Comparing Cats: A Discussion of Similarities & Differences

[Shadow]

(09-27-2020, 07:17 PM)Tigerclaw Wrote:

(09-26-2020, 01:21 PM)Shadow Wrote: This is now somewhat longer text. I might modify it with time to shorter, but now I go with this.


About average weights.

Since there seems to be some disagreement about the way to calculate, I thought to put here some thoughts.


If 15 pieces of something in two groups. Imagine figures as weights or whatever:

Group A, 10 pieces:
(101+150+113+134+120+145+119+131+140+107) Total 1260 and in average 126.

Group B, 5 pieces:
(134+148+159+155+128) Total 724 and in average 144,8

Counting all together, total number would be 1984 and in average 1 piece 132,27

If counting average like this 126+144,8=270,8 and then 270,8:2= 1 piece 135,40

In this case second method to calculate gives bigger and wrong average.


So if this would be calculating average size of fruits from one tree and having 10 fruits from yesterday and 5 fruits from today, it´s clear that right average weight is 132,27
This could be calculated by summing up all individual weights and dividing with total number.
Or (10x126+5x144,8):15 = 132,27. This could be the case if knowing only, that average weight of 10 was 126 and average weight of 5 was 144,8.

If counting 126+144,8:2 it would give that result 135,4, which could be said to be wrong in this case.

But if it would be known, that size and weight of fruits would variate every day. One day giving smaller and another day bigger, while total number would be about the same. Then situation would be a bit different.


So when comparing for instance tigers from place A and place B. If knowing without any doubt, that tigers at place A are bigger than tigers at place B, but could catch from place A for instance 8 tigers and from place B 25 tigers, situation is a bit more complicated.

Here it would be clear, that getting more reliable average weight for population B than for population A. Now if having for population A average of 215 kg and for population B 192 kg it could be said, that average weight of these two populations is 215+192:2= 203,5 kg. It could be said also, that it should be counted (215x8+192x25):33=197,58 kg

If it could be considered for sure, that population A really produce bigger tigers, then I think, that first method is ok and better, average of A + average of B divided with 2

But if there would be no certainty, just finding 8 tigers from A and 25 tigers from B, then second method, because it gives correct average for all.

And again if comparing data from 100 years ago to data from today, then if reasonable sample sizes from both, I would prefer method historical+current and divided by 2 to find out the best estimation of average weight for 100 years of time.

To give one concrete example. If people studying tigers could catch 75 Sundarban tigers with average weight of let´s say 130 kg and then 15 tigers from mainland India with average weight of 202 kg.

One could make a claim, that average weight of Bengal tigers is (75x130+15x202):90= 142 kg.  Another could say, that no, it´s 202+130 divided by 2 and result 166 kg. 

And I would say, that both failing to give right idea of the size concerning vast majority of Bengal tigers even though second method slightly closer.


What I try to say with all that is, that while calculating something is simple, getting the right answer can be way more complicated. There are many factors to consider when trying to be as objective as possible. Sample sizes, time of study, is there real and proven difference in between some populations or not, is some weight information reliable or not really etc.

I personally can´t take too seriously averages, when sample sizes are very small, just a few individuals. When something like 1-3 animals and especially if very similar sized, it´s practically useless. It just gives some idea about what it might be without any certainty.

Closer to ten and smaller and bigger included, then it starts to give at least a reasonable idea.

All in all, weights in this posting are (obviously) just random figures used to clarify things. I hope, that this opens up things and maybe some misunderstandings also can be understood if such have been there.

 Hello Shadow...

I think this should be a better example how much the first method falsify the data. (Note: if both datas have the same sample size then the 1st method can be used)
If you have 42 Tigers with a average weight of 190.5 kg and 2 Tiger with a average weight with 245 kg, 6 tigers with a average weight of 216 kg and one tiger with 197 and if we use the first method we get 212 kg for 51 tigers....

with the second method 195.7 kg.

Therefore it was good to take such errors more seriously.

Best regards

It´s a valid point to discuss about it, that how average weight should be calculated. These things can be discussed, when it´s done with good argumentation. It´s very clear, that no matter what animals or animal populations we are talking about, sample size of 1-5 isn´t enough to give reliable information for average weight. It´s more something like directional if that is the correct word. It gives just an idea what is maybe possible. So it can´t be evaluated in same way as average which have been got from some reasonable sample size, which should be at least around ten individuals and desirable more. There is too much room for coincidences when just a few individuals.

Naturally problem is, that in some occasions there simply isn´t much reliable data to use. In those cases we have just kind of estimations or guesses.

So when thinking purely mathematically, very small sample sizes are invalid in order to estimate averages for some big number of animals or animal populations. This can´t be denied, imo. 

I don´t think that this kind of thoughts wouldn´t be taken seriously, when discussed in decent way.

This kind of discussions are often poisoned by obvious or hidden agendas of people discussing. People have preset goals and it leads to cherry picking what comes to used data, also to using unreliable information etc. Here first priority has to be reliable data, no matter if it´s possible or impossible to make any conclusions from it. Reply