1. Introduction to Statistical Methods By Tom Methven Digital slides and tools available at: www.macs.hw.ac.uk/~mjc/teaching/ResearchMethods

2. Moving Bell-curves

3. Designing the Experiment 1. Define exactly what you want to measure 2. Pick which statistical test to use, first 3. Decide on your experimental design

4. Worked Example Vs.

5. Level Of Measurement (Non- Parametric) Nominal : Ordinal : TomPawelKhem MikeStefanoAl AndyPatrickLin

6. Level Of Measurement (Parametric) Interval : Ratio :

7. Statistic Basics For the results: 9,2,5,3,6,9,5,6,4,2,6

8. Worked Example Results Time (Ratio scale) Results: Interface 1Interface 2 Person 14.284.38 Person 22.784.99 Person 37.634.30 Person 47.934.27 Person 57.195.50 Person 65.735.22 Person 78.404.09 Person 85.884.46 Person 95.604.00 Person 104.894.90 Mean:6.034.61

9. Randomisation and Ordering Effects People might get better at playing virtual pianos! With many conditions or trials, it is easiest to show then in a random order 1 First2 First Person 1Person 2 Person 3Person 4 Person 5Person 6 Person 7Person 8 Person 9Person 10

10. Latin Squares A way of counter-balancing condition order E.g. For three possible conditions: Order of conditions or trials Group 1ABC Group 2BCA Group 3CAB

11. Accuracy of the Mean Variance: Standard Deviation: Standard Error:

12. Degrees of Freedom For sample populations, often ‘N – 1’ is used

13. Student’s T-Test Used for comparing the means of two groups Assumes populations are normally distributed

14. Student’s T-Test Create a ‘null hypothesis’ Create an alternate hypothesis

15. Dependent T-Test Used to compare the results of two groups = Average difference = Expected difference (0 for null hypothesis) = Standard deviation of differences = Sample Size

16. Worked Example T Result = 1.420756421 = 1.985348881 = 10 t-value = 2.26

17. Interpreting T-Value p-value = 0.025

18. Effect Size How important the result is in practical terms – r = 0.10 (small effect) – 1% of total variance – r = 0.30 (medium effect) – 9% of total variance – r = 0.50 (large effect) – 25% of the variance

19. [letter]-values t-value: Result of the t-test p-value: Is it statistically significantly? r-value: Is the effect substantial in reality?

20. Final Results p-value = 0.025 r-value = 0.60 Degrees of freedom = 9 “The results show that Wii Piano allows users to play a set tune successfully significantly faster than iPiano (p = 0.025). In addition, the effect size was large (r = 0.6), showing the result was substantial in real terms.”

21. Error Bars Error bars: Plot standard error

22. Excel Example TTEST in Excel will give a ‘p-value’ directly

23. Summing Up Dependant t-test when using a single group Avoid ordering effects Use ‘TTEST’ in Excel to get p-value easily Check p < 0.05 and quote the value and result

24. Recommended Reading