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Biostatistic course Part 10 Inferences from a proportion

Biostatistic course Part 10 Inferences from a proportion. Dr. Sc. Nicolas Padilla Raygoza Department dof Nursing and Obstetrics Division Health Sciences and Engineering Campus Celaya-Salvatierra University of Guanajuato Mexico. Biosketch.

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Biostatistic course Part 10 Inferences from a proportion

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  1. Biostatistic coursePart 10Inferences from a proportion Dr. Sc. Nicolas Padilla Raygoza Department dof Nursing and Obstetrics Division Health Sciences and Engineering Campus Celaya-Salvatierra University of Guanajuato Mexico

  2. Biosketch • Medical Doctor by University Autonomous of Guadalajara. • Pediatrician by the Mexican Council of Certification on Pediatrics. • Postgraduate Diploma on Epidemiology, London School of Hygine and Tropical Medicine, University of London. • Master Sciences with aim in Epidemiology, Atlantic International University. • Doctorate Sciences with aim in Epidemiology, Atlantic International University. • Associated Professor B, School of Nursing and Obstetrics of Celaya, university of Guanajuato. • padillawarm@gmail.com

  3. Competencies • The reader will apply a Z test to obtain inferences from a proportion. • He (she) will obtain a confidence interval from a proportion.

  4. Introduction • It is common in health studies, to measure categorical variables: • Gender: male or female, • Civil status: single, married, widow, divorced, separate, free union. • Result of detection of antigen of Entamoeba histolytic: positive or negative.

  5. Introduction • When we use variables with only two categories, summarize them with proportions or percentages.

  6. Introduction • In the study of anti-amoebic treatment, the proportion of children with amebiasis was of 0.277. • The proportion of children with amebiasis was 194/700 = 0.277 0.277(1-0.277) Standard error is: √ -------------------- = 0.017 700

  7. Notation • The notation for population and sample parameters, for proportions are shown. • Remember, we use Greek letters for population parameters and Latin letters for the sample.

  8. Example • We we can search the distribution from a binary variable, as gender in children in schools from Celaya, we take a sample of size n from teh population from all children in all schools from Celaya; a proportion, p, from all children in the sample, that they have the characteristics of interest. • To obtain conclusions about a proportion from the population, we apply the same methods to obtain inferences about means from samples.

  9. Confidence interval 95% from a proportion • If the sample size is big,we can calculate a confidence interval for a ´proportion of a sample using the common formulae: Proportion ± 1.96 x SE(proportion) p±1.96 SE(p)

  10. Hypothesis test for a proportion • If we can evaluate if the proportion has a value, we use a procedure to test hypothesis. 1.- First, we should note the null hypothesis: Ho: π= πo 2. Then, we note the alternative hypothesis: H1: π≠ πo 3. We calculate the statistic test.

  11. Hypothesis test for a proportion • The formulae is the similar that the formulae used with means, but using proportions instead of means. p – πo Z = --------- SE(p) • Where πo is the hypothesis proportion and p is the proportion observed in the sample. • Z value represent the number or standard errors between the proportions of hypothesis and the observed.

  12. Example • In the sample of 700 children, we searched amebiasis diagnosis,27.7% was detected the antigen of E. histolytic in feces. • The principal researcher was surprised, because he thought that in that area, amebiasis prevalence was 15%.

  13. Example • We can probe if the observed value is really different than expected value.  • Null hypothesis: Ho: p = πo= 0.15 • Alternative hypothesis: H1: p ≠ πo • If standard error of the proportion is 0.017, • Hypothesis test is Z = p – πo / ES(p) = 0.27 – 0.15 / 0.017= 7.05  • P-value for Z of 7.05 is <0.05.

  14. Example • The interpretation is: • If the proportion of patients with amebiasis in the population is 15%, the opportunity to observe a proportion from the sample equal or more extreme than 27% is less than 0.05.

  15. Small samples • The methods to make inferences from a sample from the population, describe in this lecture, only are valid if the sample size is big. • A rule to decide if the sample size is sufficiently big for the distributions of the proportions is Normal is:  1. π n > 5 2. (1 – π) n > 5

  16. Small samples • If the rule is not accomplished, we should calculate the Fisher exact test.

  17. Bibliografía • 1.- Last JM. A dictionary of epidemiology. New York, 4ª ed. Oxford University Press, 2001:173. • 2.- Kirkwood BR. Essentials of medical ststistics. Oxford, Blackwell Science, 1988: 1-4. • 3.- Altman DG. Practical statistics for medical research. Boca Ratón, Chapman & Hall/ CRC; 1991: 1-9.

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