Testing of Hypothesis

The hypothesis testing determines the validity of the assumption (technically described as null hypothesis) with a view to choose between the conflicting hypotheses about the value of the population hypothesis about the value of the population of a population parameter. Hypothesis testing helps to secede on the basis of a sample data, whether a hypothesis about the population is likely to be true or false. Statisticians have developed several

State H0 as well as Ha

Reject H0 Accept H0

tests of hypothesis (also known as tests of significance) for the purpose of testing of hypothesis which can be classified as:

 Parametric tests or standard tests of hypothesis ;

 Non Parametric test or distribution – free test of the hypothesis.

Parametric tests usually assume certain properties of the parent population from which we draw samples. Assumption like observations come from a normal population, sample size is large, assumptions about the population parameters like mean, variants etc must hold good before parametric test can be used. But there are situation when the researcher cannot or does not want to make assumptions. In such situations we use statistical methods for testing hypothesis which are called non parametric tests because such tests do not depend on any assumption about the parameters of parent population. Besides, most non-parametric test assumes only nominal or original data, where as parametric test require measurement equivalent to at least an interval scale. As a result non-parametric test needs more observation than a parametric test to achieve the same size of Type I &

Type II error.

4.6.1 Important Parametric Tests The important parametric tests are:

 z-test

 t-test

 x²-test

 f-test

All these tests are based on the assumption of normality i.e., the source of data is considered to be normally distributed. In some cases the population may not be normally distributed, yet the test will be applicable on account of the fact that we mostly deal with samples and the sampling distributions closely approach normal distributions.

Z-test is based on the normal probability distribution and is used for judging the significance of several statistical measures, particularly the mean. The relevant test statistic is worked out and compared with its probable value (to be read from the table showing area under normal curve) at a specified level of significance for judging the significance of the measure concerned. This is a most frequently used test in research studies. This test is used even when binomial distribution or t-distribution is applicable on the presumption that

such a distribution tends to approximate normal distribution as „n‟ becomes larger. Z-test is generally used for comparing the mean of a sample to some hypothesis mean for the population in case of large sample, or when population variance is known as z-test is also used for judging the significance of difference between means to of two independent samples in case of large samples or when population variance is known z-test is generally used for comparing the sample proportion to a theoretical value of population proportion or for judging the difference in proportions of two independent samples when happens to be large. Besides, this test may be used for judging the significance of median, mode, co-efficient of correlation and several other measures

T-test is based on t-distribution and is considered an appropriate test for judging the significance of sample mean or for judging significance of difference between the two means of the two samples in case of samples when population variance is not known (in which case we use variance of the sample as an estimate the population variance). In case two samples are related, we use paired t-test (difference test) for judging the significance of their mean of difference between the two related samples. It can also be used for judging the significance of co-efficient of simple and partial correlations. The relevant test statistic, t, is calculated from the sample data and then compared with its probable value based on t-distribution at a specified level of significance for concerning degrees of freedom for accepting or rejecting the null hypothesis it may be noted that t-test applies only in case of small sample when population variance is unknown.

X²-test is based on chi-square distribution and as a parametric test is used for comparing a sample variance to a theoretical population variance is unknown.

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 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. Test statistic, f, is calculated and compared with its probable value for accepting or rejecting the H₀.

Self Assessment Questions Fill in the Blanks

1. –––––––––- is a negative statement.

2. Type II error is –––––––––––.

3. –––––––––– is tentative statement.

4.7 Summary

A hypothesis is an assumption about relations between variables. It is a tentative explanation of the research problem or a guess about the research outcome. Before starting the research, the researcher has a rather general, diffused, even confused notion of the problem. A hypothesis gives a definite point to the investigation, and it guides the direction on the study. A hypothesis specifies the sources of data, which shall be studied, and in what context they shall be studied. 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 hypnotized value of the mean of the population.

The hypothesis is tested on a pre-determined level of significance and such the same should have specified. Generally, in practice, either 5% level or 1% level is adopted for the purpose. After deciding the level of significance, the next step in hypothesis testing is to determine the appropriate sampling distribution. The hypothesis testing determines the validity of the assumption (technically described as null hypothesis) with a view to choose between the conflicting hypotheses about the value of the population of a population parameter. Z-test is based on the normal probability distribution and is used for judging the significance of several statistical measures, particularly the mean. The relevant test statistic is worked out and compared with its probable value (to be read from the table showing area under normal curve) at a specified level of significance for judging the significance of the measure concerned. This is a most frequently used test in research studies.

T-test is based on t-distribution and is considered an appropriate test for judging the significance of sample mean or for judging significance of difference between the two means of the two samples in case of samples when population variance is not known (in which case we use variance of the sample as an estimate of the population variance). X²-test is based on

chi-square distribution and as a parametric test is used for comparing a sample variance to a theoretical population variance is unknown. F-test is based on f-distribution and is used to compare the variance of the two-independent samples.

4.8 Terminal Questions

1. What is the meaning of Hypothesis?

2 What are the criteria for Hypothesis Construction?

3. What is the need for having Working Hypothesis?

3. What are the characteristics of Good Hypothesis?

4. What are the types of Hypothesis?

5. What is Type I & Type II Errors?

6. What are Two Tailed Test & One Tailed Test?

7. What are the procedure and Flow Diagram for Testing Hypothesis?

8. Which are the important Parametric Tests?

4.9 Answers to SAQs and TQs

SAQs

1. Null hypothesis

2. Accepting a statement that is false 3. Hypothesis

TQs

1. Section 4.1 2. Section 4.2.1 3. Section 4.2.3 4. Section 4.2.4 5. Section 4.3 6. Section 4.4.3 7. Section 4.4.4 8. Section 4.5 9. Section 4.6