Timeline for Is a statistically significant difference within analytical uncertainty still valid?
Current License: CC BY-SA 4.0
6 events
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| May 7, 2020 at 14:48 | comment | added | Sean Paul | Thank you for all of the comments and answers, I am very grateful. The calculation offered by whuber is exactly the what I was after, and I feel more confident that the variation seen between tissues is real. | |
| May 6, 2020 at 21:27 | comment | added | whuber♦ | Not only is that built into the comparison, Sean Paul, you can actually back out a component of variance. Since $Z\approx -2.5,$ we know one standard error of the mean difference is $0.12/2.5=0.048$ with a variance of $0.048^2,$ whereas the measurement error contributes $2\times 0.18^2/50$ to that variance. Subtracting gives a variance component of size $0.001$ that reflects real variation among the tissue concentrations, after accounting for the measurement error. One thing demonstrated by this result is that there is detectable variation among samples despite the uncertainty. | |
| May 6, 2020 at 20:04 | history | edited | BruceET | CC BY-SA 4.0 |
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| May 6, 2020 at 19:24 | comment | added | BruceET | The weight of my pkg was 'known' only because provided simulated data. // The point is that with enough measurements on a scale of limited precision I can make the margin of error of the CI as small as I want. With 100 weighings the ME might go down to $\pm 1.4$g. The 'analytic uncertainty' of any one measurement does not limit the margin of error of a CI. // I assumed my scale has SD $\sigma = 5$g for each individual measurement. | |
| May 6, 2020 at 18:25 | comment | added | Sean Paul | Thank you very much for the thorough response! To continue the weighing scales analogy: these scales showed a 95% margin of error of 2.84 from an object with a known weight. We then used these scales to weigh parcels destined for France and Germany of an unknown weight. Those for Germany were on average 2.33g heavier, which a statistical test determined to be significant. Does that hold true when we know the scales have an error margin of 2.84? Perhaps as the magnitude of error is equal in each group, and randomly distributed, is this already built into the statistical comparison? | |
| May 6, 2020 at 17:16 | history | answered | BruceET | CC BY-SA 4.0 |