Christianity attendance science
Attitude towards – +0.4573 −0.0926
Christianity – p=0.001 p=0.010
Father’s church – – −0.0179
attendance p=ns
Interest in
science
- – –
The authors reported that there were significant relationships between attitude towards
Christianity and interest in science, and between Fathers’ church attendance and their
sons’ or daughters’ attitude towards Christianity. The authors went on to caution that
whereas a simple bivariate correlation coefficient is able to demonstrate where significant
covariation exists between variables, it is not able to detect whether this covariance is the
artefact of other significant relationships. It is therefore wise to delay interpretation of
bivariate relationships between variables until the complex patterns of inter-relationships
between all the variables have been ordered into some sequence according to
hypothesized relationships.
In this study the correlation analysis was used in both a descriptive and inferential
way. The pattern of relationships between variables was scrutinized prior to a third phase
of the analysis which involved causal modelling of the data using path analysis. As
results of statistical significance tests were reported the data was clearly used in an
inferential way. Although no mention was made about whether the data met the
assumptions required for correlational analysis, as in most papers, the reader has to
assume, in the absence of any specific information, that the variables are linearly related
and have an underlying bivariate normal distribution.
The null hypotheses tested were of the type, ‘there is no linear relationship between
attitude towards Christianity and attitude towards science’ or put simply these two
attitudes are independent. The authors concluded, following a path analysis of the data,
(causal modelling of relationships between variables) that whereas there was a significant
negative correlation between Christianity and attitude towards science, interest in science
did not influence attitude towards Christianity—a good example of the need for caution
when interpreting the meaning of significant correlations.
Prior to drawing conclusions from these findings and correlational data in general, the
reader might want to consider answers to questions such as: What is the shape of the data
distributions? What evidence is presented related to underlying assumptions required for
correlational analysis? Are the samples random, and if yes, what is the population? Is a
hypothesis test really needed? What guidance does the author give on the substantive
meaning of the size and significance of the correlations?
Worked ExampleCorrelation and regression are closely related techniques and therefore data from the
worked example in section 8.2 (shown in Table 8.2) is used to show how the Pearson
correlation r is computed from raw data. To illustrate computation of a partial correlation,
another variable, a Raven score, is added. This is a standardized (age adjusted) measure
Inferences involving continuous data 283