Fikri M Abu-Zidan, MD, FRCS, PhD, DipApplStatsFikri M Abu-Zidan, MD, FRCS, PhD, DipApplStatsStatistics Editor, Emirates Medical Journal,Associate Professor, Head, Trauma Group,

Faculty of Medicine and Health Sciences, UAE University

Statistics: When and how?Statistics: When and how?

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Helmet

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Generalised Linear ModelGeneralised Linear Model

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It is a tool to summarize and compare data in an It is a tool to summarize and compare data in an informative way and not an aim by itself. informative way and not an aim by itself.

SStatistics is a branch of mathematics dealing tatistics is a branch of mathematics dealing with the collection, analysis and interpretation with the collection, analysis and interpretation of masses of numerical data.of masses of numerical data.

Merriam- Webster 1997Merriam- Webster 1997

It can not replace proper research questions.It can not replace proper research questions.

Fishing for questions to fit the data after analyzing it is erroneous.Fishing for questions to fit the data after analyzing it is erroneous.

What is the type of the data?What is the type of the data?

How many groups are there?How many groups are there?

Are the data normally distributed?Are the data normally distributed?

One groupOne groupTwo groupsTwo groupsMore than two groupsMore than two groups

If not, either transform data or use non parametric methodsIf not, either transform data or use non parametric methods

Are the groups related or unrelated?Are the groups related or unrelated?

What is the objective of the analysis?What is the objective of the analysis?Define the research question before starting the analysisDefine the research question before starting the analysis

Questions to be answered

Types of dataTypes of data

Categorical dataCategorical data Color of the eye Color of the eye

TypeType ExampleExample

Binomial dataBinomial data Gender Gender

OrdinalOrdinal Likert Scale Likert Scale

IntervalInterval Weight Weight

Conclusions depend on1)1) Difference between the means Difference between the means 2) Variability of the results2) Variability of the results

Difference = Difference = xx11 –– xx22Difference = Difference = xx11 –– xx22Difference = Difference = xx11 –– xx22

Variance: Variance: ∑ (x-x)∑ (x-x)22 n-1n-1

xx

xx22

xx55 xx44

xxnn

xx11

xx33

Standard deviation (SD) = Standard deviation (SD) = VarianceVariance

Standard Error (SE) = Standard Error (SE) = nn

SDSD

Weight (kg)60 65 70 75 80 85 90 95

Group 1Group 1 Group 2

Assumptions involved in t testingAssumptions involved in t testing1) Normal distribution 1) Normal distribution 2) Same variability 2) Same variability

-1 SD +1 SD0

15.87%15.87%

68.26%

-1.96 SD +1.96 SD0

2.5 %

95 %

2.5 %

Height (cm)

150 155 160 165 170 175 180 185

FemalesFemales Males

Height (cm)

150 155 160 165 170 175 180 185

FemalesFemales Males

Height (cm)

160 165 170 175 180 185

Males

190

Sample sizeSample size

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We would not expect the actual differences We would not expect the actual differences to be more than approximately 2 standard to be more than approximately 2 standard errors away from zero, assuming, of course, errors away from zero, assuming, of course, that the results follows a normal distribution.that the results follows a normal distribution.

95% of all non-genuine differences will 95% of all non-genuine differences will lie between lie between ± 2± 2 standard errors. standard errors.

An innocent verdict does not necessarily An innocent verdict does not necessarily mean that a jury is convinced of a defendant’s mean that a jury is convinced of a defendant’s innocence. It may mean that the facts were innocence. It may mean that the facts were not strong enough. (Type II error)not strong enough. (Type II error)

The two groups being compared are assumed the same until proven different.

A large sample difference suggest a real A large sample difference suggest a real difference is inherently more appealing than the difference is inherently more appealing than the remote (5%) (Type I error), p < 0.05remote (5%) (Type I error), p < 0.05

Null hypothesis

Decided before analysisDecided before analysisJustified by the logic of comparisonJustified by the logic of comparisonClearly identified in report Clearly identified in report

Two-tailed testTwo-tailed test

Differences in either directionDifferences in either directionThe standard way of comparisonThe standard way of comparison

One-tailed test

Paired t-test

Do not analyze the results of a paired experiment Do not analyze the results of a paired experiment using an independent t test. This ignores the paired using an independent t test. This ignores the paired nature of the results and loses the advantages of this nature of the results and loses the advantages of this very sensitive test.very sensitive test.

BewareBeware

Pairs can be formed on natural basis (twin) or on a Pairs can be formed on natural basis (twin) or on a more arbitrary artificial basis. more arbitrary artificial basis. 

PPStatisticalStatisticalsignificancesignificance

ClinicalClinicalsignificancesignificance

PPPPPPStatisticalStatisticalsignificancesignificance

ClinicalClinicalsignificancesignificance

Placebo Placebo n=100 mean (SEM)n=100 mean (SEM) 120 (2) mmHg120 (2) mmHg

New drug New drug n=100 mean (SEM) 112 (2) mmHgn=100 mean (SEM) 112 (2) mmHg

tt = 8/2 = 4 = 8/2 = 4P < 0.05P < 0.05

Do not look through the p pinhole

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MeanMean MeanMean22

TransformationTransformation

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ylin

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ControlControl ShamShamoperatedoperated

IschaemiaIschaemiareperfusionreperfusion

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Time (Minutes)

MA

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S group, n=10

IR group, n=10

1.1.      The number of each groupThe number of each group2.2.      The mean value of each groupThe mean value of each group3.3.      The standard deviation of each groupThe standard deviation of each group4.4.      The range of resultsThe range of results5.5.      The calculated value of tThe calculated value of t6.6.      The degree of freedom involved The degree of freedom involved 7.7.      The type I error involved The type I error involved

ReportReport

ChecklistChecklist

What is the null hypothesis?What is the null hypothesis?

  What is the alternative hypothesis What is the alternative hypothesis (two-tailed or one-tailed test) ?(two-tailed or one-tailed test) ?

Are the two sets of results unrelated Are the two sets of results unrelated to one another?to one another?

What is theWhat is the critical value? critical value?5 % if you are carrying out a two-tailed test 5 % if you are carrying out a two-tailed test 10% if you are carrying out a one-tailed test10% if you are carrying out a one-tailed test

Does the t value exceeds the Does the t value exceeds the critical value?critical value?

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in p

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myl

in p

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InsulinInsulin pMpM

F = 46.6F = 46.6R = 0.82R = 0.82p < 0.0001p < 0.0001

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InsulinInsulin pMpM

F = 46.6F = 46.6R = 0.82R = 0.82p < 0.0001p < 0.0001

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F%

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MAP (mmHg)MAP (mmHg)

F = 1.8F = 1.8R = R = -- 0.220.22p < 0.2p < 0.2

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F%

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MAP (mmHg)MAP (mmHg)

F = 1.8F = 1.8R = R = -- 0.220.22p < 0.2p < 0.2

4.54.5

55

5.55.5

66

6.56.5

44 55 66 77Overall ratingOverall rating

Ave

rage

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qu

esti

ons

Ave

rage

of

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qu

esti

ons

Spearman Rank CorrelationSpearman Rank Correlation

r = 0.84p = 0.0002

CorrelationsCorrelations

Thank YouThank You