Statistics

Statistics are a method of summarising and analysing data for the purpose of drawing conclusions about the data.  

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

We can make a distinction between descriptive and inferential statistics.   Descriptive statistics simply offer us a way to describe a summary of our data. 

Inferential statistics go a step further and allow us to make a conclusion related to our hypothesis.

Descriptive Statistics

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 a test of difference (experiment) there are two main ways of summarising the data using descriptive statistics.   The first way is to carry out of measure of central tendency (mean, median or mode) for each of the two conditions. 

The mean is calculated by adding all the scores together in each condition and then dividing by the number of scores.  This is a useful statistic as it takes all of the scores into account but can be misleading if there are extreme values.  For example if the scores on a memory test were 2, 4, 5, 6, 7, 42, the mean would be 10 which is not typical or representative of the data.

The median is calculated by finding the mid point in on ordered list.   The median is calculated by placing all the values of one condition in order and finding the mid- point.  This is a more useful measure than the mean when there are extreme values. 

The mode is the most common value in a set of values.  And will not be used for your psychological investigation.

The second way of summarising and describing data is to calculate a measure of dispersion.  This simply shows us the spread of a set of data.  A simple way of calculating the measure of dispersion is to calculate the range.  The range is the difference between the smallest and largest value in a set of scores.  Although it is a fairly crude measure of dispersion as any one high or low scale can distort the data.   A more sophisticated measure of dispersion is the standard deviation which tells us how much on average scores differ from the mean. 

Inferential Statistics

As the name suggests inferential statistics attempt to make an inference about our data.  That is, which hypothesis offers the best explanation for our results?

When we carry out a test if difference we have two hypotheses.  A null hypothesis which states that the results will be due to chance, and the experimental (alternate) hypothesis, which predicts that the results are due to the manipulation of the independent variable. 

To assess the probability that the results are due to chance an inferential statistical test is used.   Inferential statistics tell us whether the difference between two sets of scores is significant or due to chance.  It is an academic convention that in psychology we accept the null hypothesis as the best explanation for out results unless there is a 5% probability (or less) of the results being due to chance.

5% probability is expressed as p<0.05 and if we find that the null hypothesis can be rejected we can be 95% confident of the conclusions.

When carrying out a test of difference (experiment) if the design is an independent measures design the appropriate inferential statistical test to use is the Mann Whitney U test.  

When carrying out a test of difference (experiment) if the design is a repeated measures design the appropriate inferential statistical test to use is the Wilcoxon signed ranks test.   To use this as a spread sheet go to www.holah.karoo.net/stats.htm

Whichever test is used a value is calculated which is called the observed value.  The value then has to be compared with the critical value to determine whether the null hypothesis can be rejected and at what value.