38 PART 1 Getting Started with Biostatistics

In estimation, both random and systematic errors reduce precision and accuracy.

You cannot control random error, but you can control systematic error by improv-

ing your measurement methods. Consider the four different situations that can

arise if you take multiple measurements from the same population:»

» ^{High precision and high accuracy is an ideal result. It means that each}

measurement you take is close to the others, and all of these are close to the

true population value.»

» ^{High precision and low accuracy is not as ideal. This is where repeat}

measurements tend to be close to one another, but are not that close to the

true value. This situation can when you ask survey respondents to self-report

their weight. The average of the answers may be similar survey after survey,

but the answers may be inaccurately lower than truth. Although it is easy to

predict what the next measurement will be, the measurement is less useful if

it does not help you know the true value. This indicates you may want to

improve your measurement methods.»

» ^{Low precision and high accuracy is also not as ideal. This is where the}

measurements are not that close to one another, but are not that far from the

true population value. In this case, you may trust your measurements, but

find that it is hard to predict what the next one will be due to random error.»

» ^{Low precision and low accuracy shows the least ideal result, which is a low}

level of both precision and accuracy. This can only be improved through

improving measurement methods.

Sampling distributions and standard errors

The standard error (abbreviated SE) is one way to indicate the level of precision

about an estimate or measurement from a sample. The SE tells you how much the

estimate or measured value may vary if you were to repeat the experiment or the

measurement many times using a different random sample from the same popu-

lation each time, and recording the value you obtained each time. This collection

of numbers would have a spread of values, forming what is called the sampling

distribution for that variable. The SE is a measure of the width of the sampling

distribution, as described in Chapter 9.

Fortunately, you don’t have to repeat the entire experiment a large number of

times to calculate the SE. You can usually estimate the SE using data from a single

experiment by using confidence intervals.