Ideally, the hypothesis-testing procedure leads to the acceptance of H0 when H0 is true and the rejection of H0 when H0 is false. Unfortunately, since hypothesis tests are based on sample information, the possibility of errors must be considered. A Type-I error corresponds to rejecting H0 when H0 is actually true, and a Type-II error corresponds to accepting H0 when H0 is false.

In testing any hypothesis, we get only two results: either we accept or we reject it.

We do not know whether it is true or false. Hence four possibilities may arise.

i) The hypothesis is true but test rejects it (Type-I error).

ii) The hypothesis is false but test accepts it (Type-II error).

iii) The hypothesis is true and test accepts it (correct decision).

iv) The hypothesis is false and test rejects it (correct decision).

**Type-I Error**

In a hypothesis test, a Type-I error occurs when the null hypothesis is rejected when it is in fact true. That is, H0 is wrongly rejected. For example, in a clinical trial of a new drug, the null hypothesis might be that the new drug is no better, on average, than the current drug. That is, there is no difference between the two drugs on average. A Type-I error would occur if we concluded that the two drugs produced different effects when in fact there was no difference

between them.

A Type-I error is often considered to be more serious, and therefore more important to avoid, than a Type-I error.

The hypothesis test procedure is therefore adjusted so that there is a guaranteed ‘low’ probability of rejecting the null hypothesis wrongly;

This probability is never 0. This probability of a Type-I error can be precisely computed as, P (Type-I error) significance level = The exact probability of a Type-I error is generally unknown.

If we do not reject the null hypothesis, it may still be false (a Type-I error) as the sample may not be big enough to identify the falseness of the null hypothesis (especially if the truth is very close to hypothesis).

For any given set of data, Type-I and Type-Il errors are inversely related; the smaller the risk of one, the higher the risk of the other.

A Type-I error can also be referred to as an error of the first kind.

**Type-II Error**

In a hypothesis test, a Type-II error occurs when the null hypothesis, Ho, is not rejected when it is in fact false. For example, in a clinical trial of a new drug, the null hypothesis might be that the new drug is no better, on average, than the current drug; that is Ho: there is no difference between the two drugs on average.

A Type-II error would occur if it was concluded that the two drugs produced the same effect, that is, there is no difference between the two drugs on average, when in fact they produced different effects.

A Type-II error is frequently due to sample sizes being too small.

The probability of a Type-II error is symbolised by â and written:

P (Type-II error) = â (but is generally unknown).

A Type-II error can also be referred to as an error of the second kind.

Hypothesis testing refers to the process of using statistical analysis to determine if the observed differences between two or more samples are due to random chance factor (as stated in the null hypothesis) or is it due to true differences in the samples (as stated in the alternate hypothesis).

A null hypothesis (H0) is a stated assumption that there is no difference in parameters (mean, variance) for two or more populations. The alternate hypothesis (H1) is a statement that the observed difference or relationship between two populations is real and not the result of chance or an error in sampling.

Hypothesis testing is the process of using a variety of statistical tools to analyse data and, ultimately, to fail to reject or reject the null hypothesis. From a practical point of view, finding statistical evidence that the null hypothesis is false allows you to reject the null hypothesis and accept the alternate hypothesis.

Because of the difficulty involved in observing every individual in a population for research purposes, researchers normally collect data from a sample and then use the sample data to help answer questions about the population.

A hypothesis test is a statistical method that uses sample data to evaluate a hypothesis about a population parameter.

The hypothesis testing is standard and it follows a specific order as given below.

i) first state a hypothesis about a population (a population parameter, e.g. mean

ii) obtain a random sample from the population and also find its mean , and

iii) compare the sample data with the hypothesis on the scale (standard z or normal distribution).