Transcript Introduction to Statistical Methods Pictorial

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
•
Vs.
Level Of Measurement (NonParametric)
• 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!
1 First
Person 1
Person 3
Person 5
Person 7
Person 9
2 First
Person 2
Person 4
Person 6
Person 8
Person 10
• With many conditions or trials, it is easiest to
show then in a random order
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
0.6
0.5
0.4
Sample Curve A
0.3
0.2
Sample Curve B
0.1
0
• 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
7
6.5
6
Mean 1
5.5
Mean 2
5
4.5
4
0
1
2
3
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