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.

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.

If there is no correlation between two variables they are said to be uncorrelated.

A **correlation coefficient** refers to a number between -1 and +1 and states how strong a correlation is. If the number is close to +1 then there is a positive correlation. If the number is close to -1 then there is a negative correlation. If the number is close to 0 then the variables are uncorrelated.

**Hypotheses for correlational analysis**

When carrying out correlational analysis it is expected that the researcher will start with a hypothesis.

It is important that the two variables are clearly stated in the hypothesis.

When a hypothesis predicts the expected direction of the results it is referred to as a **one-tailed hypothesis**. For example the hypothesis above is stating that there will be a significant positive correlation between average GCSE scores and performance on a memory test. Note that a one tailed hypothesis can also predict a negative correlation.

When a hypothesis does not predict the expected direction of the results it is referred to as a **two-tailed hypothesis**. For example a two tailed hypothesis might be that there will there will be a significant correlation between average GCSE scores and performance on a memory test.

The hypothesis that states the expected results is called the **alternate (or correlational) hypothesis** as it is alternative to the null hypothesis. When conducting a correlation it is important that we have an alternate hypothesis and a null hypothesis. A null hypothesis might be that there will there will be no significant correlation between average GCSE scores and performance on a memory test.

**Descriptive Statistics**

Correlational analysis always involves **quantitative data**.

Carrying out a correlation often involves analysing a lot of data. As psychologists therefore we need to have knowledge of statistics so that we can make conclusions about our data.

**Descriptive statistics** give us a way to summarise and describe our data but do not allow us to make a conclusion related to our hypothesis.

When carrying out correlational analysis the data is summarised by presenting the data in a **scattergraph**. It is important that the scattergraph has a title and both axes are labelled. From the scattergraph we may be able to say whether there is a strong positive correlation, a weak positive correlation, no correlation, a weak negative correlation or a strong negative correlation but we can not make a conclusion about the hypothesis.

**Strengths of Correlational Analysis**

+ Correlations are very good for showing possible relationships between variables and some times are the only practical or ethical way of carrying out an investigation.

+ Researchers may use correlational analysis as a starting point in their research and if a relationship between variables is found they can then investigate this further, perhaps using experimentation to investigate if there is a causal relationship.

**Weaknesses of Correlational Analysis**

– Correlational analysis cannot demonstrate a **cause and effect **relationship between variables. For example if we found a positive correlation between GCSE scores and attendance rates at school we cannot say that high attendance causes high achievement or that low attendance leads to low achievement. It is possible that low achievement is leading to low attendance, that low attendance is leading to low achievement or that another variable say illness is causing both low achievement and low attendance at school.