Statistics 

1. Statistics  Data measurement, probability and statistical tests

2. Learning Aims By the end of this session you are going to totally ‘get’ levels of significance and why we do statistical tests!

3. Levels of measurement • These are quantitative measures of data which are of extreme importance when conducting statistical tests • There are 4 levels of measurement

4. Also known as levels of data • Nominal: Counting into categories, e.g. there are 4 men and 4 women in the room • Ordinal: Results are put in order, they are ranked. E.g. we could rank the place that each horse came in a race

5. Levels of measurement • Interval: Data is defined as being a specific measure, this can be measured on an instrument, there are equal intervals between each piece of data. E.g. We can record the exact temperature using a thermometer. (can be minus) • Ratio: This is like interval data except the scale has a meaningful value of zero. E.g. time and length.

6. Why do we need to conduct statistical tests? • Statistical tests tell us the significance of a set of findings- did the IV really effect the DV or were the findings a fluke?! • The more significant a finding is the more effect the IV had on the DV

7. Probability: • We need to use inferential statistics to tell us if the result that we have found is due to chance or not. • To establish if our results are reliable we have to look at the probability of a result being due to chance or not. • The minimum accepted level of probability commonly used in psychology is 5%, this is represented as 0.05. • If the level of significance achieved from a test is equal to or less 0.05 than the results are said to be significant. • This would mean that we are 95% sure that the IV caused the change in the DV

8. Probability: • Can be expressed as: • A proportion: a 1 in 5 chance. • As a percentage: 20% • More commonly expressed as a decimal in psychology: 0.2. • In psychology: 10%=0.10, 5%=0.05, 1%=0.01 and 0.1%=0.001 • To go from % to decimal divide by 100, move decimal place 2 spaces to the left. • Remember the more stringent (lower) the level of significance you set the more significant the results are

9. Observed value: • Every time you perform a statistical test you get an OBSERVED VALUE. • This observed value tells you the extent to which your results are valid, you then have to compare this observed value to a table of CRITICAL VALUES to see of your results are significant or not. • To be significant the observed value should be greater or less than the critical value depending on the type of test • Note that there will be a different table of values for different statistical tests.

10. Interpreting results: • Usually in psychology if the results are significant it means that the probability of the result being due to chance is 5% or less • P<0.05 means the results are significant- so we would accept the experimental hypothesis and reject the null hypothesis

11. Interpreting results: • P is used to represent “the probability that is due to chance” • > =means greater than • < =means less than • ≥ means greater than or equal to. • ≤ means less than or equal to. SO……………… P<0.05 means that the probability that the result is due to chance is less than 5%.

12. Test your understanding • Answer the questions on the handout

13. Type 1 and type 2 errors: • The 5% level of significance has been accepted as it represents a reasonable balance between the chances of making a type 1 or type 2 error • These can occur because: • Level of probability accepted is either too lenient (too high) or too stringent (too low)

14. Type 1 and type 2 errors • Type 1 error: • Occurs when we conclude that there IS a significant difference when there is NOT • This can happen if the accepted level of probability is set TOO LENIENT • Significance level set at 20% • Type 2 error: • Occurs when we reject the experimental hypothesis and accept the null when there IS a difference • This can happen if the probability level is TOO STRINGENT • Significance level set at 1%

15. Deciding on a statistical test • You must decide the following: • Are you trying to find out if your samples are related (correlate) or different? • What design you have used- related, non related, matched pairs • What level of measurement you have used. • You can use the following table to help decide:

16. What test to use?

17. Test your understanding! • Using your newly found knowledge identify the test that would be suitable for the following: • An experiment with nominal data and an independent groups design • Ordinal data on both measures in a study to see if two measures are associated • An experiment with and independent groups design in which the DV is measured on a ratio scale • A study using a correlational technique in which one measure is ordinal and the other is ratio.

18. A study testing an association using a nominal level of measurement • An experiment in which all participants were tested with alcohol and without alcohol on a memory test • An experiment in which reaction time was tested using an independent subject design

19. An experiment with nominal data and an independent groups design = chi-squared test • Ordinal data on both measures in a study to see if two measures are associated = Spearman’s rank correlation • An experiment with and independent groups design in which the DV is measured on a ratio scale = Mann-Whitney U test

20. A study using a correlation technique in which one measure is ordinal and the other is ratio =–Spearman’s rank • A study testing an association using a nominal level of measurement = Chi-Square test of association • An experiment in which all participants were tested with alcohol and without alcohol on a memory test = Wilcoxon’s T test • An experiment in which reaction time was tested using an independent subject design = Mann-Whitney U test