Hypothesis and Hypothesis Testing
- 1. Hypothesis Testing NABIN KUNWAR DEPARTMENT OF AGRICULTURAL ECONOMICS MAY 29, 2021 1
- 2. Introduction A specific, testable and precise prediction about what the researcher assumes to happen in his/her study Hypothesis is usually considered as the principal instrument in research Involves proposing a possible relationship between two variables i.e. the dependent and independent variable A complete hypothesis must include three components i.e. the variables, the population and the relationship between the variables 2
- 3. Characteristics of Hypothesis Should be clear and precise Should be capable of being tested Should state relationship between variables (if relational hypothesis) Should be limited in scope and must be specific Should be stated as far as possible in most simple terms Should be consistent with most known facts 3
- 4. Contd… Should be amenable to testing within a reasonable time Must explain the facts that gave rise to the need for explanation 4
- 5. Types of Research Hypothesis Generally, there are four types of research hypothesis which are: 1. Null Hypothesis 2. Alternate Hypothesis 3. Directional Hypothesis 4. Non-directional Hypothesis 5
- 6. Purpose of Hypothesis Testing A statistical process of testing an assumption regarding a phenomenon or population parameter It is a critical and crucial part of the scientific method Is a systematic approach to assessing theories through observations and determining the probability that a stated statement is true or false For an analyst who makes predictions, hypothesis testing is a difficult way of backing up his prediction with statistical analysis Also helps to determine whether there is sufficient statistical evidences that support a certain hypothesis about the population parameter or not 6
- 7. Null Hypothesis Null hypothesis is normally referred to as hypothesis of no difference and it is denoted by Ho Assumes that there is no difference between the hypothetical population and the one, from which the sample under study has been drawn A/c to this hypothesis, “there is no difference between the effects of two treatments or there is no association between two attributes” 7
- 8. Contd… It declares that there is no true difference in the sample statistic and population parameter under consideration, Hence it is called ‘null’ which means invalid, void, or a mounting to nothing and the difference found is accidental, arising out of instabilities of sampling Rejecting a null hypothesis does not necessarily mean that the experiment did not produce the required results, but it sets the situation for further experimentation 8
- 9. Contd… For example, the hypothesis may be set in a form “maize variety A will give the same yield per hectare as that of the variety B or there is no difference between the average yields of maize varieties A and B” Symbolically, Ho: μ1=μ2 Thus, these hypothesis form a basis to work with and such a working hypothesis is known as null hypothesis. It is called null hypothesis because if nullifies the original hypothesis i.e. variety A will give more/less yield than variety B 9
- 10. States of Nature and Decisions on Null Hypothesis Decision on Null Hypothesis States of Nature Null Hypothesis True Null Hypothesis False Accept Correct Decision Probability=1 − 𝛼 Type II error committed Probability=𝛽 Reject Type I error committed Probability=𝛼 (𝛼 𝑖𝑠 𝑐𝑎𝑙𝑙𝑒𝑑 𝑠𝑖𝑔𝑛𝑖𝑓𝑖𝑐𝑎𝑛𝑐𝑒 𝑙𝑒𝑣𝑒𝑙) Correct Decision Probability=1 − 𝛽 (1 − 𝛽 𝑖𝑠 𝑐𝑎𝑙𝑙𝑒𝑑 𝑝𝑜𝑤𝑒𝑟 𝑜𝑓 𝑎 𝑡𝑒𝑠𝑡) Note. Adapted from “Formulating and Testing Hypothesis” by Muhammad, K. S. (2016). Basic Guideline for Research. pp. 51-71. 10
- 11. Contd… In the choice of null hypothesis, the following considerations are usually kept in view: A. Alternative hypothesis is usually the one which one wishes to prove and the null hypothesis is the one which one wishes to disprove. Thus, a null hypothesis represents the hypothesis we are trying to reject, and alternative hypothesis represents all other possibilities. B. If the rejection of a certain hypothesis when it is actually true involves great risk, it is taken as null hypothesis because the probability of rejecting it when it is true is 𝜶 which is chosen very small. C. Null hypothesis should always be specific hypothesis i.e., it should not state about or approximately a certain value. 11
- 12. Alternative Hypothesis Hypothesis that contradicts the null hypothesis i.e. rejecting the null hypothesis is known as alternative hypothesis In other words, the set of alternatives to the null hypothesis is referred to as the alternative hypothesis. An alternative hypothesis and a null hypothesis are mutually exclusive, which implies that only one of the two hypotheses can be true A/c to this hypothesis, there is a relationship between the two variables being studied (one variable has an effect on the other) and the results are not due to chance In simple words, null hypothesis means there is no effect while alternate hypothesis means there is an effect 12
- 13. Contd… Usually represented by Ha/H1 For example: “There is a significant difference between the yields of two maize varieties” Symbolically, H1: μ1≠μ2 (two tailed or non-direction alternative) If the statement is that A gives significantly less yield than B or A gives significantly more yield than B. Such statement is known as alternate hypothesis Symbolically, H1: μ1 < μ2 (left tailed) H1: μ1 > μ2 (right tailed) 13
- 14. Directional Hypothesis Directional hypothesis is also known as one-tailed hypothesis which predicts the nature of the effect of the independent variable on the dependent variable States which way you think the results are going to go For example: “Mansuli variety of rice will have more yield than that of Basmati variety”; the hypothesis compares the two groups and states which one will have more/less, be faster/slower and so on 14
- 15. Contd… Under correlational study, the directional hypothesis would state whether a positive or a negative correlation is expected, stating how the two variables will be related to each other E.g.: There will be a positive correlation between the number of tillers and yield of rice, number of irrigation and plant growth etc. The directional hypothesis can also specify a negative correlation E.g.: the higher the inflation rate in the country, lower the purchasing power of the people. 15
- 16. Contd… Here the researcher is intellectually committed to a particular outcome and the anticipated direction of the relationship between variables is also specified i.e. the investigator predicts not only the existence of a relationship but also its nature Such type of hypothesis is generally use by scientific journal If the normal or t-distribution is used, one side or one tailed test only is employed to estimate the required probabilities 16
- 17. Contd… Figure 1. Directional/One-tailed Test To reject H0: μ1 ≤ μ2 and accept H1: μ1 > μ2 0, using the normal distribution, a normal deviate greater than +1.64 (i.e. right tailed) is required for significant at the 0.05 level. 17
- 18. Contd… Likewise, to reject H0: μ1 ≥ μ2 and accept H1: μ1 < μ2, the corresponding normal curve is less than -1.64 (i.e. left tailed) The choice between a non-directional or directional alternative hypothesis should be determined by the rationale that gives rise to the study and should be made before the data are gathered. The major advantage of a directional alternative hypothesis is that it takes less of a deviation from expectation to reject the null hypothesis 18
- 19. 19 Figure 1. Directional/One-tailed Test Figure 1. Non-Directional/Two-tailed Test
- 20. Non-directional Hypothesis States that “The independent variable will have an influence on the dependent variable, but the direction of the outcome is not specified” For e.g.: “There will be a difference in the yield of two varieties of rice namely, Basmati and Mansuli being cultivated” A non-directional hypothesis only states that there exists a difference between the two group/items but does not specify which will be greater/smaller, positive/negative, faster/slower etc. Similarly, in case of correlational study, we simply state that variables will be correlated but do not state whether the relationship will be positive or negative, e.g. there will be a significant correlation between variable X and variable Y 20
- 21. Contd… We may wish to test the null hypothesis H0:μ1− μ2 = 0 against the alternative H1:μ1− μ2 ≠ 0. This means that if H0 is rejected, the decision is that a difference exists between the two means. No confirmation about the direction of the difference is made. Such test is a non-directional test. Sometime called a two-tailed or two-sided test, because if the normal distribution or t-distribution is used, the two tails of the distribution are employed in the estimation of probabilities 21
- 22. Contd… Figure 2. Non-directional/Two-tailed Test Consider a 5% significance level. If the sampling distribution is normal, 2.5% of the area of the curve falls to the right of 1.96 standard deviation units above the mean, and 2.5% lies to the left of 1.96 standard deviation units lower the mean. 22
- 23. Procedure For Hypothesis Testing 1. Making a formal statement 2. Selecting a significance level 3. Deciding the distribution to use 4. Selecting a random sample and computing an appropriate value 5. Calculation of the probability 6. Comparing the probability 23
- 24. Tests of Hypotheses IMPORTANT PARAMETRIC TESTS The important parametric tests are: (1) z-test (2) t-test (3) Chi-Square-test, and (4) F-test (All these tests are based on the assumption of normality i.e., the source of data is considered to be normally distributed) 24
- 25. z-test Based on the normal probability (z) distribution and is used for judging the significance of several statistical measures, particularly the mean z-test is generally used for comparing the mean of a sample to some hypothesized mean for the population in case of large sample (>30) Besides, this test may be used for judging the significance of median, mode, coefficient of correlation and several other measures 25
- 26. t-test t-test is based on t-distribution and is considered an appropriate test for judging the significance of a sample mean or for judging the significance of difference between the means of two samples in case of small sample(<30) In case two samples are related, we use paired t-test (aka. difference test) for judging the significance of the mean of difference between the two related samples. It can also be used for judging the significance of the coefficients of simple and partial correlations 26
- 27. Contd… t-statistic is calculated from the sample data and then compared with its probable value based on t-distribution (to be read from the table that gives probable values of t for different levels of significance for different degrees of freedom) at a specified level of significance for concerning degrees of freedom for accepting or rejecting the null hypothesis 27
- 28. Chi-Square-test Chi-Square-test is based on chi-square distribution and as a parametric test is used for comparing a sample variance to a theoretical population variance It can also be used to make comparisons between theoretical populations and actual data when categories are used. Thus, the chi-square test is applicable in large number of problems. The test is, in fact, a technique through the use of which it is possible for all researchers to: (i) test the goodness of fit (ii) test the significance of association between two attributes, (iii) test the homogeneity or the significance of population variance. 28
- 29. F-test F-test is based on F-distribution and is used to compare the variance of the two-independent samples. This test is also used in the context of analysis of variance (ANOVA) for judging the significance of more than two sample means at one and the same time. It is also used for judging the significance of multiple correlation coefficients F-statistic is calculated and compared with its probable value (to be seen in the F-ratio tables for different degrees of freedom for greater and smaller variances at specified level of significance) for accepting or rejecting the null hypothesis 29
- 30. Conclusion Research hypothesis is a specific, testable and precise prediction about what the researcher assumes to happen in their study There are four types of research hypothesis (null, alternate, directional and non- directional hypothesis) Hypothesis testing is done to determine whether there is sufficient statistical evidence that supports a certain hypothesis about the population parameter or not Null hypothesis is the hypothesis of no difference i.e. same 30
- 31. Contd… Directional hypothesis predicts the nature of the effect of the independent variable on the dependent variable i.e. direction of outcome is specified Non directional hypothesis predicts the influence of independent variable on the dependent variable, but the direction of the outcome is not specified Test for hypotheses testing: t-test, z-test, chi-square test, F-test 31
- 32. References Agresti, A., & Finlay, B. (1997). Statistical Methods for the Social Sciences (3rd ed.). Prentice Hall. CFI. (2020). Null Hypothesis. Retrieved from Corporate Finance Institute: https://corporatefinanceinstitute.com/resources/knowledge/other/null-hypothesis-2/ Development of the Research Hypothesis and Types of Hypothesis. (2018). Retrieved from THEINTACTONE: https://theintactone.com/2018/02/26/br-u1-topic-3-development-of-the- research-hypothesis-and-types-of-hypothesis/ McLeod, S. (2018, August 10). What is a hypothesis. Retrieved from Simply Psychology: https://www.simplypsychology.org/what-is-a-hypotheses.html Muhammad, K. S. (2016). Formulating and Testing Hypothesis. In Basic Guideline for Research (pp. 51-71). 32
- 33. THANK YOU! 33