Editing 2311: Confidence Interval
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This is another one of [[Randall|Randall's]] [[:Category:Tips|Tips]], this time a [[:Category:Science tip|Science Tip]]. This is the second time that a category of tips (with the first being "[[:Category:Protip|Protip]]") has been re-used. | This is another one of [[Randall|Randall's]] [[:Category:Tips|Tips]], this time a [[:Category:Science tip|Science Tip]]. This is the second time that a category of tips (with the first being "[[:Category:Protip|Protip]]") has been re-used. | ||
| β | Graphs of continuous functions' predicted values often show {{w|confidence interval}}s, a region (either shaded or marked with dotted lines, the latter used here) that indicates the {{w|observational error|margin of error}} for the prediction at any point. The joke in this comic is that the estimate has so much uncertainty that the confidence interval extends off the top and bottom of the chart, which in a real report would usually prevent it from being printed and require a re-scaled chart to show it (if not declined altogether, as data with such wide variance might be deemed useless). This may be a tip as if it's outside the printable area, it won't be seen by anyone who reads it, and thus they won't realize how bad your model is, though this is more of a tip in how to trick people into falsely thinking you've shown a good result with your work than it is a tip in | + | Graphs of continuous functions' predicted values often show {{w|confidence interval}}s, a region (either shaded or marked with dotted lines, the latter used here) that indicates the {{w|observational error|margin of error}} for the prediction at any point. The joke in this comic is that the estimate has so much uncertainty that the confidence interval extends off the top and bottom of the chart, which in a real report would usually prevent it from being printed and require a re-scaled chart to show it (if not declined altogether, as data with such wide variance might be deemed useless). This may be a tip as if it's outside the printable area, it won't be seen by anyone who reads it, and thus they won't realize how bad your model is, though this is more of a tip in how to trick people into falsely thinking you've shown a good result with your work than it is a tip in performing an actual legitimate useful scientific result. |
In the title text, a millisigma would be an error of +/- 1/1000th of a {{w|standard deviation}}. Statistical error and uncertainty is typically measured by {{w|standard deviation}}, which is written in formulas with the Greek letter {{w|sigma}}, and is also frequently referred to by the word "sigma." Measurements of sample means, one of the most common experimentally determined variables, will tend to follow a {{w|normal distribution}}, such that 68 percent of members of the population will fall within one sigma (plus or minus) of the mean value, 95 percent within two sigma, and 99.7 percent within three sigma. Any of these intervals may be usefully reported as the confidence interval, so long as it's made clear to the reader, but two- or three-sigma are sufficient for most applications. However, this graph shows data of such poor quality (or such poorly-chosen {{w|y-axis|''y''-axis}} bounds) that even the millisigma confidence interval (0.08% of the population -- not often used in science, but occasionally found in e.g. [https://researchservices.pitt.edu/sites/default/files/flexAnalysis%20User%20Manual.pdf molecular analysis tools]) does not fit on the graph. Variations in the curve that are small compared to the {{w|error bar}} typically can't be distinguished from errors. Therefore, the shape of the curve - and the entire graph in this example - is meaningless. | In the title text, a millisigma would be an error of +/- 1/1000th of a {{w|standard deviation}}. Statistical error and uncertainty is typically measured by {{w|standard deviation}}, which is written in formulas with the Greek letter {{w|sigma}}, and is also frequently referred to by the word "sigma." Measurements of sample means, one of the most common experimentally determined variables, will tend to follow a {{w|normal distribution}}, such that 68 percent of members of the population will fall within one sigma (plus or minus) of the mean value, 95 percent within two sigma, and 99.7 percent within three sigma. Any of these intervals may be usefully reported as the confidence interval, so long as it's made clear to the reader, but two- or three-sigma are sufficient for most applications. However, this graph shows data of such poor quality (or such poorly-chosen {{w|y-axis|''y''-axis}} bounds) that even the millisigma confidence interval (0.08% of the population -- not often used in science, but occasionally found in e.g. [https://researchservices.pitt.edu/sites/default/files/flexAnalysis%20User%20Manual.pdf molecular analysis tools]) does not fit on the graph. Variations in the curve that are small compared to the {{w|error bar}} typically can't be distinguished from errors. Therefore, the shape of the curve - and the entire graph in this example - is meaningless. | ||
