Lecture 6 Hypothesis.pdf hypothesis. pdf
- 1. Hypothesis Testing And Errors in Hypothesis Dr. Abdur Rasheed
- 2. Inferential Statistics Consist of generalization from sample to population, performing estimation and hypothesis test, determining relationship among variables and making predictions.
- 3. Let’s say you wanted to know about the favorite ice cream flavors of everyone in the world. Well, there are about 8 billion people in the world, and it would be impossible to ask every single person about their ice cream preferences. Instead, you would try to sample a representative population of people and then extrapolate your sample results to entire population. While this process isn’t perfect and it is very difficult to avoid errors, it allows researcher to make well reasoned inference about the population in question. This is the idea behind the inferential statistics. Inferential Statistics
- 4. Hypothesis A hypothesis is an assumption about one or more population parameters. A parameter is a characteristic of the population, like its mean or variance. The parameter must be identified before analysis. I assume the mean height of a class is 5.3 feet
- 5. Purpose of hypothesis The purpose of hypothesis testing is to aid clinician, researcher or administrator in reaching a conclusion about a population by examining a sample from that population.
- 6. Examples of hypothesis • Mean height of IoBM students is μ = 5.1 feet • The population mean monthly cell phone bill of city is: μ = 425 • The average number of TV sets in U.S. Homes is equal to three; μ = 3
- 7. • It Is always about a population parameter, not about a sample statistic. • Sample evidence is used to assess the probability that the claim about the population parameter is true Hypothesis Remember
- 9. Research Hypothesis • It is the assumption that motivate the research. • It is usually the result of long observation by the researcher. • This hypothesis led directly to the second type of hypothesis
- 10. Statistical Hypothesis • This is stated in a way that can be evaluated by appropriate statistical technique.
- 11. 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” Alternative hypothesis (HA): Apposite null hypothesis
- 12. Properties of Null hypothesis • Always contains ‘=‘ sign i.e., (=, ≤, ≥ ) e.g., the average height of students of a class is 5.6 feet. H0 : µ = 5.6 • Null hypothesis may or may not be rejected. Null Hypothesis H0 • H0: µ = 5.6 • H0: µ ≤ 5.6 • H0: µ ≥ 5.6 Examples of Null hypothesis
- 13. • Apposite of null hypothesis • Never contains ‘=‘ sign but include( ≠, < ,>) e.g., the average height of students of a class is < 5.6 feet. HA : µ < 5.6 • Alternative hypothesis may or may not be accepted. • Is generally the hypothesis that the researcher is trying to prove. Evidence is always examined with respect to H1, never with respect to H0. Properties of Alternative hypothesis
- 14. Examples of Alternative hypothesis • HA: µ ≠ 5.6 • HA: µ < 5.6 • HA: µ > 5.6
- 15. Remember What we hope or expect to able to conclude as a result of the test usually should be placed in alternative hypothesis The null hypothesis should contain statement of equality (=, ≤, ≥ ) The null hypothesis is the hypothesis that is tested. The null and alternative hypothesis are complementary
- 16. Possible situations • H0: µ = 5.6 • HA: µ ≠ 5.6 • H0: µ ≤ 5.6 • HA: µ > 5.6 • H0: µ ≥ 5.6 • HA: µ < 5.6
- 17. Researchers are interested in the mean age of certain population. Let us say that they are asking the question. Can we conclude that the mean age of this population is different from 30 years? Example H0: µ = 30 years (i.e. population mean age is not different from 30) HA: µ ≠ 30 years (i.e. population mean age is different from 30)
- 18. Rejection of null hypothesis means acceptance of alternative hypothesis Rejection of alternative hypothesis means acceptance of null hypothesis Errors
- 19. We test null hypothesis We will either reject or accept null hypothesis There is a possibility that we may reject true null hypothesis or accept false null hypothesis
- 20. Errors Type I error This error is committed when true null hypothesis is rejected. Reject null hypothesis when it is true The rate of type I error is also called size of the test The probability of committing type I error is α (level of significance) If type I error is fixed as 5%, it means that there are about 5 chance in 100 that we will reject null hypothesis when null hypothesis is true.
- 21. Errors Type II error This error is committed when false null hypothesis is accepted Accept = Fail to reject. Accept null hypothesis when it is false The probability of committing type II error is β NOTE: we do not say that we accept the null hypothesis if a statistician is around… Fail to reject false null hypothesis
- 22. Actual state of nature H0 is true H0 is false Decision Reject H0 Correct Correct Type I Error Type II Error Accept H0
- 23. Power of the test “Power” of a test is the probability of rejecting null hypothesis when it is false. “Power” = 1 -P(Type II error) To minimize the P(Type II error), we equivalently want to maximize power. But power depends on the value under the alternative hypothesis ... Probability of rejection of false null hypothesis
- 24. Power of the test Power is probability, so number between 0 and 1. 0 is bad! 1 is good! Need to make power as high as possible.
- 25. 11.25 Hypothesis Testing… The probability of a Type I error is denoted as α (Greek letter alpha). The probability of a type II error is β (Greek letter beta). The two probabilities are inversely related. Decreasing one increases the other, for a fixed sample size. In other words, you can’t have and β both real small for any old sample size. You may have to take a much larger sample size, or in the court example, you need much more evidence.
- 26. The goal is to determine whether there is enough evidence to infer that the alternative hypothesis is true, or the null is not likely to be true. There are two possible decisions: Conclude that there is enough evidence to support the alternative hypothesis. Reject the null. Conclude that there is not enough evidence to support the alternative hypothesis. Fail to reject the null.