Testing of hypothesis and tests of significance
- 2. Hypothesis Hypothesis means a mere assumption or some supposition or a possibility to be proved or disproved For a researcher, hypothesis is a formal questions to be resolved.
- 3. A hypothesis is a tentative generalization, the validly of which remains to be tested – Geroge A.Lundberg A proposition which can be put to test to determine validity -Goode and Hatt A hypothesis is a statement capable of being tested and thereby verified or rejected- Rummel and Balline
- 4. Hypotheses reflect the research worker’s guess as to the probable outcome of his experiment and they place clear and specific goals before the researcher and provide him with a basis for selecting samples and research procedures to meet these goals -Walter R.Borg A hypothesis is an atempt at explanation: a provisional supposition made in order to explain scientifically some facts or phenomenon -Coffey -
- 5. Different types of hypothesis Descriptive hypothesis Descriptive hypotheses are prepositions that describe the existence, size, form or distribution of some variables Eg: The per capital income of Indian is lower than that of Chinese Relational Hypothesis It describes the relationship between two variables. Eg: “Families with higher income spend more on recreation”
- 6. Working hypothesis The working hypothesis indicates the nature of data and methods of analysis for the study. Working hypothesis are subject to modification as the investigation proceeds. Null hypothesis: when a hypothesis is stated negatively, it is called a null hypothesis. A null hypothesis should always be specific. The null hypothesis is the one which one whishes to disprove - It is generally a symbolized as H0 eg: “Age of the respondents does not influence their job satisfaction: “The drug is not effective in curing malaria”
- 7. Alternative hypothesis The set of alternatives to the null hypothesis is referred to as the alternative hypothesis. Alternative hypothesis is usually the one which one wishes to prove. -It is generally a symbolized as Ha Eg:“Age of the respondents influences their job satisfaction” Statistical hypothesis: it is a quantitative statement about a population. When the researcher derives hypothesis from a sample and hopes it to be true for the entire population it is known as statistical hypohtesis. eg: “Group X is older than Group Y”
- 8. Simple hypothesis or Common sense hypothesis: -- It states the existence of certain empirical uniformities. Many empirical uniformities are common in sociological research. eg: Fresh students conform to the conventions set by the seniors. Composite hypothesis: These hypothesis aim at testing the existence of logically derived relationship between empirical uniformities obtain
- 9. Explanatory hypothesis It states the existence of one independent variable causes or leads to an effect on dependent variable Eg: “yield of tomato is influenced by the application of fertilizers”
- 10. Role of a hypothesis 1. A hypothesis gives a definite way to the investigation and it guides the direction of the study 2. It systematizes knowledge and helps in the verification of facts. 3. It helps in that test of theories developed by the social scientist to explain a phenomenon 4. It determines the most appropriate technique of analysis 5. It describes the relationship between two variables 6. It helps in drawing a specific conclusion
- 11. What is hypothesis testing? Hypothesis testing refers to 1. Making an assumption called hypothesis about a population parameter 2. Collecting sample data. 3. Calculating a sample statistic. 4. Using the sample statistic to evaluate the hypothesis (how likely is it that our hypothesized parameter is correct. To test the validity of our assumption we determine the difference between the hypothesized parameter value and the sample value.)
- 12. Hypothesis testing It means to test some hypothesis about parent population from which the sample is drawn. For example: we can take a hypothesis that sugarcane cultivated in Cubcum valley has an average height of 200cms. Estimation: It means to use the statistics obtained from the sample as estimate of the unknown parameter of the population. For example, a researcher may like to know about the average weight and variance in number of young ones yielded by a rabbit during a given period on the basis of one or more young ones drawn from the numbers. In both cases , the inference about the population values made from sample data
- 13. Test of significance A procedure to assess the significance of a statistics or difference between two independent statistics is known as test of significance
- 14. Procedure for testing a hypothesis 1. Set up hypothesis hypothesis is a tentative conclusion logically drawn about a population parameter. First step is to set up a hypothesis of assume a certain value for a population mean For example: The average weight of fish reared in a research station is 2.6kg A given antibiotic cures 80% of the patients taking it. The cost of production of wheat is less than any other eatable cultivation
- 15. To test the validity of our assumption (hypothesis), we gather sample data and determine difference between hypothesized value and the actual value of the sample mean. The smaller the difference , the greater the likelihood that our hypothesized value for the mean is correct The larger the difference, the smaller the likelihood. Thus, if the statistical tests show that the difference is significant, the hypothesis is rejected.
- 16. Two hypothesis Null hypothesis Alternative hypothesis Null hypothesis: This hypothesis asserts that there is no true difference in the sample and the population in the particular matter under consideration and that the difference is accidental and unimportant arising out of fluctuations of sampling. In other words, a hypothesis which is stated for the purpose of possible acceptance is called null hypothesis
- 17. Null hypothesis id usually denoted by H0. If we want to find out whether a particular drug is effective in curing malaria, we will take the null hypothesis that “the drug is not effective in curing malaria”. The rejection of the null hypothesis indicates that the drug is effective in curing malaria ie. It indicates success in the project.
- 18. The null hypothesis may be used under the following conditions: 1. If we want to test the significance of the difference between a sample statistics and population parameter r between sample statistics, we set null hypothesis that the difference is not true H0:µ= mean 2. To test any statement about the population, we set up the null hypothesis that it is true. For example, if we want to find out whether average yield of paddy per hectare in Tamil Nadu is 10 tones, then we set up null hypothesis. H0:µ= 10 tonnes
- 19. Alternative hypothesis Any hypothesis which is complementary to the null hypothesis is called alternative hypothesis and is denoted as H1 or Ha For example, if we want to test the null hypothesis that the average height of the soldiers is 162cm H0=µ=162cm Alternative hypothesis could be H1 :µ =162cm H1:µ >162cm H1:µ <162cm
- 20. Set up a suitable significance level (or) Selecting and interpreting significance 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. E.g testing a hypothesis at 5% level of significance means that 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)
- 21. Type I and Type 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
- 22. Select test criterion This involves selecting an appropriate probability distribution for the particular test. Some common probability distribution which are used in testing are Z, t, chi square or F distributions. While testing, appropriate probability distribution should be applied
- 23. Doing computations These calculations include the testing statistics and standard error of the testing statistics
- 24. Making decisions The final step is to decide whether to accept the hypothesis or reject the null hypothesis the decision depends on whether the computed value of the test criterion falls in the region of rejection or in the region of acceptance. that is if the calculated value of test criterion is greater than table value, then we can reject the null hypothesis. If it is less than, we can accept hypothesis
- 25. Reference Statistical methods for Biologists_S.Palanichamy and M.Manoharan Research methodology – Dr.Peer mohamed, Dr.Akbar batcha and Dr. Shazuli ibrahim