standard, 1,000 lb of which was prepared by the National Institute of Standards and Technology (NIST) in 1977 from French beet harvests. The results from AMS testing are in the form of ratios of , , and , which are used to calculate Fm, the "fraction modern". This is defined as the ratio between the / ratio in the sample and the / ratio in modern carbon, which is in turn defined as the / ratio that would have been measured in 1950 had there been no fossil fuel effect. Both beta counting and AMS results have to be corrected for fractionation. This is necessary because different materials of the same age, which because of fractionation have naturally different / ratios, will appear to be of different ages because the / ratio is taken as the indicator of age. To avoid this, all radiocarbon measurements are converted to the measurement that would have been seen had the sample been made of wood, which has a known δ value of −25‰. Once the corrected / ratio is known, a "radiocarbon age" is calculated using: The calculation uses 8,033 years, the mean-life derived from Libby's half-life of 5,568 years, not 8,267 years, the mean-life derived from the more accurate modern value of 5,730 years. Libby's value for the half-life is used to maintain consistency with early radiocarbon testing results; calibration curves include a correction for this, so the accuracy of final reported calendar ages is assured. Errors and reliability The reliability of the results can be improved by lengthening the testing time. For example, if counting beta decays for 250 minutes is enough to give an error of ± 80 years, with 68% confidence, then doubling the counting time to 500 minutes will allow a sample with only half as much to be measured with the same error term of 80 years. Radiocarbon dating is generally limited to dating samples no more than 50,000 years old, as samples older than that have insufficient to be measurable. Older dates have been obtained by using special sample preparation techniques, large samples, and very long measurement times. These techniques can allow measurement of dates up to 60,000 and in some cases up to 75,000 years before the present. Radiocarbon dates are generally presented with a range of one standard deviation (usually represented by the Greek letter sigma as 1σ) on either side of the mean.