The Correlation Coefficient (DP IB Psychology): Revision Note

The correlation coefficient

• A correlation is not a research method but an analysis of the relationship between two co-variables.

  In correlational research:

  • Variables are not manipulated (no IV).

  • Instead, two co-variables are measured and compared to identify relationships

Types of co-variables

• One or both of the co-variables could be pre-existing, e.g.,

  • School attendance (days present in Year 11) and number of GCSEs achieved.

  • Average August temperature and number of arrests for violent behaviour in a town

• One or both of the co-variables could be collected data, e.g.,

  • Number of arguments with a partner in a month and self-reported stress levels

  • Average hours of sleep in a week and number of caffeinated drinks consumed

How correlations are measured

• Each participant contributes two scores (one for each co-variable)

• Data are plotted on a scattergraph, with each point representing paired scores

• Scattergraphs typically show one of three outcomes:

  • Positive correlation: as one increases, the other increases (e.g., calories consumed and weight gained)

  • Negative correlation: as one increases, the other decreases (e.g., hours sitting and fitness level)

  • Zero correlation: no relationship (e.g., hair colour and IQ)

• Analysing the relationship between co-variables can be done by

  • visually 'eyeballing' the scattergraph to see the direction of the relationship (positive, negative or none at all)

  • calculating the correlation coefficient, which is expressed as a numerical value

The correlation coefficient

• A numerical value between –1 and +1 showing both the strength and direction of a relationship

  • +1 is a perfect positive correlation

  • –1 is a perfect negative correlation

  • 0 is a no correlation

• Strength can be described as weak, moderate, or strong (applies to both positive and negative)

  • +0.03 is a weak positive correlation

  • –0.05 is a moderate negative correlation

  • –0.09 is a strong negative correlation

• The correlation coefficient represents both the direction and the strength of the r

Evaluation of the correlation coefficient

Strengths

• The correlation coefficient is a quick and easy way to analyse data

  • This is a strength, as it enables the researcher to access large amounts of data that would otherwise be impossible to gather if they tried to amass this from scratch

  • Large amounts of quantitative data mean that the research is high in reliability

• Correlation coefficients allow researchers to make predictions as to the relationship between co-variables

  • E.g., knowing that there is a relationship between school absence and GCSE results could be used to identify students at risk and to implement interventions to help them achieve their potential

Limitations

• Extraneous factors connected to one or both co-variables may affect the result and lead to invalid conclusions being made

  • E.g., number of days of absence from school may be due to illness rather than to choice 

  • a low GCSE score may be due to a high turnover of teachers in one school rather than to student absence

• Correlations cannot establish cause and effect — only association

• Correlation coefficients are useful for analysing linear relationships (height and shoe size)

  • They are less successful when dealing with non-linear relationships (number of hours worked and level of happiness)