# Lesson 4: Bias and Random Error

### Introduction

Error is defined as the difference between the true value of a measurement and the recorded value of a measurement. There are many sources pf error in collecting clinical data. Error can be described as random or systematic.

**Random error** is also known as variability, random variation, or ‘noise in the system’. The heterogeneity in the human population leads to relatively large random variation in clinical trials.

Systematic error or **bias** refers to deviations that are not due to chance alone. The simplest example occurs with a measuring device that is improperly calibrated so that it consistently overestimates (or underestimates) the measurements by X units.

Random error has no preferred direction, so we expect that averaging over a large number of observations will yield a net effect of zero. The estimate may be imprecise, but not inaccurate. The impact of random error, imprecision, can be minimized with large sample sizes.

Bias, on the other hand, *has* a net direction and magnitude so that averaging over a large number of observations does not eliminate its effect. In fact, bias can be large enough to invalidate any conclusions. Increasing the sample size is not going to help. In human studies, bias can be subtle and difficult to detect. Even the suspicion of bias can render judgment that a study is invalid. Thus, the design of clinical trials focuses on removing known biases.

Random error corresponds to imprecision, and bias to inaccuracy. Here is a diagram that will attempt to differentiate between imprecision and inaccuracy. (Click the 'Play' button.)

See the difference between these two terms? OK, let's explore these further!

### Learning objectives & outcomes

Upon completion of this lesson, you should be able to do the following:

- Distinguish between random error and bias in collecting clinical data.
- State how the significance level and power of a statistical test are related to random error.
- Accurately interpret a confidence interval for a parameter.