## Statistical Inference

The use of hypothetical testing in any educational or scientific research has been considered as essential to analyze the data and information collected in a scientific manner to validate the results of the research. Hypothesis testing is an integral part of the analysis of variances normally used by the researchers. Hypothetical testing is an inferential procedure where sample data is used to evaluate the credibility of a hypothesis about a population (Chapter 8). The logic behind hypothesis testing is the state a hypothesis about a population and the next step is to obtain a random sample from the population. In the final stage, the sample data is compared with the hypothesis to find the nature of the population.

If the data are consistent with the hypothesis then, it can be concluded that the hypothesis is reasonable and accepted. On the other hand, if there exists a large discrepancy between the data and the hypotheses, the conclusion is that the hypothesis is wrong. Since there is a possibility that the researcher might make an error when making his judgment of the results of the experiment, hypothetical testing as a standard procedure has been established.

## Hypothesis Testing Procedure

In the hypothetical testing, the researcher normally makes two opposing hypothesis; one is the ‘null hypothesis’ or H0 and the ‘alternative hypothesis’ or H1. Example of a hypothesis is “babies born to women who smoke during pregnancy will be more likely to be of low birth weight”. The hypothesis usually has two variables on which data is to be collected from the samples selected randomly. They are:

- independent variable and
- dependent variable.

Independent variable is the one, which forms the grouping in the samples. Dependent variable is that which is assumed as the result of manipulating the test variable (7). In the example hypothesis stated above ‘smoking during pregnancy’ is the independent variable and ‘birth weight’ is the dependent variable.

The treatment effect of the independent variable is likely to add or subtract a constant from every individual’s score. The null hypothesis predicts that the independent variable will have no effect on the dependent variable for the population. Alternative hypothesis predicts that the independent variable will have an effect on the dependent variable for the population. The researcher, before conducting the actual test, based on the results of the previous research or the theory reviewed will have reason to conclude that there might be a difference in a specified direction. It is also possible that because of a sampling error there is the likelihood of a discrepancy between the mean value of the samples and the mean value of the population.

## Errors in Hypothetical Testing

There are two types of errors possible in the treatment of sample data in hypothetical testing. In Type 1 error, the researcher rejects the null hypothesis when the treatment in fact has no effect. In Type 2 errors, the researcher fails to reject the null hypothesis, when in reality the treatment has an effect. This implies that the researcher fails to reject a null hypothesis, which is in reality a false assumption (CJ526).

## Alpha Level

It is important that the researcher determine which sample means are likely when the null hypothesis becomes true and the means that are unlikely. It is called the significance level, which refers to the probability value that defines the unlikely possibilities and is usually set at 0.05 or 5%, which is known as ‘alpha level’. The alpha level divides the sample distribution into two different parts – one contains sample means, which is comparable with the null hypothesis and the next one where the sample means are significantly different from the null hypothesis.

Three questions that need to be asked to the researcher:

- Is the researcher satisfied with the number of samples selected, randomly to represent the population?
- Has the null hypothesis been evolved by duly considering all the treatments?
- What are his assumptions regarding the mean values, which may go, below the alpha level?

## References

7, E. (n.d.). *Statistical Methods Applied to Education*. Web.

Chapter8. (n.d.). *Hypothesis Testing*. Web.

CJ526. (n.d.). *Introduction to Hypothesis Testing*. Web.