1.3: Statistical Analysis: Overview
When we take repeated measurements on the same or replicated samples, we will observe inconsistencies in the magnitude. These inconsistencies are called errors. To categorize and characterize these results and their errors, the researcher can use statistical analysis to determine the quality of the measurements and/or suitability of the methods.
One of the most commonly used statistical quantifiers is the mean, which is the ratio between the sum of the numerical values of all results and the total number of results. Another commonly used quantifier is the median, which is the middle value amongst all the results arranged in the increasing or decreasing order of their numerical values. In the presence of extremely large or small values in the data set, the median can be a more suitable measure for the data set overall. Both the mean and median can be useful measures of the central value of a set of measurements. In addition to the central value, the range is another way to characterize the distribution of a set of values. It is the numerical difference between the highest and lowest values in a set of results.
Precision and accuracy are two important measures of observed errors in the data set. Precision is the measure of closeness between the replicate measurements. In a precise data set, the values of different measurements cluster close together. The values are farther apart or more scattered in an imprecise data set. Often, the range of an imprecise data set will be high. On the other hand, accuracy is a measure of closeness between the measurements and the true or expected value. This means that the magnitude of errors in a more accurate data set is smaller than that of a less accurate data set.
