of organisational climate.
So looking at the table we can see that the coercive (0.26) and
pacesetting ( 0.25) styles have a negative overall correlation with
organisational climate. Whereas, the authoritative
(+0.54), affiliative (0.46), democratic (+0.43) and coaching (+0.42) – styles have
a positive correlation correlation with organisational climate. However, Goleman notes that all styles can have
their uses, and no one style should be relied upon nor excluded, when seeking
to tackle the ranges of circumstances which are faced by leaders.
Table 2 Leadership style and organisational climate (Goleman, 2000 p19)
Interpreting
the correlation coefficient
(Cumming and CalinJageman, 2017) argue that when interpreting an r value – let’s say 0.54 – and
which hints at some relationship between two variables X (leadership style)and
Y (organisational climate), a number of different things could be going on.
 · There may be a causal link between leadership style and organisational climate changes in leadership style may lead to changes in organisational climate, or changes in organisational climate are leading to changes in organisational style.
 · Something else may be going one, with other variables impacting on either leadership style or organisational culture or both.
 · There are no causal links, and what we are seeing is what Cumming and Calin Jageman describe as ‘seeing a face in the clouds’.
As such Cumming and Calin Jageman note that
all correlations do is to give use some form of guidance as to what to
investigate further. The r values may
suggest what and where to look, however, it needs to be made clear that
correlation does not imply causation. In
other words, just because X appears to be linked with changes in Y, that does
not mean that changes in X are causing changes in Y
So far we have made no reference to how
should interpret the size of different correlation coefficient or r values – be
they 1, 0, 0.5. 0.7 or +1. For example
in Table 3, (Hinkle et al., 2003) provided the following guidance for interpreting correlation.
Table 3 – Rule of Thumb for Interpreting
the Size of a Correlation Coefficient
Size of Correlation

Interpretation

0.90 to 1.00 ( 0.90 to –1.0)

Very high positive (negative) correlation

0.70 to 0.90 ( 0.70 to  0.90)

High positive (negative) correlation

0.50 to 0.70 (  0.50 to 0.70)

Moderate positive (negative) correlation

0.30 to 0.50 (  0.30 to 0.50)

Low positive (negative) correlation

0.00 to 0 0.30 ( 0.00 to 0.30)

Little if any correlation

If we were to use this table as a guide,
this would suggest that in general, with the exception of the authoritative style,
there is little/low levels of correlation between leadership styles and
organisational climate. Nevetheless, (Cumming and CalinJageman, 2017) argues that r values need to be interpreted in context, as
correlation is used in such a wideranging number of ways and settings, that
reference values for r provide little help in interpreting the data. Indeed, Cummings and Calin Jageman argue that
an r value of 0.3 may suggest there is a relationship between two variables,
even though when graphed the data looks like a shotgun blast.
What
about the correlation determinant r squared.
However, if we are looking for the strength
of association between the two variables, we may wish to use the coefficient of
determination r squared – which gives you the proportion of shared
variance. So if we have two variables (A
– the independent variable and B the dependent variable) and we have a
correlation coefficient + 0.5 then our coefficient of determination will be
0.25.
So what does a coefficient of determination
of 0.25 mean, well Professor Steve Higgins (@profstig) of the University of
Durham, has provided me some useful guidance.
Well at best
 A might cause B 25% of the time OR
 B might cause A 25% of the time OR
 C causes them both (and is not present all of the time) OR
 it is a pure coincidence OR
 it is some of the above in some unknown combination
We can now calculate Goleman’s correlation coefficient into the coefficient
determinant and interpret what it means for the relationship between leadership style and organisational climate
Table 4 Leadership style, correlation coefficient and correlation coefficient determinant
Leadership style

Correlation Coefficient r

Coefficient determinant r squared

Coercive

 0.26

+ 0.07

Authoriative

+ 0.54

+ 0.29

Affiliative

+0.46

+ 0.21

Democratic

+0.43

+ 0.18

Pacesetting

0.25

+ 0.06

Coaching

+ 0.42

+0.18

So what does this suggest, well for both
the coercive and pacesetting styles relatively small amounts of variances in
leadership style and organisational climate appear to be shared (0.07 and 0.06
respectively) As for the relationship between an authoritative style and
organisational climate the data suggests that at best only 29% of the total
variance between the two variables is shared.
Other
issues to take into account when interpreting the correlation coefficient
Again, I would like to thank Professor
Steve Higgins for bringing these issues to my attention. First, the correlation coefficient should be
calculated from a random sample of the population. In the case of Goleman’s work, this would
appear to be the case with 4,000 executives randomly selected from a database
of 20,000 executives worldwide. That
said, those 20,000 executives were not in themselves a random sample of executives. Second, Goleman does not report the error
associated with these correlations, as such, we do not know how precise they
are, as no confidence limits have been reported.
Implications
It would seem to me that there are a number
of implications in using ‘correlation’ when making recommendations about
leadership and management.
 Correlation does not mean there is a causal link between two variables – in other just because you have a positive correlation that does not mean the changes in leadership style have caused the change in organisational climate. Indeed, it may be the change in organisational climate may cause the change in leadership style.
 It’s important to have some rules of thumb for interpreting the size of the correlation coefficient. In this example the largest correlation coefficient (authoritative 0.54) is around the borderline between positive and low correlation. In other words, just because you have is for your study the largest correlation coefficient does not mean that the size of correlation coefficient is large.
 If you are looking to make judgments about the strength of the relationship between two variables, then you need to calculate the coefficient of determination. Again, in this example, we have two values (coercive 0.06 and pacesetting 0.07) which are close to zero, which suggests there very little of the variance in leadership style and organisational climate seem to be shared.
 Before making recommendations about leadership and management which uses correlations, it might be useful to look at a basic statistical textbook.
References
CUMMING, G.
& CALINJAGEMAN, R. 2017. Introduction
to the New Statistics: Estimation, Open Science, and Beyond, Abingdon,
Routledge.
GOLEMAN, D. 2000. Leadership that gets results. Harvard business review, 78, 417.
HINKLE, D. E., WIERSMA, W. & JURS, S. G. 2003.
Applied statistics for the behavioral sciences.
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