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1 Introduction and General Comments This document is intended for students who have heard the general language of probability applied to experimental data analysis and are in need only of formalism and detail. Material presented is non-linear and early sections may require understanding basics of concepts from latter sections. 1.1 Sections still needed Discarding data Significant Digits Statistical Process Control (Control Charts, UCL, LCL, assignable causes, ) Statistical Design of Experiments 1.2 Critical Rules 1. Always look critically at your data. Statistics applied blindly will yield meaningless results. Most analysis requires random uncorrelated errors – and certainly experimental mistakes will skew any analysis. 2. Garbage in Garbage Out holds. The last nine checks I wrote (and yes I still consider Pluto a planet) correlate extremely well with the relative masses of the planets in sequence from Mercury to Pluto. But I doubt that has diddly squat to do with anything. 3. Statistics help good experiments yield meaningful answers. Can’t do anything to help a hopeless or sloppy experiment. 1.3 Significant figures When no uncertainty is given in a numerical result, there is nonetheless an implied uncertainty from how the number is written. 3 . 141592654 implies that the value is accurate to the ninth decimal place. Similarly, writing v = 3 . 2284728372 implies significance to the last presented decimal position (which is typically ludicrous in experimental measurements). From Bevington, the number of significant figures in a result without a specific uncertainty is 1. The leftmost nonzero digit is the most significant digit 2. If there is no decimal point, the rightmost nonzero digit is the least significant digit 3. If there is a decimal point, the rightmost digit is the most significant digit even if it is a zero 4. All digits between the least and most significant digits are counted as significant digits. In cases of ambiguity (with large integers), it is preferable to go to scientific notation to express the value. For example, 73100 implies only three significant digits, but 7 . 310 × 10 4 implies four significant digits. When quoting uncertainty, there should never be more than two significant digits in the uncertainty, and then only if the first digit is a 1 (or sometimes a 2). The least significant digit of the result should be the same as the least significant digit of the uncertainty. For a measurement of 1 . 979, with an uncertainty of 0 . 012, the result could be presented as 1 . 979 ± 0 . 012 or 1 . 98 ± 0 . 01. If the uncertainty were 0 . 035, then the value should be reported as 1 . 98 ± 0 . 03. For rounding, the rules are 1. Above 0.5 round up, and below 0.5 round down 2. If exactly 0.5, round toward an even number The second rule ensures averaging of rounding for a large number of values. Both 1 . 275 and 1 . 285 become 1 . 28 after rounding.
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