Some Qs people asked me on science and my replies to them - Part 20 - SCI-ART LAB2023-03-25T23:18:47Zhttps://kkartlab.in/forum/topics/some-qs-people-asked-me-on-science-and-my-replies-to-them-part-20?groupUrl=some-science&feed=yes&xn_auth=no335
(In statistics, the value…tag:kkartlab.in,2016-12-01:2816864:Comment:1431672016-12-01T07:28:35.085ZDr. Krishna Kumari Challahttps://kkartlab.in/profile/DrKrishnaKumariChalla
<p>335</p>
<p>(In statistics, the value of sigma you accept is a choice. 2 sigma (the usual choice in climate science) on a bell shaped curve corresponds to P <0.05. This means that 1 in 20 times you will get the result by chance. A 5 sigma corresponds to P <0.0001. This, of course, means that only 1 time in 10,000 will the result be by chance. A greater sigma or lower p value does <b>not </b>indicate greater certainty. Instead, it indicates the odds that the result will occur by chance.…</p>
<p>335</p>
<p>(In statistics, the value of sigma you accept is a choice. 2 sigma (the usual choice in climate science) on a bell shaped curve corresponds to P <0.05. This means that 1 in 20 times you will get the result by chance. A 5 sigma corresponds to P <0.0001. This, of course, means that only 1 time in 10,000 will the result be by chance. A greater sigma or lower p value does <b>not </b>indicate greater certainty. Instead, it indicates the odds that the result will occur by chance. We <b>choose </b>to accept the risk that the results were by chance. This is the Type I (or alpha) error in statistics.)</p>
<p class="qtext_para">Science, in general, has decided that we will accept p < 0.05. It was a <i>choice</i>. You could also accept the same p value. That you do not does not confer greater certainty to your results or provide more support for your theory. Your insistence on 5 sigma could indicate 1) an ignorance of statistics, 2) a very cautious and risk-averse personality, or 3) your data has very little variance. I suspect the latter is involved. Physics, being deterministic, has very little variance.</p>
<p class="qtext_para">Biology has much greater variance, as individuals vary by quite a bit. Climate science has even more variance, since there are quite a few variables, and even more interactions. Therefore the variance precludes using a 5 sigma. You would simply never see an effect that is actually there. This is a type II error. It’s always a balance trying to avoid either the type I or the type II error.</p>
<p class="qtext_para">It is also possible that climate data is not bell-shaped. Everything we have been talking about is based on “parametric” data, which includes a bell-shaped distribution of values. What’s more, the really drastic effects may fall before the 2 sigma level. If climate data does not have that, then a higher p value may be better: <span class="qlink_container"><a href="http://www.huffingtonpost.com/michael-e-mann/the-fat-tail-of-climate-change-risk_b_8116264.html" rel="noopener nofollow" target="_blank" class="external_link">The 'Fat Tail' Of Climate Change Risk</a></span></p>
<p class="qtext_para">You might find this discussion of statistics and climate change interesting: <span class="qlink_container"><a href="http://www.stats.org/climate-change-statistical-significance-and-science/" rel="noopener nofollow" target="_blank" class="external_link">Climate Change, Statistical Significance, and Science - STATS</a></span></p>