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Hypothesis
- 1. HYPOTHESIS TYPE-1 & TYPE-IIERROR AMIT SHARMA ASSOCIATE PROFESSOR DEPT. OF PHARMACY PRACTICE ISF COLLEGE OF PHARMACY MOBILE: 09646755140, 09418783145
- 2. What ishypothesis? and its type What is hypothesis testing? Type I and Type II errors In this session ….
- 3. A hypothesisis a formal tentative statement of the expected relationship between two or more variables under study. A hypothesis helps to translate the research problem & objectives into a clear explanation A clearly stated hypothesis includes the variables to be measured, identifies the population to be examined, & indicates the proposed outcome for the study. In general- Hypothesis is a tentative prediction or explanation of the relationship between two variables Definition……
- 4. What is HypothesisTesting? Hypothesis testing refers to 1. Making an assumption, called hypothesis, about a population parameter. 2. Collecting sample data. 3. Calculating a sample statistic. 4. To test the validity of our assumption we determine the difference between the hypothesis parameter value and the sample value.)
- 5. HYPOTHESI S TESTING Null hypothesis,H0 Alternative hypothesis,HA State the hypothesized value of the parameter before sampling. The assumption we wish to test (or the assumption we are trying to reject) E.g population mean µ = 20 There is no difference between coke and diet coke All possible alternatives other than the null hypothesis. E.g µ ≠ 20 µ > 20 µ < 20 There is a difference between coke and diet coke
- 6. Null Hypothesis • TheNull hypothesis H0 represents a theory that has been put forward either because it is believed to be true. • it is used as a basis for an argument and has not been proven. • For example, in a clinical trial of a new drug, the null hypothesis might be that the new drug is no better, on average, than the current drug. We would write H0: there is no difference between the two drugs on an average.
- 7. Alternative Hypothesis • Thealternative hypothesis, HA, is a statement of what a statistical hypothesis test is set up to establish. • For example, in the clinical trial of a new drug, the alternative hypothesis might be that the new drug has a different effect, on average, compared to that of the current drug. We would write • HA: the two drugs have different effects, on average. or • HA: the new drug is better than the current drug, on average. The result of a hypothesis test: ‘Reject H0 in favor of HA’ OR ‘Do not reject H0’
- 8. Selecting and interpretingsignificance level 1. Deciding on a criterion for accepting or rejecting the null hypothesis. 2. Significance level refers to the percentage of sample means that is outside certain prescribed limits. 3. e. g. testing a hypothesis at 5% level of significance means we reject the null hypothesis if it falls in the two regions of area 0.025. Do not reject the null hypothesis if it falls within the region of area 0.95. 3. The higher the level of significance, the higher is the probability of rejecting the null hypothesis when it is true. (acceptance region narrows)
- 9. Type I andType II Errors 1. Type I error refers to the situation when we reject the null hypothesis when it is true (H0 is wrongly rejected). e.g H0: there is no difference between the two drugs on average. Type I error will occur if we conclude that the two drugs produce different effects when actually there isn’t a difference. Prob (Type I error) = significance level = α 2. Type II error refers to the situation when we accept the null hypothesis when it is false. H0: there is no difference between the two drugs on average. Type II error will occur if we conclude that the two drugs produce the same effect when actually there is a difference. Prob (Type II error) = ß
- 10. In the contextof testing of hypothesis, there are basically two types of errors we can make:-
- 11. Type I ErrorTypeI Error A type I error, also known as an error of the first kind It occurs when the null hypothesis (H0) is true, but is rejected. The rate of the type I error is called the size of the test. It is denoted by the Greek letter α (alpha). It usually equals the significance level of a test. If type I error is fixed at 5 %, it means that there are about 5% chances in 100% that we will reject H0 when H0 is true.
- 12. Type II ErrorTypeII Error Type II error, also known as an error of the second kind It occurs when the null hypothesis is false, but due to error fails to be rejected. Type II error means accepting the hypothesis which should have been rejected. A Type II error is committed when we fail to believe a truth. The rate of the type II error is denoted by the Greek letter β (beta) and related to the power of a test (which equals 1-β ).
- 13. In the tabularform two error can be presented as follows
- 15. If there isa diagnostic value change in the choice of two means, moving it to decrease type I error will increase type II error (and vice-versa)
- 18. Reducing Type IErrors Prescriptive testing is used to increase the level of confidence, which in turn reduces Type I errors. The chances of making a Type I error are reduced by increasing the level of confidence.
- 19. Reducing Type IIErrors Descriptive testing is used to better describe the test condition and acceptance criteria, which in turn reduces Type II errors. This increases the number of times we reject the Null hypothesis – with a resulting increase in the number of Type I errors (rejecting H0 when it was really true and should not have been rejected).
- 20. Type I andType II Errors – Example • Your null hypothesis is that the battery for a heart pacemaker has an average life of 300 days, with the alternative hypothesis that the average life is more than 300 days. • You are the quality control manager for the battery manufacturer. • Would you rather make a Type I error or a Type II error? • Based on your answer to part (a), should you use a high or low significance level?
- 21. Type I andType II Errors – Example Given H0 : average life of pacemaker = 300 days HA: Average life of pacemaker > 300 days (a) It is better to make a Type II error (where H0 is false i.e average life is actually more than 300 days but we accept H0 and assume that the average life is equal to 300 days) (b) As we increase the significance level (α) we increase the chances of making a type I error. (c) Since here it is better to make a type II error we shall choose a low α.
- 22. Many statisticiansare now adopting a third type of error, a type III When Null hypothesis was rejected for the wrong reason. Type III Errors
- 23.