Hypothesis Testing PDF

University of Fallujah College of Medicine Department of Community & Family Medicine HYPOTHESIS TESTING Purpose The purpose of hypothesis testing is to help the researcher or administrator in reaching a decision concerning a population by exa...

University of Fallujah College of Medicine Department of Community & Family Medicine HYPOTHESIS TESTING Purpose The purpose of hypothesis testing is to help the researcher or administrator in reaching a decision concerning a population by examining a sample from that population … Research Hypothesis… It is the assumption that motivate the research. It is usually the result of long observation by the researcher. Example nSmoking and lung cancer nThere is association between smoking and lung cancers Statistical Hypothesis… This is stated in a way that can be evaluated by appropriate statistical technique. Using sample data … Statistical hypothesis It is composed of two types: Null hypothesis( Ho): It is the particular hypothesis under test, and it is the hypothesis of “no difference” “ no association” Alternative hypothesis (HA): which disagree with the null hypothesis Q: is Ho important to researcher ?? Example … nSmoking and lung cancer nH0 there is no association between smoking and lung cancers nH1 there is association between smoking and lung cancers Test Statistic It is a mathematical expression of sample values which provides a basis for testing a statistical hypothesis. The result of this test will determine whether we will accept the null hypothesis and so the HA will be rejected , or we reject the null hypothesis and so the HA will be accepted.  Errors There are possible errors to come to the wrong conclusion: Type 1 error: rejection of the null hypothesis when it is true. It is presented by alpha, which is the level of significance, often the 5%, 1%, and 0.1% (α=0.05, 0.01, and 0.001) levels are chosen. The selection depends on the particular problem… Confidence α -value Z-value level 90% 0.1 1.645 95% 0.05 1.96 99% 0.01 2.58 P-value ….. It is the smallest value of α for which the Ho can be rejected It gives a more precise statement about probability of rejection of Ho when it is true than the alpha level So instead of saying the test statistic is significant or not , we will mention the exact probability of rejecting the Ho when it is true. P value is measured by computer programs Example: p=0.004, p=0.7….  Steps in conducting hypothesis testing Hypothesis testing can be presented as steps: 1.Data The nature of the data whether it consists of counts, or measurement will determine the test statistic to be used Qualitative or Quantitive variables 2.Hypotheses Null Hypothesis (Ho): which is the hypothesis of no difference Alternative hypothesis( HA) which disagrees with Null Hypothesis Example nSmoking and lung cancer nH0 there is no association between smoking and lung cancers nH1 there is association between smoking and lung cancers 3.Test statistic It uses the data of the sample to reach to a decision to reject or to accept the null hypothesis. The general formula for a test statistic is:  Test statistic— statistical tests For computed value … Example: Ø Z test Ø t test Ø Chi-square test (χ2) Ø Correlation 4. Decision Rule The critical values that discriminate between acceptance and rejection regions depends on alpha level of significance If the value of the test statistic falls in the rejection region area , it is considered statistically significant If it falls in the acceptance area it is considered not statistically significant 4. Decision Rule Whenever we reject a null hypothesis , there is always a possibility of type 1 error( rejection of Ho when it is true). This is why we should decrease this error to the least possible. Critical values The values of the test statistic that separate the rejection region from the acceptance region Critical value =Z value (according to α value) Confidence α -value Z-value level 90% 0.1 1.645 95% 0.05 1.96 99% 0.01 2.58 5. Statistical decision It consists of rejecting or not rejecting the Ho. It is rejected if the computed value of the test statistic falls in the rejection area It is not rejected if the computed value of the test statistic falls in the acceptance region 6. Conclusion If Ho is rejected , we conclude that HA is true. If Ho is not rejected we conclude that Ho may be true. Example: lung cancer and smoking …  Compute value from statistical test ( Chi square test ) … Determine the computed value falls in the rejection area or in acceptance region Decision: whether we reject or accept the null hypothesis that stated there is no association between smoking and lung cancer … EXAMPLE THANKS