Testing of Hypotheses
Basic Concepts Concerning Testing Of Hypotheses
(a) Null hypothesis and alternative hypothesis: In the context of statistical analysis, we often talk about null hypothesis and alternative hypothesis. If we are to compare method A with method B about its superiority and if we proceed on the assumption that both methods are equally good, then this assumption is termed as the null hypothesis. As against this, we may think that the method A is superior, or the method B is inferior, we are then stating what is termed as alternative hypothesis. The null hypothesis is generally symbolized as H0 and the alternative hypothesis as Ha.
(b) The level of significance: This is a very important concept in the context of Testing of Hypotheses.
It is always some percentage (usually 5%) which should be chosen with great care, thought and reason. In case we take the significance level at 5 per cent, then this implies that H0 will be rejected when the sampling result (i.e., observed evidence) has a less than 0.05 probability of occurring if H0 is true. In other words, the 5 per cent level of significance means that researcher is willing to take as much as a 5 per cent risk of rejecting the null hypothesis when it (H0) happens to be true. Thus, the significance level is the maximum value of the probability of rejecting H0 when it is true and is usually determined in advance before Testing of Hypotheses.
(c) Decision rule or test of hypothesis: Given a hypothesis H0 and an alternative hypothesis Ha, we make a rule which is known as decision rule according to which we accept H0 (i.e., reject Ha) or reject H0 (i.e., accept Ha). For instance, if (H0 is that a certain lot is good (there are very few defective items in it) against Ha) that the lot is not good (there are too many defective items in it), then we must decide the number of items to be tested and the criterion for accepting or rejecting the hypothesis. We might test 10 items in the lot and plan our decision saying that if there are none or only 1 defective item among the 10, we will accept H0 otherwise we will reject H0 (or accept Ha). This sort of basis is known as decision rule.
(d) Type I and Type II errors: In the context of testing of hypotheses, there are basically two types of errors we can make. We may reject H0 when H0 is true and we may accept H0 when in fact H0 is not true. The former is known as Type I error and the latter as Type II error. In other words, Type I error means rejection of hypothesis which should have been accepted and Type II error means accepting the hypothesis which should have been rejected. Type I error is denoted by a (alpha) known as a error, also called the level of significance of test; and Type II error is denoted by b (beta) known as b error.
(e) Two-tailed and One-tailed tests: In the context of hypothesis testing, these two terms are quite important and must be clearly understood. A two-tailed test rejects the null hypothesis if, say, the sample mean is significantly higher or lower than the hypothesised value of the mean of the population. Such a test is appropriate when the null hypothesis is some specified value and the alternative hypothesis is a value not equal to the specified value of the null hypothesis.
