t Test

Appropriate techniques of statistical analysisAnil C Mathew PhDProfessor of Biostatistics &General Secretary ISMSPSG Institute of Medical Sciences and ResearchCoimbatore 641 004Types of studiesCase studyCase seriesCross sectional studiesCase control studyCohort studyRandomized controlled trialsScreening test evaluationData analysis-Case seriesMeasures of averagesMean, Median, ModeLength of stay for 5 patients1,3,2,4,5Mean length of stay 3 daysMedian length of stay 3 daysMode length of stay No mode

Which is the best averageMeanMedianModeDBP817976Height180 180180SAL7.57.68.1Data analysis-case seriesFrequency distribution

RBCFrequencyRelative frequency5.95-7.9510.0297.95-9.9580.2299.95-11.95140.40011.95-13.9590.25713.95-15.9520.05715.95-17.9510.029Total351.000Design of Cohort Study TimeDirection of inquiryPopulationPeople without the diseaseExposedNot Exposedno disease diseaseno diseasedisease6

Is obesity associated with adverse pregnancy outcomes? Women with a Body Mass Index > 30 delivering singletons. Ref- University of Udine, Italy,2006Preterm Birth No preterm birth%Obese1635T=5131.4Normal46487T=5338.6RR=3.65Design of Case Control Study DiseaseNo Disease Not ExposedExposed Not Exposed Exposed8Results of a Case Control Study Lung Cancer(D+)No Lung Cancer (D-)Totals Exposed (E+)80 a30 ba + bNon exposed (E-)20 c70 dc + dTotals 100 a + c100 b + d9Analysis of Case-control study Odds ratio = a*d/b*c =80*70/30*20 =9.3Data Analysis-Screening Test Evaluation-Whether the plasma levels of (Breast Carcinoma promoting factor) could be used to diagnose breast cancer?Positive criterion of BCPF >150 units vs. Breast Biopsy (the gold standard) D+ D-BCPF TestT+570150720T-30850880 600 1000 1600 TP = 570FN = 30FP = 150TN = 850Sensitivity = P (T+/D+)=570/600 = 95%Specificity = P(T-/D-) = 850/1000 = 85%False negative rate = 1 sensitivityFalse positive rate = 1 specificityPrevalence = P(D+) = 600/1600 = 38%Positive predictive value = P (D+/T+) = 570/720 = 79%Tradeoffs between sensitivity and specificityWhen the consequences of missing a case are potentially graveWhen a false positive diagnosis may lead to risky treatment

Data analysis-case seriesMeasures of variation

RangeStandard deviation

Group 1Group 2292530303135

Data analysis- Analytical studiesTests of significanceCase Study 1: Drug A and Drug BAim: Efficacy of two drugs on lowering serum cholesterol levels

Method: Drug A 50 Patients Drug B 50 Patients

Result: Average serum cholesterol level is lower in those receiving drug B than drug A at the end of 6 months What is the Conclusion?Drug B is superior to Drug A in lowering cholesterol levels : Possible/Not possible

B) Drug B is not superior to Drug A, instead the difference may be due to chance: Possible/Not possible

C) It is not due to drug, but uncontrolled differences other than treatment between the sample of men receiving drug A and drug B account for the difference: Possible/Not possible

D) Drug A may have selectively administrated to patients whose serum cholesterol levels were more refractory to drug therapy: Possible/Not possibleObserved difference in a study can be due to

1) Random change

2) Biased comparison

3) Uncontrolled confounding variablesSolutions: A and BTest of Significance p valueP Table REJECT Ho

GENERAL STEPS IN HYPOTHESIS TESTING 1) State the hypothesis to be tested

2) Select a sample and collect data

3) Calculate the test statistics

4) Evaluate the evidence against the null hypothesis

5) State the conclusion

Commonly used statistical testsT test-compare two mean valuesAnalysis of variance-Compare more than two mean valuesChi square test-Compare two proportionsCorrelation coefficient-relationship of two continuous variablesData entry formatTreatmentAgeweightDiabetesPainscore-bPainscore-aVomiting1215019601245301090125551991128500106112960010501206501080026600990025901991024801991028890108102286110910224501090Example t testBody temperature cSimple febrile seizureN = 25Febrile without seizureN =25P valueMean39.0138.64P