1. Data Analysis for the BSc Year
Sachin Ananth BSc (Hons)
Respiratory Science BSc (Class of 2018)

2. Lecture Objectives To understand common statistical terms
To learn how to calculate common statistical terms using raw data
To learn which statistical test to use during your projects

3. Analysing Published Data
This is important for ICAs and background reading for your project

4. Null and Alternative Hypotheses
Null Hypothesis (H0)
No statistical difference between the variables
Alternative Hypothesis (H1)
Statistical difference between the variables
Null Hypothesis = nothing interesting going on (Null is Dull)
I am explaining this as the Null Hypothesis is important in the definition of the P value
Null Hypothesis = nothing interesting going on
You want to NULLify the NULL hypothesis – because you do want to see a difference!

5. Type I vs Type II Error Type I Error
Probability of rejecting Null Hypothesis when it is actually true
i.e. false positive
Type II Error
Probability of accepting Null Hypothesis when it is actually false
i.e. false negative

6. Statistical Power
Ability of a study to pick up a difference when it actually exists
i.e. probability that a Type II error will NOT be made
Increase power by:
Increase sample size
Increase effect size
Increase precision of measurement
Remember: type II error is a false negative

7. P Value
“Probability of observed result occurring when Null Hypothesis is true”
Translation: probability of finding a difference where there actually is no difference
P < 0.05 = significant result
A lower P value does not mean that the difference is meaningful – it just shows that there is a difference
P < 0.05 means that there is less than 5% chance of detecting a difference when there is no difference
A lower P value does not mean that the difference is meaningful – it just shows that there is a difference e.g. average BP 120/80 vs 117/78 could have a P < 0.05 if there is a large enough n number ... But is this difference clinically meaningful? If you comment on an example like this in your ICA/project = will look really clever!

8. Relative Risk (RR)
Relative Risk (RR) = risk of developing disease in exposed group vs unexposed group
Used in prospective studies
1.0
0.5
1.5
↓50% risk
Equal risk
↑50% risk
You will see relative risk LOTS when you are reading papers – understanding what these values actually mean will make it MUCH easier to read the results sections of papers

9. Relative Risk (RR)
Relative Risk (RR) = risk of developing disease in exposed group vs unexposed group
Used in prospective studies
Diseased
Not diseased
Exposed A B
Not exposed C D
Camera = take pic of this slide if you want
A / (A+B)
C / (C+D)
RR =

10. Relative Risk (RR)
Relative Risk (RR) = risk of developing disease in exposed group vs unexposed group
Used in prospective studies
100
100
Diseased
Not diseased
Exposed A B
Not exposed C D 80 20 30 70 80 30 80
A / (A+B)
C / (C+D)
100
RR =
= 2.7 (↑170% risk) 30
100

11. Relative Risk (RR)
Relative Risk (RR) = risk of outcome in treatment group vs control group
Used in prospective studies
100
100
Diseased
Not diseased
Treatment A B
Control C D 40 60 60 40
Relative Risk can also be calculated in treatment group vs control group (just substitute treatment for exposed and control for not exposed in the table) 40 60 40
A / (A+B)
C / (C+D)
100
RR =
= 0.67 (↓33% risk) 60
100

12. Relative Risk (RR)
Relative Risk of early preterm delivery in n-3 group?
You have 90 seconds to answer!
Diseased
Not diseased
Exposed A B
Not exposed C D
A / (A+B)
C / (C+D)
RR =

13. Relative Risk (RR)
Relative Risk of early preterm delivery in n-3 group?
Diseased
Not diseased
Exposed A B
Not exposed C D 61
A / (A+B)
C / (C+D)
2734 61
2673
RR =
= 1.12 55
2752 55
2697

14. Hazard Ratio (HR)
Similar to Relative Risk – used when risk is not constant with respect to time
Used in context of survival over time
Uses info collected at different times
Will not be expected to calculate Hazard Ratio, just expected to interpret it
In this graph, survival changes with respect to time (it is worst in the first 100 days, as this is when most complications of TB occur)
HR = 0.79  means 21% reduction of risk in people treated with isoniazid, over 500 days

15. Odds Ratio (OR)
Odds Ratio (OR): odds that outcome will occur with exposure vs without exposure
Used in retrospective studies (esp case-control)
1.0
0.5
1.5
↓50% odds
Equal odds
↑50% odds
Case-control = take cases (diseased patients) and controls (un-diseased patients)  look back at the differences in exposures to risk factors in cases and controls

16. Odds Ratio (OR)
Odds Ratio (OR): odds that outcome will occur with exposure vs without exposure
Used in retrospective studies (esp case-control)
Diseased
Not diseased
Exposed A B
Not exposed C D
Use the same table that you would use for Relative Risk – the calculation is different
Camera = take pic of this slide if you want
A / C
B / D
OR =

17. Odds Ratio (OR)
Odds Ratio of previous suicide attempt in suicidal group?
Diseased
Not diseased
Exposed A B
Not exposed C D
You have 90 seconds to answer!
= study which contains this table
A / C
B / D
OR =

18. Odds Ratio (OR)
Odds Ratio of previous suicide attempt in suicidal group?
Diseased
Not diseased
Exposed A B
Not exposed C D
89.6
A / C
B / D
10.4
89.6
71.6
OR =
= 3.42
71.6
28.4
10.4
28.4

19. 95% Confidence Interval
The population mean will lie within this range 95% of the time
Example:
Translation: if you repeat this experiment 100 times, the average height will be between cm 95 times
Average height = 170cm (95% CI cm)

20. 95% Confidence Interval
The population mean will lie within this range 95% of the time
Narrower 95% confidence intervals are better
Confidence intervals can be used for Relative Risk, Odds Ratio
e.g. RR was 1.30 (95% CI ) = negative result as confident interval crosses 1

21. Incidence vs Prevalence
Number of new cases over specific period of time
e.g. 10,000 new cases of diabetes per year
Prevalence
Number of cases at a specific period of time
e.g. 50,000 cases of diabetes in the UK

22. Absolute Risk Reduction (ARR)
Difference in the incidence of disease between 2 groups
P(event occurring in control group) – P(event occurring in treatment group)
100
30% risk of death
ARR = 30 – 20
= 10%
100
20% risk of death

23. Relative Risk Reduction (RRR)
Absolute Risk Reduction
P (event occurring in control group)
X 100
100
30% risk of death
ARR = 30 – 20
= 10%
RRR = (10/30) x 100
= 33.3%
100
20% risk of death

24. Number Needed to Treat (NNT)
Number of patients needed to be treated to prevent one event 1
ARR (in decimal format)
100
30% risk of death
If you read a paper and work out the NNT by yourself, and then use this in an ICA/project thesis = will look really good
ARR = 30 – 20
= 10%
NNT = 1/0.1
= 10
100
20% risk of death

25. Number Needed to Treat (NNT)
Calculate the Number Needed to Treat
ARR = P(event occurring in control group) – P(event occurring in treatment group)
NNT = 1/ARR
You have 90 seconds to answer!

26. Number Needed to Treat (NNT)
Calculate the Number Needed to Treat
ARR = P(event occurring in control group) – P(event occurring in treatment group)
NNT = 1/ARR
ARR = 5.9% - 5.1% = 0.8%
Important to realise that “standard-treatment” group is the control group, and “genotype-guided group” is the treatment group
Remember: to calculate the NNT, you divide 1 by the ARR in decimal format (hence we have divided 1 by in this example)
NNT = 1/0.008 = 125!

27. Summary Absolute Risk Reduction (ARR):
P(event occurring in control group) – P(event occurring in treatment group)
Relative Risk Reduction (RRR):
Number Needed to Treat (NNT): 1
ARR (in decimal format)
Absolute Risk Reduction
P (event occurring in control group)
X 100

28. Sensitivity vs Specificity
Sensitivity = % of true positives that are identified as positives
Specificity = % of true negatives that are identified as negatives
Sensitivity = a/a+c
Specificity = d/d+b
Gold Standard
Positive
Negative
Your Test a b c d

29. Analysing Experimental Data

30. Parametric vs Non-Parametric
Parametric Test for normally distributed data
Non-Parametric Test for non-normally distributed data
Can turn non-normal data into normal by plotting the log of the non-normal variable – I would advise against doing this though…

31. Statistical Tests
Reason for test
Parametric Test
Non-Parametric Test
Compare 2 samples from same population
e.g. boys’ heights vs girls’ heights
Unpaired t-test
Mann-Whitney U test
Compare 2 sets of observations on a single sample = “paired data”
e.g. weight of babies before and after feed
Paired t-test
Wilcoxon matched-pairs test
= one-tailed vs two-tailed t-test eplaination
Paired data = each data point in one data set is related to one data point in another data set
Always pick “two-tailed t-test”, rather than “one-tailed t-test”

32. Statistical Tests Reason for test Parametric Test Non-Parametric Test
Compare 3+ sets of observations on a single sample
e.g. plasma glucose 1, 2 and 3hrs after a meal
One-way ANOVA
One-way ANOVA by ranks = “Kruskal Wallis Test”
As above, but testing influence of 2 different variables
e.g. if above differs between men and women
Two-way ANOVA
Two-way ANOVA by ranks = “Friedman Test”
ANOVA stands for Analysis of Variance

33. Statistical Tests Must show r value and P value Reason for test
Parametric Test
Non-Parametric Test
Relationship between 2 continuous variables
e.g. HBA1c vs triglycerides
Pearson’s r
Spearman’s rank correlation coefficient
This graph was from my BSc project!
Must show r value and P value

34. Statistical Tests Reason for test Parametric Test Non-Parametric Test
Relationship between 2 continuous variables
e.g. HBA1c vs triglycerides
Pearson’s r
Spearman’s rank correlation coefficient
Relationship between 2 continuous variables, allowing one value to predict the other
e.g. how peak flow varies with height
Regression by least-squares method
N/A
Relationship between 1 dependent variables and many predictor variables
e.g. how BP is affected by age, BMI, salt intake
Multiple regression by least-squares method
N/A

35. What is “regression”?
Regression = equation that allows one variable to predicted from another
E.g. input patients’ heights into a computer to create an equation that predicts their weights
Multiple regression = equation that allows one variable to predicted from many variables
E.g. input patients’ heights, ages, sex, diet… into a computer to create an equation that predicts their weights
You will read the word “regression” lots in papers – it is important to know what it means (roughly!)

36. Data Dredging
= analysing your data based on various subgroups (age, gender, height, favourite colour) so that you find a significant result
Bad because the more tests you do = more likely to find a result by chance (if P < 0.05, 1 in 20 statistically significant results are by chance!)
Need to do Bonferroni Correction:
0.05
Number of tests you will do
Example of data dredging: you try to identify a difference between a treatment group and control group. So you decided to stratify the groups based on many different variables, like gender, age, presence of certain risk factors… if you do enough tests, you are bound to find a difference in the groups (e.g. there could be a specific difference if you looked at groups stratified by presence of atopy)
= new significance level

37. Question
Which test would you use to compare patients’ blood pressures before and after they go on a rollercoaster? The data is not normally distributed.
Unpaired t-test
Paired t-test
Mann-Whitney U test
Wilcoxon matched-pairs test
Harry Styles test

38. Question
Which test would you use to compare patients’ blood pressures before and after they go on a rollercoaster? The data is not normally distributed.
Unpaired t-test
Paired t-test
Mann-Whitney U test
Wilcoxon matched-pairs test – paired, non-parametric
Harry Styles test

39. Microsoft Excel for Statistics
T-test
ANOVA (one-way and two-way)
Linear regression
YouTube tutorials are very helpful for this!

40. GraphPad Prism for Statistics
Can do most statistical tests on GraphPad Prism
Easy to use
Graphs look professional
Get a 30-day free trial during your project
The software remembers your computer, so you cannot sign up for multiple trials using different addresses!
Ask the researchers on your team if they have a free pirated copy of GraphPad Prism (most do- even Heads of Department…)

41. GraphPad Prism for Statistics
Select your data and click “Analyse”
Select your data

42. GraphPad Prism for Statistics
Click the appropriate test

43. GraphPad Prism for Statistics
Choose further options

44. GraphPad Prism for Statistics
Results sheet
P value summary
NS: P > 0.05
*: P < 0.05
**: P < 0.01
***: P < 0.001

45. Mentimeter Champions

46. Any Questions?
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