Hypothesis Testing 2 PDF

Kingdom of Saudi ‫ملكة العربية السعودية‬/‫ا‬ Arabia ‫وزارة التعليم‬ Ministry of education ‫جامعة القصيم‬ Qassim University...

Kingdom of Saudi ‫ملكة العربية السعودية‬/‫ا‬ Arabia ‫وزارة التعليم‬ Ministry of education ‫جامعة القصيم‬ Qassim University ‫الكلية التطبيقية‬ Applied College Introduction into Biostatistics and Epidemiology Hypothesis Testing Dr. Amjad Alharbi [email protected] 1 Intended learning outcomes 1. Differentiate between population parameter and sample statistic. 2. Differentiate between population distribution and distribution of sample means. 3. State the prominent features of central limit theorem.  Inferential statistics Statistical inference is the procedure by which we reach a conclusion about a population on the basis of the information contained in a sample drawn from that population. Sunday, October 6, 2024 inference Inference involves making a generalization about a larger group of individuals on the basis of a subset or sample. ‘Statistic’ and ‘Parameter’ Sunday, October 6, 2024  Distribution of Sample Means CENTRAL LIMIT THEOREM: GIVEN A SUFFICIENTLY LARGE SAMPLE SIZE FROM A POPULATION WITH A FINITE LEVEL OF VARIANCE, THE MEAN OF ALL SAMPLES FROM THE SAME POPULATION WILL BE APPROXIMATELY EQUAL TO THE MEAN OF THE POPULATION. Sunday, October 6, 2024  Distribution of Sample Means Central Limit Theorem: The standard deviation of sample means is smaller than that of the population and it is called the standard error of the mean. It is equal to the standard deviation of the population divided by the square root of the sample size i.E. Sunday, October 6, 2024  Distribution of Sample Means Central Limit Theorem: AS THE SIZE OF THE SAMPLE (N) INCREASES AND REACHES 30, THE DISTRIBUTION OF SAMPLE MEANS BECOMES APPROXIMATELY NORMAL REGARDLESS OF WHETHER THE POPULATION DISTRIBUTION IS NORMAL OR NOT. Sunday, October 6, 2024  Distribution of Sample Means Central Limit Theorem: As ‘n’ increases the SE (x¯) which is basically standard deviation becomes smaller Sunday, October 6, 2024 Distribution of Sample Means Central Limit Theorem: Sunday, October 6, 2024 Distribution of Sample Means Central Limit Theorem: Sunday, October 6, 2024 HYPOTHESIS TESTING Hypothesis : may be defined simply as a statement about one or more populations. Hypothesis testing aimed to find out whether the observed variation among sampling is explained by sampling variations, chance or is really a difference between groups.  Hypothesis Testing NULL HYPOTHESIS: A CLAIM (OR STATEMENT) THAT IS ASSUMED TO BE TRUE UNTIL IT IS PROVED FALSE. IT IS DENOTED BY H0. ALTERNATIVE HYPOTHESIS: A CLAIM THAT WILL BE TRUE IF THE NULL HYPOTHESIS IS FALSE. IT IS DENOTED BY H1. Sunday, October 6, 2024 Sunday, October 6, 2024  Hypothesis Testing You can see that a null hypothesis is usually a statement that there is no difference between two or more factors, and the alternative hypothesis is a statement that some kind of difference exists and often gives the direction of this relationship. Sunday, October 6, 2024  Null Hypothesis The case when the two groups are equal Null Hypothesis = H0 This is the hypothesis actually being tested H0 is assumed to be true Alternative Hypothesis The case when the two groups are not equal; when there is some treatment difference; when other possibilities exist Alternative Hypothesis = H1 Or Ha H1 is assumed to be true when the H0 is false.  Hypothesis Testing Example: Suppose a study is being conducted to answer questions about differences between two types of pit and fissure sealants. One question that could be asked is, “ After ten years, is there a difference in retention between a chemical-curing sealant and a sealant that requires ultraviolet light for polymerization?” Sunday, October 6, 2024  Hypothesis Testing Step 1: The null hypothesis for this type of experimental study may be: “There is no difference between the retention of a chemical-cured sealant and a sealant that requires ultraviolet light for polymerization 10 years after placement”. Step 2: The alternative hypothesis would be: “There is a difference between the retention of the two different sealants after 10 years.” Monday, October 7, 2024  Hypothesis test Steps The procedure for testing a hypothesis is: Step 1) State Null hypothesis (H0) Step 2) State the Alternate hypothesis (Ha) Step 3) Determine Significance Level (α) Step 4) Calculate p-value Step 5) Conclusion The null and alternative hypotheses Step 1 H0 There is no treatment effect The drug has no effect Step2 H1 There is a treatment effect The drug had an (some, any) effect  Step 3) Determine Significance Level (α) Need to decide on a Significance Level: The probability that the test statistic will reject the null hypothesis when the null hypothesis is true Significance is a property of the distribution of a test statistic, not of any particular draw of the statistic Determines the Region of Rejection Generally 5% or 1%  Step 4) Calculate p-value A p-value is a statistical measurement used to validate a hypothesis against observed data. A p-value measures the probability of obtaining the observed results, assuming that the null hypothesis is true. If the data are not consistent with the null hypotheses, the difference is said to be “statistically significant”. If the data are consistent with the null hypotheses it is said that we accept it i.e. statistically insignificant. The lower the p-value, the greater the statistical significance of the observed difference. A p-value of 0.05 or lower is generally considered statistically significant. Step 5) Conclusion The final step is to make a decision from your results and draw up your conclusion. There are two basic decisions that you can make when you’ve interpreted the results: Reject the null hypothesis and support the alternative hypothesis. Fail to reject the null hypothesis.  References 1. Bulman JS, Osborn JF. Statistics in dentistry 1989. British Dental Journal. Chapter.1. 2. Bluman AG. Elementary statistics 2008. McGraw-Hill Education. Chapter.2. Thank you