1. Data measurement, probability and statistical tests
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 There are 4 levels of data
You need to know which level of data you are dealing with in order to select the right statistical test

4. Nominal Level
The data can be counted into categories, e.g. there are 4 men and 4 women in the room
There were 8 brown horses and 1 white one!

5. Ordinal Level
Results are put in order, they are ranked. E.g. we could rank the place that each horse came in a race

6. The other 2 levels
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 (no minus).

7. 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 just a fluke?
The more significant a finding is the more effect the IV had on the DV

8. Probability:
We need to use inferential statistics to tell us if the result that we have found is 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 is equal to or less 0.05 than the results are said to be significant i.e. not just a fluke.
This would mean that we are 95% sure that the IV caused the change in the DV
However there is still a 5% chance it didn’t!

9. Probability: In psychology: 10%=0.10, 5%=0.05, 1%=0.01 and 0.1%=0.001
As a percentage 20% as a proportion: a 1 in 5 chance.
But more commonly expressed as a decimal in psychology:
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
1% is more significant than 5%

10. Observed value:
Every time you perform a statistical test you get an OBSERVED VALUE.
This observed value is also known as the calculated value because it is the one you calculated.
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.

11. 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

12. 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%.

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: Type 2 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. Which non-parametric test to use?
Design
Nominal
Ordinal
Correlation/
association
Chi-square test of association
Spearman’s Rho R
Independent measures
Chi-squared test of independent samples
Mann Whitney U
Repeated Measures
Sign Test
Wilcoxon T

17. Test your understanding!
Using the grid on the previous slide, identify the non-parametric test that would be suitable for the following:
Nominal data on both measures in a study to see if two measures are associated
An experiment with an independent measures design in which the DV is measured on an ordinal scale
A study using a correlational technique in which one measure is ordinal and the other is interval.
An experiment in which all participants were tested with alcohol and without alcohol on a memory test

18. Answers
Nominal data on both measures in a study to see if two measures are associated = chi square
An experiment with an independent measures design in which the DV is measured on an ordinal scale = Mann Whitney U
A study using a correlational technique in which one measure is ordinal and the other is interval. = Spearman’s rho
An experiment in which all participants were tested with alcohol and without alcohol on a memory test = Wilcoxon T
If Interval data is used then the test will be ‘parametric’ which we look at next year 