Bias is a measure of a systematic measurement error, the component of measurement error that remains constant in replicate measurements.
The bias can be expressed in absolute measurement units or as a percentage relative to the known value. A point estimate is a single value that is the best estimate of the true unknown parameter; a confidence interval is a range of values and indicates the uncertainty of the estimate.
The bias is an estimate of the true unknown bias in a single study. If the study were repeated, the estimate would be expected to vary from study to study. Therefore, if a single estimate is compared directly to 0 or compared to the allowable bias the statement is only applicable to the single study. To make inferences about the true unknown bias you must perform a hypothesis test:
There are two common hypotheses of interest that can be tested:
- Equality test
The null hypothesis states that the bias is equal to 0, against the alternative hypothesis that it is not equal zero. When the test p-value is small, you can reject the null hypothesis and conclude that the bias is different to zero.
It is important to remember that a statistically significant p-value tells you nothing about the practical importance of what was observed. For a large sample, the bias for a statistically significant hypothesis test may be so small
as to be practically useless. Conversely, although there may some evidence of bias, the sample size may be too small for the test to reach statistical significance, and you may miss an opportunity to discover a true meaningful bias. Lack of evidence against the null hypothesis does not mean it has been proven to be true, the belief before you perform the study is that the null hypothesis is true and the purpose is to look for evidence against it. An equality test at the
5% significance level is equivalent to comparing a 95% confidence interval to see if it includes zero.
- Equivalence test
The null hypothesis states that the bias is outside an interval of practical equivalence, against the alternative hypothesis that the bias is within the interval considered practically equivalent. When the test p-value is small, you can reject the null hypothesis and conclude that the bias is practically equivalent, and within the specified interval.
An equivalence test is used to prove a bias requirement can be met. The null hypothesis states the methods are
not equivalent and looks for evidence that they are in fact equivalent. An equivalence hypothesis test at the 5% significance level is the same as comparing the 90% confidence interval to the allowable bias interval.