Correlations Correlations Correlation refers to a measure of how strongly two or more variables are related to each other. A positive correlation means that high values of one variable are associated with high values of the other. Or if you like, the variables increase together. Example of a positive correlation: A negative correlation means that high values of one variable are associated with low values of the other. Or if you like, as one variable increases the other decreases. Note that like a positive correlation, a negative correlation still indicates that some kind of relationship exists. Example of a negative correlation: If there is no correlation between two variables they are said to be uncorrelated.

Definition Correlation measures how strongly two or more variables are related to each other. Used a lot in psychology investigations, for example Maguire et al.(2000) who demonstrated a link between parts of the brain and highly developed spatial memories in London taxi drivers. They did this by correlating volume of brain matter with time spent as a taxi driver. Do not ever make the mistake of thinking that a correlation between two variables means that one caused the change in the other. CORRELATION DOES NOT EQUAL CAUSE

Correlation refers to a measure of how strongly two or more variables are related to each other Which of the following is a positive, negative and zero correlation? Shoe size has no relationship with exam grades As the temperature increases, so do ice-cream sales The more relaxation you do, the less stress you suffer Add one of your own to each box.

Correlation – operationalising variables

When conducting correlational analysis it is important to operationalise the variables. YOUR TURN: What does operationalise mean? Saying in a clear way how the two variables (or co-variables) are going to be measured. E.g. intelligence & memory - operationalise the variables Intelligence might be measured by average GCSE score YOUR TURN: How could you operationalise memory? Performance on a memory test Note: The usefulness of correlational analysis can be affected by how the variables are measured. E.g. is average GCSE score a valid measure of intelligence?

Hypotheses YOUR TURN: What is a hypothesis? A hypothesis is a testable, predictive statement. The hypothesis will state what the researcher expects to find out. For example… There will be a significant positive correlation between average GCSE scores and performance on a memory test This is one-tailed/directional. YOUR TURN: Re-write it as a non-directional

When a hypothesis does not predict the expected direction of the results it is referred to as a two-tailed or directional hypothesis. For example a directional hypothesis might be … There will there will be a significant correlation between average GCSE scores and performance on a memory test. Is the following directional or non-directional? There will be a significant negative correlation between age and performance on a memory test

Analysis of correlation For a correlational study, the data can be plotted as points on a scatter graph. A line of best fit is then drawn through the points to show the trend of the data. If both variables increase together, this is a positive correlation

Negative Correlation If one variable increases as other decreases this is a negative correlation.

No Correlation If no line of best fit can be drawn then there is no correlation

Correlation coefficient Correlation can be quantified by using a correlation coefficient – a mathematical measure of the degree of relatedness between sets of data. A correlation coefficient will have a value from –1 to +1. +1 = perfect positive correlation all points on straight line, as x increases y increases. A value close to one indicates a strong positive correlation. 0 = no correlation points show differing degrees of correlation. -1  = perfect negative correlation all points on straight line, as x increases y decreases. A value close to –1 indicates a strong negative relationship.

Strengths of correlation Calculating the strength of a relationship between variables. Useful as a pointer for further, more detailed research. The procedures can be repeated which means that the findings are confirmed. Can be used when an experiment would be unethical or impractical .

Weaknesses of Correlation Cannot assume cause and effect, strong correlation between variables may be misleading Lack of correlation may not mean there is no relationship, it could be non linear, e.g.