Student Notes: Biostatistics and Epidemiology - Davao Doctors College PDF

DAVAO DOCTORS COLLEGE MEDICAL LABORATORY SCIENCE DEPARTMENT STUDENT NOTES: Biostatistics and Epidemiology INTRODUCTION TO INFERENTIAL STATISTICS 2. Interval estimate...

DAVAO DOCTORS COLLEGE MEDICAL LABORATORY SCIENCE DEPARTMENT STUDENT NOTES: Biostatistics and Epidemiology INTRODUCTION TO INFERENTIAL STATISTICS 2. Interval estimate ▪ a range of numbers, called a ✔ These provide a means for drawing conclusions about a confidence interval indicating, can population given the data actually obtained from the sample. be regarded as likely containing the They allow a researcher to make generalizations to a larger true value number of individuals, based on information from a limited ▪ an interval or a range of values used number of subjects. They are based on: to estimate the parameter. o Probability theory ▪ This estimate may or may not ▪ The basis for decision-making statistical contain the value of the parameter inferences. It refers to a large number of being estimated experiences, events or outcomes that will happen in a population in the long ❖ Three properties of a good estimator: run. Likelihood and chance are similar 1. The estimator should be an unbiased terms. estimator. That is, the expected value or the ▪ Examples are usually based on tossing a mean of the estimates obtained from samples coin and finding heads or tails. of a given size is equal to the parameter being Probabilities are statements of likelihood estimated expressed in values from 0 to 1.0. 2. The estimator should be consistent. For a p = the number of outcomes consistent estimator, as sample size the total possible outcomes increases, the value of the estimator approaches the value of the parameter o Statistical inference estimated ▪ statistics enable us to judge the 3. The estimator should be a relatively efficient probability that our inferences or estimator. That is, of all the statistics that can estimates are close to the truth be used to estimate a parameter, the relatively efficient estimator has the smallest variance. o Sampling distributions ▪ are theoretical distributions developed by ❖ Methods of Point Estimates: mathematicians to organize statistical 1. Method of Moments outcomes from various sample sizes so ▪ Advantage: simplest approach for that we can determine the probability of constructing an estimator something happening by chance in the ▪ Disadvantage: usually are not the population from which the sample was “best” estimators possible drawn. They allow us to know the relative frequency or probability of occurrence of 2. Maximum Likelihood any value in the distribution ▪ Before an experiment is performed the outcome is unknown. Probability ❖ ESTIMATION allows us to predict unknown ❖ Estimator - Statistic whose calculated value is used to outcomes based on known estimate a population parameter parameters ▪ After an experiment is performed the outcome is known. Now we talk ❖ Estimate - A particular realization of an estimator about the likelihood that a parameter would generate the observed data ❖ Types of Estimators: 3. Bayesian 1. Point Estimate ▪ The classic philosophy (frequentist) ▪ single number that can be regarded assumes parameters are fixed as the most plausible value quantities that we want to estimate ▪ specific numerical value estimate of as precisely as possible a parameter. ▪ Bayesian perspective is different: ▪ The best point estimate of the parameters are random variables population mean is the sample with probabilities assigned to mean particular values of parameters to  reflect the degree of evidence for that value ❖ Interval Estimates ⮚ Confidence level o is the probability that the interval estimate will contain the parameter, assuming that a large number of samples are selected and that the estimation process on the same parameter is repeated. ⮚ Confidence interval o is a specific interval estimate of a parameter determined by using data obtained from a sample and by using the specific confidence level of the estimate. REFERENCES: Daniel, W. W. (2005). Biostatistics: A foundation for analysis in the health sciences (8th ed.). Philippines: Mindmover Publishing. doi:570.15195/D221 Nuevo, J. M. (2019). Biostatistics and epidemiology. Powerpoint presentation. Bluman, A. G. (2012). Elementary statistics: a step by step approach (8th ed.). 1221 Avenue of the Americas, New York, NY 10020: McGraw-Hill Companies