Hypothesis testing
A hypothesis is a tentative explanation that accounts for a set of facts and can be tested by further investigations. The purpose of testing hypothesis is to assist researchers in making decisions. Quantitative research is well suited for the testing of these hypotheses, most common in experimental designs. In hypothesis testing, the researcher should define the population, state the hypotheses to be tested, specify the significance level, select a sample from the population, select a test statistics, perform the calculation for the statistical test, draw a conclusion, and develop appropriate interpretation of the conclusion. Traditionally, we look at two distinct types of hypothesis: the null hypothesis (H0) and the alternative
On the other hand, not rejected, meaning there is not enough evidence to reject the hypothesis (4). However, two types of incorrect decisions can be made: rejecting null hypothesis when it is true (type I error) and not rejecting null hypothesis when it is false (type II error) (Figure 1). The probability of committing a type I error is denoted by α (alpha) and the probability of committing a type II error is denoted by β (beta). The type I error is generally considered the most serious and need to be minimized. However, having a small type II error is also important. When null hypothesis is not rejected, one should not say that the null hypothesis is accepted because we may have committed a type II error. One way of doing this is by increasing the sample size as errors can occur in small samples due to the influence of small number of extreme values (outliers). Therefore, a larger sample will decrease the chances of making both type I and type II
A larger sample means higher power and traditionally this has been taken as 0.8 or occasionally 0.9. A power of 0.5 implies that there is only a 50% chance that a true alternative hypothesis will be detected; this is an unacceptable risk. The precision with which sample statistics estimate population parameters is strongly influenced by the sample size. Statistical power analysis provides a method of determining the sample sizes needed to control for errors in hypothesis testing. Power is largest when the effects being studied are large and the sample is large. A justification for the sample size and power calculations should be reported when publishing