10.3 Statistics - Terminology

Before jumping into the kinds of analyses useful for shooting and load evaluation that ShotStat can provide, it is helpful to define some terms so that their meaning in the following discussions is precise.

Average

there are several statistical averages, such as the mean, the mode, the median, etc. In this discussion, average is the mean, which is the common definition of average.

Chaos

Often, the terms chaos and random are used interchangeably or together. However, these terms have very different meanings. Understanding the difference is essential to proper data analysis. Statistics typically addresses measurements involving random errors; chaos implies a dynamical dependence, such as the fifth value depending on the fourth (which depended on the third, etc).

Confidence Interval

the range of values between which an estimation is made with a stated certainty. For example, one may speak of a 90% confidence interval. One standard deviation represents the 68.3% confidence interval, and 3 times the standard deviation represents the 99.7% confidence interval.

F-Test

an analytical test used to determine if the difference between the variances of two sets of measured data is significant, given a stated Significance Level.

Hypothesis

a statement to be tested by measurement; for using statistics, the hypothesis is actually a mathematical expression (such as ``the standard deviation of muzzle velocity for Load A is less than the standard deviation of muzzle velocity for Load B''). In general, statistics can be used to reject a special hypothesis called the Null Hypothesis (rejecting the Null Hypothesis implies an Alternate Hypothesis may be true) to within a stated Significance Level.

Population

the entire ``true'' data set under consideration. For example, you may wish to measure the average point of impact (relative to point of aim) for a Lot of ammunition. Because the test is destructive, you probably do not want to test the entire Lot, but that would be the only way to actually measure the average point of impact. In this case, you would select a Sample to test, and use the analysis of the sample data to draw conclusions about the entire Population.

Random Error

errors in measurement in a population or sample that follow no pattern. Random errors are assumed to occur in a Gaussian distribution (also called a normal distribution); this means small errors occur more frequently than larger errors.

Range

in a set of data, the maximum value minus the minimum value.

Sample

the portion of a population that is selected to actually test. ShotStat can be used with samples of twenty or smaller. Larger samples result in more meaningful analyses. Note that an average or standard deviation only represents an approximation to the true, population average or standard deviation. An F-Test or T-Test gives an idea of how close is this approximation.

Significance Level

the probability of rejecting a Null Hypothesis that is actually true; for example, a 5% Significance Level means one has a 5% chance of rejecting the Null Hypothesis that is actually true. A smaller Significance Level implies more certainty in rejecting the Null Hypothesis.

Standard Deviation

the average difference between the sample average and the individual measurements. It is the square root of variance.

Statistic

a value computed from a set of measurements, such as mean, variance or standard deviation

Systematic Error

errors in measurement that follow a pattern; these tend to be constant within one set of measurements, but they can be very hard to discover. An example of a systematic error might be using a ruler that is cut-off at 1/4 inch to measure targets; all measurements will be 1/4 inch too short.

T-Test

an analytical test used to determine if the difference between the averages of two sets of measured data is significant, given a stated Significance Level.

Variance

the average of the squared differences of measured values from the average value.