Type of errors

There are two types of ERROR that we will dealing during conducting hypothesis testing;

• TYPE I ERROR: The probability of rejecting the Ho when Ho is TRUE.
• TYPE II ERROR: The probability of accepting the Ho when Ha is TRUE.

TYPE I ERROR is serious form of error thus, it is denoted by alpha and is commonly referred as the SIGNIFICANCE LEVEL. TYPE II ERROR is usually denoted by beta where 1-beta is the POWER OF THE TEST. POWER OF THE TEST is the probability of rightly rejecting Ho when it is FALSE. In order words, we are RIGHT on deciding to accept Ha as our decision.

There are some factors need to be considered when looking into the power of the test;

1. When the significance level or a is made smaller, then the power will be decreases.
2. In condition where the standard deviation of individual observation increases, the power will be decreases.
3. By increasing sample size, then the power will be increasing too.
4. The power of the test will be increases if the alternative mean is shifted further away from the null mean (|Ho – Ha|).

In order for statistician to make conclusion base on sampled data, they need to first decide the SIGNIFICANCE LEVEL or alpha value. The Ho will be accepted if the range of calculated test statistics is within the ACCEPTANCE REGION. It will be rejected if the range of calculated test statistics within the REJECTION REGION. Traditionally, a value of 0.05 is considered as cut-off level for either accepting or rejecting Ho. We usually reject Ho if p-value calculated is less than (<) 0.05 and vice-versa. Means that we will accept Ho if p-value obtained more than (>) 0.05.

In writing up results of the study, we need to make distinction between scientific and statistical significance, because these two terms do not necessarily coincide. Sometimes the results of a study may be scientifically important but the results show statistically insignificance. If the results were obtained from a small sample size, encouraging researchers to perform larger studies to confirm these results may be warranted, thus could confirm the findings and possibly reject Ho.