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