![Example-2
Example: Prevalence of diabetes
in gazetted employees in
Mubmbai in 400 randomly
selected officers was 5%. What
is your estimate about
prevalence of diabetes in these
officers?
p i.e. proportion of affected is 5 % = 0.05
1-p i.e. proportion of unaffected = (1-0.05) = 0.95
SEp = √ { (p x (1-p)/ n) = √ [(0.05 x 0.95)/400] = 0.011
P est = 0.05 +/- 2(0.011) = 0.0228; 0.072](https://izqule7twkl7vq3ljkxejyz-s-a2157.bj.tsgdht.cn/16-180508135943/85/Inferential-statistics-8-320.jpg)
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Inferential statistics
- 1. Inferential Statistics Dr. A.P. Kulkarni
- 2. Outline Null hypothesis Common situations What is inferential statistics? Concept of probability Choice of statistical test
- 3. What is inferential statistics? Process of drawing conclusions from descriptive statistics Scientific process & not half-hazard Use of concepts like Confidence limits Null hypothesis Probability
- 4. Common situations Association in two/ more variables Difference in two samples Population parameter from sample Correlation in two / more variables Choice of statistical test
- 5. Estimate about population from sample Population constant = Parameter Estimate from sample = Sample statistics (Point estimate) Variable could be: QUANTITATIVE QUALITATIVE Test statistics calculated is Standard Error Presumption: Sample is representing population
- 7. Example-1 Example: Mean Hb% of medical students (allopathic) of Maharashtra is unknown. In a representative sample of 500 medicos it was found to be 11.2 gm% with SD of 2.0 gm% What is your estimate of Hb% of medicos? SE m = SD / ⱱ(n) = 3.5 / ⱱ(500) = 0.1565 M est = m ± 2SEm = 11.2 ± (2* 0.1565) = 10.88, 11.51
- 8. Example-2 Example: Prevalence of diabetes in gazetted employees in Mubmbai in 400 randomly selected officers was 5%. What is your estimate about prevalence of diabetes in these officers? p i.e. proportion of affected is 5 % = 0.05 1-p i.e. proportion of unaffected = (1-0.05) = 0.95 SEp = √ { (p x (1-p)/ n) = √ [(0.05 x 0.95)/400] = 0.011 P est = 0.05 +/- 2(0.011) = 0.0228; 0.072
- 9. Hypothesis test about difference If there is difference in two or more samples then two questions 1. Has the difference occurred due to sampling variation ? (NULL Hypothesis accepted) 2. Is the difference because samples belong to populations with different parameters? (Research hypothesis accepted) The variable being examined could be: QUALITATIVE QUANTITATIVE 3. Here we use various tests of significance
- 10. Tests of Significance Basic steps in any test of significance are Identify the variables & choose appropriate test of significance Calculate the test statistics like Z, t, Chi-Sq & other required things like degrees of freedom) Find probability Interpret: A) Accept NH & Reject RH B) Reject NH, Accept RH Decision level of Probability = 0.05 If P => 0.05: Accept NH P < 0.05: Reject NH
- 11. Common Tests of Significance Type of variable Sample size Groups compared Test of choice Test statistic Qualitative Large 2 Z-test (Difference in 2 proportions) Z > 2 Chi-square Chi-square, DF Small 2 or more Chi-square Chi-square, DF Small 2 Fischer Exact test P Quantitative Large 2 Z-Test (Difference in 2 means) Z Small 2 t-test t, df >2 ANOVA F, DF
- 12. Example-1 Example: In clinical trial of two drugs (A,B - new) in a disease 100 patients were treated with drug A, 80 were cured. In 200 comparable patients treated with drug-B, 190 were cured. Cure rate with drug A = 80% Cure rate with drug B = 95% What is NH? What is AH? What is type of variable? Which test? Why?
- 13. Example-2 Example: In 100 pregnant mothers mean Hb% was 9.0 gm% with SD 2 gm%. In comparable 200 non-pregnant women Hb% was 11 gm % with SD 2.5 gms% What is NH? What is AH? What is type of variable? Which test? Why?
- 14. Example-3 Example: In 15 AIDS patients mean CD4 count was 200 with SD 10. In 20 comparable patients with no AIDS it was 700 with SD 15 What is NH? What is AH? What is type of variable? Which test? Why?
- 15. Example-4 Example: In a trial two anti-anemic drugs, these were compared with standard treatment of Ferrous sulphate. The patients were randomized in 3 groups of 50 each. Mean Hb% with SD after 3 months are compared. What is NH? What is AH? What is type of variable? Which test? Why?
- 16. Example-5 Example: Following data shows weight gain in mice after giving two drugs What is NH? What is AH? What is type of variable? Which test? Why? Drug Weight gain YES Weight gain NO Total A 4 2 6 B 1 5 6 Total 5 7 12
- 17. Errors in test of significance Alpha (Type-1) Probability of rejecting a true NH Possibility of bringing a useless drug in market It is the P level of test Usually kept at 0.05 (5%) Confidence Level = 1-alpha Beta (Type-2) Probability of accepting a false NH Possibility of prohibiting a good drug from entering market Usually kept at 0.20 (20%) Power of test = 1-beta
- 18. Association between two variables This situation is seen in ANALYTICAL studies The test statistics is Odds Ratio or Relative Risk This being estimate from sample, requires 95% CI Software can find 95% CI
- 19. Interpretation of OR/ RR Theoretical Range: 0.0 to infinity NH : OR / RR = 1.0, observed value due to sampling variation Lower 95% CI, Point Estimate Higher 95% CI 0.0 1.0 Infinity NH Rej NH Acc NH Acc NH Rej
- 20. Interpretation of Correlation Relationship between two QUANTITATIVE variables (say like Ht & Wt) Test statistics: (r) Correlation coefficient Theoretical range: -1.0 to +1.0 If (-) ve: Negative correlation If (+) ve: Positive correlation If above 0.6, strong correlation
- 21. Interpretation of Correlation NH: r =0.0, observed value due to sampling variation Calculate 95 % CI -1.0 0.0 +1.0 NH Rejected NH Accepted NH Accepted NH Rejected