Here's yet another table from that " How many rarities are missed?" thingy. This time they're looking for " weekend bias". Apparently, in some places more rare birds get found at the week-ends. Coo !! But something is missing/not explained that would be quite useful ... but it isn't there. There's a bit of a clue there for you ..... . . . . ↓ Well... they haven't told us readers what that "Chi-sq" thingy is. It's very kind of them to assume that we all know what it is and what it tells us ... but it would be kinder to tell us as well, just in case. So ... I'm going to tell you instead, seeing as they can't be bothered. You've probably noticed that Holkham has the BIGGEST chi-squared value ( 54.1) and the Holkham numbers are quite varied... the biggest result (30) is a massive ! 10 x the smallest rarity count ( 3) . Basically, they're all over the bloody place. On the other hand, the location with the lowest chi-sq value (Dungeness, 2.9) has results which are pretty similar .... the largest (17) is only about 1½ x the smallest (11). So ,the chi-squared result is a measure of how "all-over-the-bloody-place" your results are. Please excuse the technical terms there. The "posh" way of putting it is to say that the results are/aren't "homogenous" or "clustered closely around the mean/expected value". So..... now you need to how how to work out that vital chi-squared number. Because it will tell you exactly how " all-over-the-place" the results are. [ At this point, I offer you the option of not bothering to learn how to do it. ] [ I suspect there are "apps" that will do it for you ] [ Whatever "apps" are ] I'm going to go through it all myself, but I found this nifty video which is reasonably good ..... it's not perfect though. * But it does show you the basic "worky-out" process. You will need to bung your " picture quality" up to max to stop the numbers getting rather blurred when you enlarge it all to full screen mode. So ....that's how you get your chi-squared numbers. And now I'm going to show you how they worked out that previously-mentioned " Dungeness" one in the table I put on at the beginning, ( Chi-sq = 2.9) using the same process .. here's the numbers .. 13 12 11 11 11 16 17 First we work out the mean ..... we add them all up (91) ... and we divide by 7 = 13 That's what he called the "expected" number ... "E " Right then ... the first result is 13. We subtract E, our "average" from it 13- 13 ... = 0 ( that was a tricky one) Then we square it ... 0 x 0 = 0 Then we divide by the average, "expected" number ..... 0 ÷13 = 0 ........................................................ We now move on to the 2nd result ... 12 We again work out O - E = 12 -13 = -1 and we square it ... -1 x -1 = 1 Then we divide it by E ( 13) .... 1 ÷ 13 = 0.0769 ........................................... Moving on to our 3rd result ... 11 We subtract 13 again ........ 11-13 = -2 We square it ....................... -2 x -2 = 4 We divide that by E again .... 4 ÷ 13 = 0.3077 there's three lots of 11 .. ... so we add all three up ... 0.3077 + 0.3077 = 0.3077 = 0.923 ......................................... Let's "do" the next one ... 16. 16 - 13 = 3 3² = 9 9 ÷13 = 0.6923 ..................................................... Now the last one phew! 17. 17 -13 = 4 4² = 16 16 ÷ 13 = 1.231 Woo !! We've worked all the chi-squared thingys out. Now we add them all up to get the total chi squared essential result ... 0 + 0.0769 + 0.923 + 0.6923 + 1.231 = 2.92 ( 2.9 in the table up top) So Chi² = 2.92 with 6 degrees of freedom. (What ?) Never mind the technicalities... D of F is just 1 less than the number of numbers you've got. 7-1= 6 OK ..... working that out is the first step. So .... I want you to have a go at working out the chi-sq result for the site with the biggest chi-sq ... Holkham. It "ought" to be 54.1 or thereabouts ... it depends how much rounding-off you did. [ Note ... this is not compulsory .... you could try that "app" I mentioned ] [ Or just , er, do something else. Birding is usually relaxing ] [ I seem to remember that nobody "did" that Poisson distribution thing either ] And then I'll show you how to "use" that number to confirm/reject the crucial .. NULL HYPOTHESIS ! You can't wait !! Come to think of it, if you've got this far, you probably know it already. or you can work it out yourselves. There ought to be a band/song with the title " Null Hypothesis". Would you believe it ... there is !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Briwsion ! * And I couldn't type that big thingy that looks like a an M that's tipped over backward after drinking too much.
It just means "add up all your calculated results"
0 Comments
Leave a Reply. |
AuthorThat's the author up there ... I was young and sprightly then. Archives
October 2022
|