Process and Errors in Hypothesis Testing | Educational Statistics | 8614 |

QUESTION

Explain the process and errors in hypothesis testing. 

Course: Educational Statistics

Course code 8614

Level: B.Ed Solved Assignment 

ANSWER 

Four-Step Process for Hypothesis Testing

The process of hypothesis testing goes through the following four steps.

i)  Stating the Hypothesis

The process of hypothesis testing begins by stating a hypothesis about tn. Usually, a researcher states two opposing hypotheses. Both hypotheses are stated in terms of population unknown population parameters.

The first and most important of the two hypotheses is called the null hypothesis. A null hypothesis states that the treatment has no effect. In general, the null hypothesis states that there is no change, no effect, no difference – nothing happened. The null hypothesis is denoted by the symbol Ho (H stands for hypothesis and 0 denotes that this is a zero effect).

The null hypothesis (Ho) states that in the general population, there is no change, no difference, or no relationship. In an experimental study, the null hypothesis (Ho) predicts that the independent variable (treatment) will have no effect on the dependent variable for the population.

The second hypothesis is simply the opposite of the null hypothesis and it is called the scientific or alternative hypothesis. It is denoted by H1. This hypothesis states that the treatment has an effect on the dependent variable.

The alternative hypothesis (H1) states that there is a change, a difference, or a relationship for the general population. In an experiment, H1 predicts that the independent variable (treatment) will have an effect on the dependent variable.

ii)  Setting Criteria for the Decision

In a common practice, a researcher uses the data from the sample to evaluate the authority of the null hypothesis. The data will either support or negate the null hypothesis. To formalize the decision process, a researcher will use the null hypothesis to predict exactly what kind of sample should be obtained if the treatment has no effect. In particular, a researcher will examine all the possible sample means that could be obtained if the null hypothesis is true.

iii)  Collecting data and computing sample statistics

The next step in hypothesis testing is to obtain the sample data. Then raw data are summarized with appropriate statistics such as mean, standard deviation, etc. then it is possible for the researcher to compare the sample mean with the null hypothesis.

iv)  Make a Decision

In the final step, the researcher decides, in the light of the analysis of data, whether to accept or reject the null hypothesis. If analysis of data supports the null hypothesis, he accepts it and vice versa

 

Uncertainty and Error in Hypothesis Testing

Hypothesis testing is an inferential process. It means that it uses limited information obtained from the sample to reach general conclusions about the population. As a sample is a small subset of the population, it provides only limited or incomplete information about the whole population. Yet hypothesis test uses information obtained from the sample. In this situation, there is always the probability of reaching an incorrect conclusion.

Generally, two kinds of errors can be made.

i)  Type I Errors

A type I error occurs when a researcher rejects a null hypothesis that is actually true. It means that the researcher concludes that the treatment does have an effect when in fact the treatment has no effect.

Type I error is not a stupid mistake in the sense that the researcher is overlooking something that should be perfectly obvious. He is looking at the data obtained from the sample that appear to show a clear treatment effect. The researcher then makes a careful decision based on available information. He never knows whether a hypothesis is true or false.

The consequences of a type I error can be very serious because the researcher has rejected the null hypothesis and believed that the treatment had a real effect. it is likely that the researcher will report or publish the research results. Other researchers may try to build theories or develop other experiments based on false results.

ii)  Type II Errors

A type II error occurs when a researcher fails to reject the null hypothesis that is really false. It means that a treatment effect really exists, but the hypothesis test has failed to detect it. This type of error occurs when the effect of the treatment is relatively small. That is the treatment does influence the sample but the magnitude of the effect is very small.

The consequences of Type II errors are not very serious. In case of Type II error, the research data do not show the results that the researcher had hoped to obtain. The researcher can accept this outcome and conclude that the treatment either has no effect or has a small effect that is not worth pursuing. Or the researcher can repeat the experiment with some improvement and try to demonstrate that the treatment does work. It is impossible to determine a single, exact probability value for a type II error.

Summarizing we can say that a hypothesis test always leads to one of two decisions.

i)  The sample data provides sufficient evidence to reject the null hypothesis and the researcher concludes that the treatment has an effect.

ii)  The sample data do not provide enough evidence to reject the null hypothesis. The researcher fails to reject the null hypothesis and concludes that the treatment does not appear to have an effect.