# Inferential Statistics

Descriptive statistics help to summarise large sets of raw data, helping make them more palatable, so we can see if there are any trends or patterns for example. Let’s say we see a trend on our scattergram, or there does appear to be a difference in the average scores obtained by each of our two groups; how can we be sure that this outcome would be repeated? Might it not have been due to chance? Inferential statistics help us to answer that question; they help us to know what we can infer from the data, whether we could infer that these results are generalisable to the target population, whether general laws can be proposed which would help us to predict behaviour, whether two variables actually are related or whether a difference actually does exist between these two conditions or these two groups.

What is the point of a stats test? The stats test will tell us the probability of our results arising if the null hypothesis was true/correct, another way of putting this is that we are working out the probability that our results arose due to chance alone.

If this probability is less than 5% (p<0.05 or 1 in 20) we can accept the experimental/ alternative hypothesis and reject the null hypothesis.

If the probability is more than 5% (p>0.05 or 1 in 20) then we must…accept the null hypothesis and reject the experimental or alternative hypothesis

Choosing a test: First off we need to know which level of measurement has been used when collecting the data. Data can be nominal, ordinal, interval or ratio. Then we need to know whether we are testing for an association (correlation) or a difference between groups (independent measures) or conditions (repeated measures). Once we have this information, we are good to go, so long as we can remember this little table:

 Nominal Ordinal/Interval/Ratio Test of association between two variables (correlation) *Edexcel don’t require you to know this Spearman’s Rho Test of difference: independent measures (two groups of different people are compared) Chi Squared Mann Whitney U test Test of difference: repeated measures (the same group of people are tested twice under two differing sets of conditions) Sign test (Edexcel don’t require you to know this) Wilcoxons

*the appropriate tests for these cells are not required knowledge for Edexcel Psychology; I have not included the name of the tests so as not to confuse you.

Conducting the test:  Having decided which test to use, the next stage is to complete the test following the instructions with care and recording calculations neatly so that they can be checked for accuracy.

Once you have calculated your observe value, you will need to interpret this using critical values tables in order to decide whether to accept or reject your hypothesis based on the level of significance.

## Ranking

Some stats test require you to be able to “rank” the data, this is often sued to turn interval or ratio data into ordinal data for use with non-parametric tests such Spearman’s, Mann Whitney and Wilcoxon’s. Follow the link to find out how to rank if you are not sure!

Practice Questions:

1. Regis carried out a chi-squared (x2 ) statistical test on his data. Two reasons why he carried out a chi-squared test are that it

A uses nominal data

B uses ordinal data

C uses an independent measures design

D uses a repeated measures design

2. Neil carried out a correlation. To analyse his data Neil decided to carry out a Spearman’s test. He carried out the Spearman’s test because he was

A looking for a difference

B looking for a relationship

C using an independent groups design

D using nominal data

E using ordinal data

3. Researchers carried out a Mann Whitney U test on their data from a study. Their observed value was 13. They looked up the critical value at the p=0.05 level for a one tailed test and found that it was 27. They knew that their observed value of U is only significant if it is equal to or less than the critical value. Using the information in the table, the researchers would have concluded that there was

A a significant difference

B no significant difference

C a significant correlation

D no significant correlation

4. p≤0.05 means the probability that the results are due to chance is

A equal to or less than 0.05%

B equal to or less than 0.5%

C equal to or less than 5%

D equal to or less than 50%

5. Megan collected ordinal data from her experiment. Which statistical test should Megan use to analyse her data?

A Mann Whitney U

B Chi-squared

C Spearman’s rho

6. Caroline conducted a study where she asked male and female Pps to throw a ball at a target and recorded how many times each Pp hit the target. She then worked out the mean for males (30) and the mean for females (25) and plotted them on a bar chart. She now wants to know whether the difference in the means is significant or not.

1. Which inferential (statistical) test should Caroline use on the results of her study (1)
2. Give two reasons why Caroline would be able to use the inferential (statistical) test you identified in (b)(i). (2)