1. Data measurement, probability and Spearman’s Rho
Statistics 
Data measurement, probability and Spearman’s Rho

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. Just a recap …. On your whiteboards.. On your own…
What is the IV?
What is the DV?
What is a directional hypothesis?
What is a non-directional hypothesis?
What is the mean?
What is the median?
What is the mode?
What are these 3 tests called?
What we manipulate
What we measure
Prediction – direction
Usually based on previous research
Prediction – no direction
Average
Middle value
Most common
Descriptive statistics

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

5. 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

6. 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 – YOU DO NPT NEED THIS.. This data can be classed as Interval

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 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
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

9. 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

10. 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

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: These can occur because:
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%

16. 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:

17. See handout… What test to use? Looking for a difference
Looking for a correlation

18. What test to use? rho Looking for a difference Chi-square Sign Test
LOOKING FOR A CORRELATION
Groups will be separate
DATA LEVEL
INDEPENDENT
GROUPS DESIGN
REPEATED MEASURES DESIGN
NOMINAL
Chi-square
Sign Test
ORDINAL
Mann-Whitney U test
Wilcoxon test
Spearman’s
rho
INTERVAL OR RATIO
Unrelated t test
Related t test
Pearsons r

19. What test to use? rho Looking for a difference Chi-square Sign Test
LOOKING FOR A CORRELATION
Groups will be separate
DATA LEVEL
INDEPENDENT
GROUPS DESIGN
REPEATED MEASURES DESIGN
NOMINAL
Chi-square
Sign Test
ORDINAL
Mann-Whitney U test
Wilcoxon test
Spearman’s
rho
INTERVAL OR RATIO
Unrelated t test
Related t test
Pearsons r

20. 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 ordinal scale
A study using a correlational technique in which one measure is interval and the other is ratio.
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

21. ANSWERS
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 / Rho
An experiment with and independent groups design in which the DV is measured on a Ordinal scale
Mann-Whitney U test
A study using a correlation technique in which one measure is interval and the other is ratio
Pearsons r
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
Unrelated T-Test

22. PRACTICAL: What goes in a results section?
Measure of central tendency (mean)
Measure of dispersion (range)
Graph (all elements need to be present!)
Statistical test
Raw data goes in your Appendix

23. Our example for today…. You should relate each of these steps to your practical
Aim: A psychologist is investigating the relationship between sleep and cognitive function.
Hypothesis is that “There will be a positive relationship between hours of sleep the night before a test and the score on the test”.
What would her null hypothesis be?
What kind of hypothesis is this?

24. Our raw data for today: Participant Hours of sleep Test score (%) A 3
Appendix
Participant
Hours of sleep
Test score (%) A 3 12 B 6 71 C 9 83 D 4 46 E 5 38 F 13 94 G 10
100 H 1 15 I 8 32 J 87
Which stats test do you think we’ll be using?
What type of data is this?
What is the research design?

25. First things first…
Produce a graph to visually present this information
What does your graph suggest about the relationship between these two variables?
You should have this already for your practical!
Participant
Hours of sleep
Test score (%) A 3 12 B 6 71 C 9 83 D 4 46 E 5 38 F 13 94 G 10
100 H 1 15 I 8 32 J 87
Scattergraph required

27. Measures of central tendency and dispersion
You then need to calculate the mean for both sets of data, and the range
What can you conclude from these calculations?
Again you should have this already for your practical!
Hours of sleep
Test score (%)
Mean
Range

28. Spearman’s Rho
Using your colourful, informative table, why would we use this test?
A correlation / relationship
ordinal data

29. Spearman’s Rho
Used to check for statistical significance between two variables
To calculate the correlation coefficient, you need values for two different variables (e.g. hours of revision and average test scores, or ugliness and fear)
! You do not need to calculate the test by hand… but you need to understand what the process is

30. Step Rank the scores for both variables from lowest to highest
Additional info
Step
Rank the scores for both variables from lowest to highest
Participant
Hours of sleep
Rank
Test score (%) A 3 12 B 6 71 C 9 83 D 4 46 E 5 38 F 13 94 G 10
100 H 1 15 I 8 32 J 87

31. Step Rank the scores for both variables from lowest to highest
Additional info
Step
Rank the scores for both variables from lowest to highest
Participant
Hours of sleep
Rank
Test score (%) A 3 2 12 1 B 6 5 71 C 9 7 83 D 4 46 E 38 F 13 10 94 G 8
100 H 15 I 32 J 87

32. Step Participant Hours of sleep Rank Test score (%) d A 3 2 12 1 B 6 5
Additional info
Now calculate the difference (d) in ranks for each student (hours of sleep – test score = d)
Participant
Hours of sleep
Rank
Test score (%) d A 3 2 12 1 B 6 5 71 C 9 7 83 D 4 46 E 38 F 13 10 94 G 8
100 H 15 I 32 J 87

33. Additional info
Step
Now calculate the difference (d) in ranks for each student (hours of sleep – test score = d)
Participant
Hours of sleep
Rank
Test score (%) d A 3 2 12 1
2-1 = 1 B 6 5 71
5-6 = -1 C 9 7 83
7-7 = 0 D 4 46
3-5 = -2 E 38
4-4 = 0 F 13 10 94
10-9 = 1 G 8
100
8-10 = -2 H 15
1-2 = -1 I 32
6-3 = 3 J 87
9-8 = 1

34. Additional info
Step
Now square the difference (d) to produce d2, and add up this column to create
Participant
Hours of sleep
Rank
Test score (%) d d2 A 3 2 12 1 B 6 5 71 -1 C 9 7 83 D 4 46 -2 E 38 F 13 10 94 G 8
100 H 15 I 32 J 87
Total

35. Step
Additional info
Now square the difference (d) (multiple by itself) to produce d2, and add up this column to create
Participant
Hours of sleep
Rank
Test score (%) d d2 A 3 2 12 1 B 6 5 71 -1 C 9 7 83 D 4 46 -2 E 38 F 13 10 94 G 8
100 H 15 I 32 J 87
Total 22

36. r Step The calculation: N = number of participants
Additional info
Step
The calculation:
N = number of participants
For our example, that’s 10 r

37. Additional info
Step r
So…
Becomes… r
10 x
102
X 22

38. r Step r = + 0.867 Calculate the observed value of r 6 x 22 = 132
Additional info
Step
Calculate the observed value of r
6 x 22 = 132
10 x (100 – 1) = 990
132/990 = 0.133
r = r
10 x
102
X 22
This is your observed value – the one which you have calculated. What type of correlation does it suggest?

39. WHAT’S A CRITICAL VALUE?!
Additional info
Step
Compare your observed value to the critical value to find out whether your results are statistically significant (and if you can reject the null hypothesis!)
WHAT’S A CRITICAL VALUE?!
WHAT’S THE P VALUE?

40. Additional info
Step
Compare your observed value to the critical value to find out whether your results are statistically significant (and if you can reject the null hypothesis!)
In order to find the critical value that you compare to, you need to know the answers to these questions:
Is your hypothesis directional or non-directional
Does that mean it’s one-tailed or two-tailed?
What level of significance does Psychology use?
How many participants did we have in our experiment? (how many animals)
The stats package you will use for your practical does this all for you!

41. Step
Additional info
Compare your observed value to the critical value to find out whether your results are statistically significant (and if you can reject the null hypothesis!)
Level of significance for two-tailed test
0.10
0.05
0.02
0.01
Level of significance for one-tailed test N
0.025
0.005 7
714
786
0.893
0.929 8
643
738
0.833
0.881 9
0.600
0.700
0.783 10
0.564
0.648
0.745
0.794 11
0.536
0.618
0.709
0.755 12
0.503
0.587
0.671
0.727

42. Additional info
Step
Compare your observed value to the critical value to find out whether your results are statistically significant (and if you can reject the null hypothesis!)
Level of significance for two-tailed test
0.10
0.05
0.02
0.01
Level of significance for one-tailed test N
0.025
0.005 7
714
786
0.893
0.929 8
643
738
0.833
0.881 9
0.600
0.700
0.783 10
0.564
0.648
0.745
0.794 11
0.536
0.618
0.709
0.755 12
0.503
0.587
0.671
0.727

43. SPEARMANS RHO = Observed > Critical to be significant
Step
Observed value =
Critical value =
SPEARMANS RHO = Observed > Critical to be significant

44. Step How to write this up: The results are significant
suggesting there is a strong positive relationship between hours of sleep and scores on a test.
The observed value (+0.867) is greater than the critical value (+0.564)
at p<0.05, one-tailed, N=10.
Therefore, we can reject the null hypothesis.

45. In the exam You will NEVER have to calculate the test
But you do need to be able to use the observed value to decide whether the result is significant, and write a concluding statement.
Have a go with some past paper questions on the rest of this slide 

46. So…your data…
On the Blog, I will put the Excel package so you can run Spearmans Rho yourselves. This is what you need to do…. Spearmans practice (Bennett) Spearmans practice for PP.xls

47. Exam Practice
Jan 2012

49. Jan 2013

51. June 2010