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Introduction to Statistical Methods
By Tom Methven
Digital slides and tools available at:www.macs.hw.ac.uk/~mjc/teaching/
ResearchMethods
Moving Bell-curves
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
Worked Example
Level Of Measurement (Non-Parametric)
• Nominal :
• Ordinal :
Tom Pawel Khem
Mike Stefano Al
Andy Patrick Lin
Level Of Measurement (Parametric)
• Interval :
• Ratio :
Statistic Basics
• For the results: 9,2,5,3,6,9,5,6,4,2,6
Worked Example Results
• Time (Ratio scale)• Results:
Interface 1 Interface 2
Person 1 4.28 4.38
Person 2 2.78 4.99
Person 3 7.63 4.30
Person 4 7.93 4.27
Person 5 7.19 5.50
Person 6 5.73 5.22
Person 7 8.40 4.09
Person 8 5.88 4.46
Person 9 5.60 4.00
Person 10 4.89 4.90
Mean: 6.03 4.61
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 First 2 FirstPerson 1 Person 2Person 3 Person 4Person 5 Person 6Person 7 Person 8Person 9 Person 10
Latin Squares
• A way of counter-balancing condition order
• E.g. For three possible conditions:
Order of conditions or trials
Group 1 A B C
Group 2 B C A
Group 3 C A B
Accuracy of the Mean
• Variance:
• Standard Deviation:
• Standard Error:
Degrees of Freedom
• For sample populations, often ‘N – 1’ is used
Student’s T-Test
• Used for comparing the means of two groups
• Assumes populations are normally distributed
Student’s T-Test
• Create a ‘null hypothesis’• Create an alternate hypothesis
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
Worked Example T Result
= 1.420756421
= 1.985348881
= 10
t-value = 2.26
Interpreting T-Value
p-value = 0.025
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
[letter]-values
• t-value: Result of the t-test
• p-value: Is it statistically significantly?
• r-value: Is the effect substantial in reality?
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.”
Error Bars
Error bars: Plot standard error
Excel Example
• TTEST in Excel will give a ‘p-value’ directly
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
Recommended Reading