Test of significance application in biostatistics

Test of significance.. identifies which statistical test will be useful to analyse parametric and non Parametric data

1. WHAT TEST TO DO WHEN Dr.P.Parameshwari,M.D Senior Asssistant professor Chengalpattu Medical College

2. INTRODUCTION Data do not give up their secrets easily. They must be tortured to confess . Jeff Hopper, Bell Labs Statistics is an applied science to make sense out of this uncertainty . Serves as basis for inference in the medical research.

3. DESCRIPTIVE STATISTICS

4. DATA TYPES

5. LEVELS OF MEASUREMENT

6. NORMAL DISTRIBUTION(Gaussian)

7. SKEWED DISTRIBUTION

8. INFERENTIAL STATISTICS

9. INFERENTIAL STATISTICS Method of drawing conclusion about the population from the sample data Statistical inference is the act of generalizing from sample of the population with the calculated degree of certainty

10. STEPS IN STATISTICAL INFERENCE

11. NULL AND ALTERNATE HYPOTHESIS

12. NULL HYPOTHESIS ( H0) The null hypothesis is a statement of “no difference.” ALTERNATIVE HYPOTHESIS ( Ha ) The alternative is one-sided if it states that a parameter is larger or smaller than the null hypothesis value. It is two-sided if it states that the parameter is different from the null value (it could be either smaller or larger). H1 ≡ A > B or H2 ≡ B > A

13. ALPHA LEVEL Alpha ( α ) is the probability of making the wrong decision when null hypothesis is true .   Alpha  level, is also called the “significance level.” If the confidence level is 95%, then  alpha  would equal 1 - 0.95 or 0.05 . It is normally set at 5% (0.05) which means that there is a 1 in 20 chance of rejecting the null hypothesis when it is true.

14. POWER OF THE STUDY Power of the study is the probability of correctly rejecting null hypothesis when it is false Acceptable value of β is set at 1 in 5, i.e., a probability of 0.2 (β )(20%) Detecting a real difference when it does exist. i.e., power = (1− β ) of no less than 0.8(i.e., 80%).

15. TYPE I and TYPE II ERROR Type I error Rejecting the null hypothesis when it is true. Indicates false positives Patient to have a disease when in fact the patient does not have the disease Type II error Accepting the null hypothesis when it is false. Indicates false negatives Blood test failing to detect the disease it was designed to detect, in a patient who really has the disease ;

16. P VALUE P value gives the probability of any observed difference having happened by chance . P = 0.05 means that the probability of the difference having happened by chance is 0.05, i.e. 1 in 20. The lower the P value, the less likely it is that the difference . P values make an informed judgment as to whether the observed effect is likely to be due to chance taken in the context of other available evidence

17. P VALUE INTERPRETATION • A small P value (<0.05) indicates strong evidence against the null hypothesis , so it is rejected. The alternative hypothesis may be accepted although it is not 100% certain that it is true. The result is said to be statistically “significant” • An even smaller P value (<0.01) indicates even stronger evidence against the null hypothesis. The result may be considered statistically “highly significant” • A large P value (>0.05) indicates weak evidence against the null hypothesis. Therefore, it cannot be rejected, and the alternate hypothesis cannot be accepted

18. CONFIDENCE INTERVAL (CI) A  confidence interval  is an  interval  estimate combined with a probability statement . I f we used the same sampling method to select different samples and computed an  interval  estimate for each sample, we would expect the true population parameter to fall within the  interval  estimates 95% of the time . It i s an alternate w ay of expressing stat i stical significance. (Statistical percision ) The narrower the CI, the more likely the true

19. CONFIDENCE INTERVAL

20. Check For Normality P a r am e tric Non- P a r am e tric YES NO

21. Normality SD > ½ mean Non-normal / Skewed data S D < ½ mean Normal data

22. TESTS FOR NORMALITY Kolmogorov -Smirnov (K-S) test Shapiro- Wilk test D’Agostino -Pearson omnibus test Jarque-Bera test Pearson's chi-squared test.

23. POST HOC TEST

24. OBJECTIVE PARAMETRIC NONPARAMETRIC Two groups- continuous Student’s t-test Mann-Whitney U test > 2 groups - continuous One-way ANOVA Kruskal-Wallis test Within group Paired t-test Wilcoxon signed-rank Linear association between two continuous variables Pearson correlation Spearman’s rank test

25. REMEMBE R . . . Statistical significance does not imply clinical importance Bad analysis can be redone but bad designs cannot be refixed

26. Any questions