Dr.MUSTAQUE AHMED MBBS,MD(COMMUNITY MEDICINE), FELLOWSHIP IN HIV/AIDS HYPOTHESIS TESTING Dr.MUSTAQUE AHMED MBBS,MD(COMMUNITY MEDICINE), FELLOWSHIP IN HIV/AIDS

Objectives 1. To understand the ELEMENTS OF TESTING HYPOTHESIS. 2. To DESCRIBE NULL HYPOTHESIS AND ALTERNATE HYPOTHESIS 3. TO UNDERSTAND THE TYPES OF ERROR AND POWER OF TEST.

INTRODUCTION Statistics is the science of collecting, organizing, summarising, analysing, and making inference from data Descriptive stat. Includes collecting, organizing, summarising, analysing, and presenting data Inferential stat. Includes Making inferences, hypothesis testing Determining relationship, and making prediction There are two broad areas in statistics :descriptive and inferential stat.

Elements of Testing hypothesis Null Hypothesis Alternative hypothesis Level of significance P-value Test statistics Power of the test Conclusion

Hypothesis Testing A Statistical hypothesis is a ASSUMPTION about a population parameter. This ASSUMPTION may or may not be true. The null hypothesis, symbolized by H0, is a statistical hypothesis that states that there is no difference between a parameter and a specific value or that there is no difference between two parameters. 7 7

Elements of Hypothesis Testing The alternative hypothesis, symbolized by H1, is a statistical hypothesis that states a specific difference between a parameter and a specific value or states that there is a difference between two parameters. 8 8

NULL HYPOTHESIS EXPRESSION

Elements of Hypothesis Testing A statistical test uses the data obtained from a sample to make a decision about whether or not the null hypothesis should be rejected. The numerical value obtained from a statistical test is called the test value. In the hypothesis-testing situation, there are four possible outcomes. 13 13

NULL HYPOTHESIS OUTCOMES

P-value An indicator which measures the likelihood of observing values as extreme as the one observed based on the sample information, assuming the null hypothesis is true. P-value is also known as the observed level of significance.

The level of significance ( ) The level of significance is the maximum probability of committing a type I error. This probability is symbolized by  ( alpha). That is, P(type I error)=. P(type II error) =  (beta). Typical significance levels are: 0.10, 0.05, and 0.01. For example, when  = 0.10, there is a 10% chance of rejecting a true null hypothesis. 18 18

Type I and Type II errors Type I error is committed when a true null hypothesis is rejected.  is the probability of committing type I error. Type II error is committed when a false null hypothesis is not rejected.  is the probability of committing type II error.

Power of a test The power of a test is the probability that a false null hypothesis is rejected. Power = 1 - , where  is the probability of committing type II error.

Select the Suitable Test of significance or Test Statistic Whether the test involves one sample, two samples, or samples? Whether two or more samples used are independent or related? Is the measurement scale nominal, ordinal, interval, or ratio?

CONCLUSION The critical value(s) separates the critical region from the noncritical region. The critical or rejection region is the range of values of the test value that indicates that there is a significant difference and that the null hypothesis should be rejected. The noncritical or Acceptance region is the range of values of the test value that indicates that the difference was probably due to chance and that the null hypothesis should not be rejected. 21 21

Establish Critical or Rejection region

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