1. Statistics for biological data
Significance tests for continuous variables
Aya Elwazir
Teaching assistant of medical genetics, FOMSCU
PHD student, University of Sheffield

2. NOT normally distributed
Choice of test
Normally distributed
NOT normally distributed
Descriptives
Mean ± SD
Median (IQR)
Significance tests
Parametric tests
Non-Parametric tests
≤2 groups
T test
Wilcoxon
Kruskal Wallis
Friedman
> 2 groups
ANOVA

3. T-test One sample t-test Independent samples t-test Dependent samples
Group 1
Sample
Group 2
Sample A
Sample B
Sample
Population
Same group

4. One sample t-test H0 x̄ = µ x̄ = 72 H1 x̄ ≠ µ x̄ ≠ 72
Compare the mean of the sample [x̄] with a pre-specified value (population mean [µ])
Continuous
Average score of medical students in UK universities = 72
Student name
Score
John
63.5
Sue
71.2
Sarah
56.6
Nick
80.0
Ben
79.4
We think that the average score of medical students in the University of Sheffield will be different H0
x̄ = µ
x̄ = 72 H1
x̄ ≠ µ
x̄ ≠ 72

5. Independent sample t-test
Compare the mean between 2 independent groups [x̄1 , x̄2]
Categorical
(grouping)
Continuous
Average score of medical students between University of Sheffield & University of Leeds
Student name
University
Score
John
Sheffield
63.5
Marwa
71.3
Sarah
56.5
Nick
80.0
Ben
79.3
Ruby
Leeds
83.3
Ahmed
73.5
Beth
55.0
Sue
67.0
Claire
46.5 H0
x̄1 = x̄2 H1
x̄1 ≠ x̄2

6. Independent sample t-test
Assumptions
Normality
Independent groups
Equal variance between groups
Group 1
Group 2

7. Independent sample t-test
Why does variance matter?
Equal mean - Equal variance
Different mean - Equal variance
var.equal = T
Group 1
Group 2
t- test
Group 1
Group 2
Assumes Equal variance
‘R’ Default
Equal mean - Different variance
Different mean - Different variance
Welch
t- test
Group 1
Group 2
Group 1
Group 2
Assumes Different variance

8. Dependent sample t-test
Categorical
(grouping)
Also called paired t-test
Continuous
Compare the mean between 2 dependent groups [x̄ , x̄’]
Student name
Pre/
post
Score
John
Pre
63.5
Sue
71.2
Sarah
56.6
Nick
80.0
Ben
79.4
Post
65.5
80.3
52.5
80.5
86.3
Average score of medical students at University of Sheffield before & after a ‘course revision’ module
Continuous
Student name
Pre
Post
John
63.5
65.5
Sue
71.2
80.3
Sarah
56.6
52.5
Nick
80.0
80.5
Ben
79.4
86.3 H0
x̄ = x̄‘ H1
x̄ ≠ x̄‘
Wide format
Long format

9. NOT normally distributed
Choice of test
Normally distributed
NOT normally distributed
Descriptives
Mean ± SD
Median (IQR)
Significance tests
Parametric tests
Non-Parametric tests
≤2 groups
T test
Wilcoxon
Kruskal Wallis
Friedman
> 2 groups
ANOVA

10. One-Sample Wilcoxon Signed Rank Test Wilcoxon Signed-Rank Test
Wilcoxon-test
One-Sample Wilcoxon Signed Rank Test
Wilcoxon–
Mann–Whitney test
Wilcoxon Signed-Rank Test
Sample
Group 1
Sample
Group 2
Sample A
Sample B
Sample
Population
Same group

11. NOT normally distributed
Choice of test
Normally distributed
NOT normally distributed
Descriptives
Mean ± SD
Median (IQR)
Significance tests
Parametric tests
Non-Parametric tests
≤2 groups
T test
Wilcoxon
Kruskal Wallis
Friedman
> 2 groups
ANOVA

12. Repeated measures ANOVA
One-way
ANOVA
Two-way
ANOVA
Repeated measures ANOVA
1 categorical
(grouping variable>2 levels)
1 numeric/continuous variable
2 categorical
(grouping variables)
1 numeric/continuous variable
Equivalent to dependant t-test
But >2 repeated measures

13. One-way ANOVA H0 x̄1 = x̄2 = x̄3 H1 x̄1 ≠ x̄2 ≠ x̄3
Equivalent to independent t-test but for > 2 groups
Categorical
(grouping)
Continuous
Compare the mean between 3 or more independent groups [x̄1 , x̄2, , x̄3 ]
Student name
University
Score
John
Sheffield
63.5
Marwa
71.3
Sarah
56.5
Nick
Manchester
80.0
Ben
79.3
Ruby
83.3
Ahmed
Leeds
73.5
Beth
55.0
Sue
67.0
Claire
46.5
Average score of medical students between University of Sheffield, University of Leeds and University of Manchester H0
x̄1 = x̄2 = x̄3 H1
x̄1 ≠ x̄2 ≠ x̄3

14. Two-way ANOVA 2 categorical (grouping variables)
Continuous
Student name
University
Gender
Score
John
Sheffield
Male
63.5
Marwa
Female
71.3
Sarah
56.5
Nick
Manchester
80.0
Ben
79.3
Ruby
83.3
Ahmed
Leeds
73.5
Beth
55.0
Sue
67.0
Claire
46.5
Average score of medical students between University of Sheffield, University of Leeds and University of Manchester AND between males & females

15. Repeated measures ANOVA
Categorical
(grouping)
Equivalent to paired t-test but for >2 repeated measures
Compare the mean between > 2 dependent groups [x̄ , x̄’ , x̄’’]
Continuous
Student name
Exam
Score
John
Mid-term
63.5
Sue
71.2
Sarah
56.6
Term
65.5
80.3
52.5
Final
85.5
86.0
50.5
Average score of medical students at University of Sheffield for mid-term, term & final H0
x̄ = x̄‘ = x̄‘‘
Student name
Mid-term
Term
Final
John
63.5
65.5
85.5
Sue
71.2
80.3
86.0
Sarah
56.6
52.5
50.5 H1
x̄ ≠ x̄‘≠ x̄‘‘
Long format
Wide format

16. Post Hoc test
Only done if ANOVA result is significant (p<0.05) Indicates the significant result was due to differences in which groups
Sheffield
Manchester
Leeds -
0.032
0.251
0.042
Sheffield ≠ Manchester
Leeds ≠ Manchester

17. NOT normally distributed
Choice of test
Normally distributed
NOT normally distributed
Descriptives
Mean ± SD
Median (IQR)
Significance tests
Parametric tests
Non-Parametric tests
≤2 groups
T test
Wilcoxon
Kruskal Wallis
Friedman
> 2 groups
ANOVA

18. Kruskal Wallis - Friedman
Wallis test
Friedman test
Equivalent to one-way ANOVA
for non-parametric data
Equivalent to repeated measures ANOVA
for non-parametric data

19. Statistics for biological data
Course Objectives
Introduction to statistics
1. Contingency tables & testing for categorial variables
2. Normality testing & Descriptive statistics
3. Testing for continuous variables
Lots of practice!