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<p>[QUOTE="Roerbakmix, post: 4802130, member: 100731"]As an epidemiologist, I really like these kind of data analyses. However, I believe there are some flaws in your statistics. First, since your aim is to infer causality and reject the null hypothesis (H0 = hammer prices increase and estimates increase accordingly; H1=i.e. hammer prices increase while estimates stay low), you have to correct for confounding. Next, since you're looking at the relation between this hypothesis over time, you have to think about time-varying confounders (e.g. auctions in winter, near Christmas tend to yield higher hammer prices than those in autumn). Some other confounders come to mind:</p><ul> <li>what is the distribution of coins in the auction? Some coins tend to be more popular than others for no particular reason (at least, not a reason I've found out). This is probably unmeasured confounding, but you should be able to correct for the proportion of e.g. greek coins, roman coins, etc.</li> <li>More importantly: what is the distribution of estimates in the auction. E.g. an auction with mainly low estimates may have a different <b>estimate:hammer-price ratio</b> than those with mainly high estimates. In fact, I looked into the effect of estimate on hammer price in a recent CNG auction (copied from a post here <a href="https://www.cointalk.com/threads/estimates-for-ancient-coin-auctions.360318/#post-4517298" class="internalLink ProxyLink" data-proxy-href="https://www.cointalk.com/threads/estimates-for-ancient-coin-auctions.360318/#post-4517298">https://www.cointalk.com/threads/estimates-for-ancient-coin-auctions.360318/#post-4517298</a>):</li> </ul> <blockquote><p><i>Here we see the relation between the estimated price (x-axis) and the realized price (y-axis);<i>(n=856 coins)</i>. The dotted 45-degree line would mean that the coin was sold at the estimated price (i.e. perfect agreement between estimate and hammer).</i></p><p><i><img src="https://www.cointalk.com/attachments/upload_2020-5-21_13-26-43-png.1119170/" class="bbCodeImage wysiwygImage" alt="" unselectable="on" /></i></p><p><i>So, eyeballing this graph, most coins are in the 0-5000 hammered price, and the relation between the estimated price and hammered price seems fairly linear. However, zoomed in at the 0-5000 price range...</i></p><p><i><img src="https://www.cointalk.com/attachments/upload_2020-5-21_13-33-52-png.1119177/" class="bbCodeImage wysiwygImage" alt="" unselectable="on" /></i></p><p><i>... it becomes clear however that <b>coins in this price range usually hammer higher than the estimate</b>, with only a few hammering at or lower than the estimate. When looking at the relation between the estimate and the <b>ratio hammer prize / estimated price</b>, we see this again: most coins at the lower end result in a higher hammered price</i></p><p><i><img src="https://www.cointalk.com/attachments/upload_2020-5-21_13-36-59-png.1119178/" class="bbCodeImage wysiwygImage" alt="" unselectable="on" /></i></p><p><i>indeed, the <b>ratio between the hammered prize and the estimated price in the 0-5000 estimate range is 1.67 (95% CI 1.62 - 1.71)</b>; for the 5000 to max estimate range, this is 1.24 (95% CI 1.16-1.32), an obvious difference (though the 5000 cut-off is of course arbitrarily chosen).</i></p></blockquote><p><br /></p><p>Speaking about statistics, you've drawn a linear regression line through your data-points which is probably not a good fit. In the graphs above, I plotted a LOESS curve, which is a sort of modeled smoother based on the Y- and X-values in combination with a couple of other parameters, but other regression methods may be better suited for your data. </p><p><br /></p><p>Ideally, we would have a dataset with the following:</p><ul> <li>the date of the auction (should be easily extractable)</li> <li>the estimated price</li> <li>the hammered price</li> <li>the number of active bidders (which CNG would probably not disclose) per coin</li> <li>the type of coin (i.e. Greek / Roman republican / British, etc.) (less easily extractable, but doable)</li> <li>the condition (should be extractable, but is determined by CNG)</li> <li>the rarity (which is also difficult to determine)</li> <li>provenance (but, which provenance yields higher hammer prices?)</li> <li>etc. etc. </li> </ul><p>Then, we would be able to conduct a multivariabel model, and try to infer a relation between the estimated price (corrected for all these confounders) and the hammered price. This obviously would be nice to do, but it's quite an amount of work.[/QUOTE]</p><p><br /></p>
[QUOTE="Roerbakmix, post: 4802130, member: 100731"]As an epidemiologist, I really like these kind of data analyses. However, I believe there are some flaws in your statistics. First, since your aim is to infer causality and reject the null hypothesis (H0 = hammer prices increase and estimates increase accordingly; H1=i.e. hammer prices increase while estimates stay low), you have to correct for confounding. Next, since you're looking at the relation between this hypothesis over time, you have to think about time-varying confounders (e.g. auctions in winter, near Christmas tend to yield higher hammer prices than those in autumn). Some other confounders come to mind: [LIST] [*]what is the distribution of coins in the auction? Some coins tend to be more popular than others for no particular reason (at least, not a reason I've found out). This is probably unmeasured confounding, but you should be able to correct for the proportion of e.g. greek coins, roman coins, etc. [*]More importantly: what is the distribution of estimates in the auction. E.g. an auction with mainly low estimates may have a different [B]estimate:hammer-price ratio[/B] than those with mainly high estimates. In fact, I looked into the effect of estimate on hammer price in a recent CNG auction (copied from a post here [URL]https://www.cointalk.com/threads/estimates-for-ancient-coin-auctions.360318/#post-4517298[/URL]): [/LIST] [INDENT][I]Here we see the relation between the estimated price (x-axis) and the realized price (y-axis);[I](n=856 coins)[/I]. The dotted 45-degree line would mean that the coin was sold at the estimated price (i.e. perfect agreement between estimate and hammer). [IMG]https://www.cointalk.com/attachments/upload_2020-5-21_13-26-43-png.1119170/[/IMG] So, eyeballing this graph, most coins are in the 0-5000 hammered price, and the relation between the estimated price and hammered price seems fairly linear. However, zoomed in at the 0-5000 price range... [IMG]https://www.cointalk.com/attachments/upload_2020-5-21_13-33-52-png.1119177/[/IMG] ... it becomes clear however that [B]coins in this price range usually hammer higher than the estimate[/B], with only a few hammering at or lower than the estimate. When looking at the relation between the estimate and the [B]ratio hammer prize / estimated price[/B], we see this again: most coins at the lower end result in a higher hammered price [IMG]https://www.cointalk.com/attachments/upload_2020-5-21_13-36-59-png.1119178/[/IMG] indeed, the [B]ratio between the hammered prize and the estimated price in the 0-5000 estimate range is 1.67 (95% CI 1.62 - 1.71)[/B]; for the 5000 to max estimate range, this is 1.24 (95% CI 1.16-1.32), an obvious difference (though the 5000 cut-off is of course arbitrarily chosen).[/I][/INDENT] Speaking about statistics, you've drawn a linear regression line through your data-points which is probably not a good fit. In the graphs above, I plotted a LOESS curve, which is a sort of modeled smoother based on the Y- and X-values in combination with a couple of other parameters, but other regression methods may be better suited for your data. Ideally, we would have a dataset with the following: [LIST] [*]the date of the auction (should be easily extractable) [*]the estimated price [*]the hammered price [*]the number of active bidders (which CNG would probably not disclose) per coin [*]the type of coin (i.e. Greek / Roman republican / British, etc.) (less easily extractable, but doable) [*]the condition (should be extractable, but is determined by CNG) [*]the rarity (which is also difficult to determine) [*]provenance (but, which provenance yields higher hammer prices?) [*]etc. etc. [/LIST] Then, we would be able to conduct a multivariabel model, and try to infer a relation between the estimated price (corrected for all these confounders) and the hammered price. This obviously would be nice to do, but it's quite an amount of work.[/QUOTE]
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