UKC

Hi there,

I know there are one or two maths bods out there and I'm in need of clarification.

Background - waxcaps (fungi) grow on grasslands..nothing revealing there..

Analysis results - a negative -0.272 r value (not significant) has been produced when sward height was put against waxcap richness.

The result would be significant if they both increased simultaneously thus producing a positive result.

In my eyes therefore this negative value suggests that as sward height increases, waxcap richness decreases, correct? and whilst not significant I actually don't want it to be as the theory is that as sward height increases this smothers the fungi's ability to produce a fruiting body so waxcaps decrease (above ground, not necessarily below). I would conclude by saying as sward height increased, waxcap species richness decreased and whilst the result was not significant (in a statistical sense) it does in fact fit with X, Y and Z's findings.

A whistle stop tour but I think you get the gist?

Thanks in advance,
Stuart.

In reply to greylag:

I'm a biologist not a statistician but could you be a bit clearer,
"as sward height increases, waxcap richness decreases"
do you mean species richness? or abundance of sporocarps?

In reply to Doug:

Hi Doug,

Thanks for your reply.

Waxcap species richness though you're right to mention sporocarps. I'm using the term waxcap species richness but as the following extract from a journal explains the two are linked; ''The absence of mowing or grazing also has a deleterious effect on fruit body production... cropped vegetation does make it very much easier for the mycologist to find and thus record fruit bodies.''

In reply to greylag:

I don't know much about waxcaps, but used to work on ectomychorrhizal fungi where diversity of fruiting bodies (sporocarps) bore little or no relation to the 'real' diversity, ie that belowground. Is it the same for waxcaps ? Isn't what you are seeing, more like short swards increase fruit body production ? (with no real change in spp-richness)

In reply to Doug:

Yes short swards do facilitate fruiting body production as mentioned.

Again you're right that short swards don't necessarily increase waxcap species richness. The thinking is though is that a well grazed / mown grassland is low in nutrients (provided more nutrients are removed than put in to the grassland). Low nutrient levels may not necessarily be a direct influence on waxcap species richness, but it is a direct influence on vascular plant species richness. Such grasslands are often species rich and aren't dense stands of rye-grass for arguments sake. As such a short sward is conducive to a rich waxcap population.

I think that makes sense..I'm in riddles with this. I'm trying to draw conclusions and things I don't think even exist!

What I've read makes me think that waxcaps are under recorded rather than rare. Some of the best sites for waxcaps are on botanically mundane, sometimes nutrient rich grasslands which goes against what I've just written above!!!

Thanks.

In reply to greylag:
Yes its well known that low nutrient levels are associated with vascular plant species richness, but these don't necessarily have short swards - think of spp-rich haymeadows

Although this hasn't helped find a statistician

In reply to Doug:

ha no that's fine Doug you've made me think..and my thinking has not produced an answer so either I'm stupid (definite possibility) or the answer isn't black and white and we know that to be the case with all biology / ecology.

Thanks

In reply to greylag:


I know nothing about sward height or waxcap richness, but I have worked with statistics and correlation and Pearson's r for decades. I am very willing for any mathematician/ statistician to disagree, however, my comments are as follows:

An r value of -0.272 or 0.272 is very, very low and means that there is no or almost no meaningful relationship between the two variables. A common way to see how meaningful is the relationship revealed in an r value is to square the number. For example with a positive r of 0.272, the actual relationship revealed by the correlation is 0.074 [0.272 squared] - and .9 or .8 is a high correlation, .6 or .5 is medium, and .4 or so or below is low or very low and usually of almost no interest.

You also said your result is "not significant". But statistical significance with correlation / Pearson's r is not a function or expression of the closeness of the relationship between the two variables, but a function of how many measurements you took: so a result of .4 or below, with a statistical significance of say .999, is still of almost no interest.

In reply to greylag:

Can you give a little more detail on the statistical test you are applying? It sounds like you could be doing a one-tailed for a positive r-value. In which case you will never get a statistically significant result a negative correlation.


It's ok to say that the negative r-value you found is a result consistent with the XYZ theory that the correlation should be negative. What matters is how strong a piece of evidence your result is for XYZ theory. The statistical tests I think you could be doing are only one very small part of understanding this.

Caveat lector: not a statistician, but a physicist.

In reply to greylag:

I'm not sure I get you, but if it's not significant it's not significant.

A low r squared value can be significant but if it's not it's not.

You've got to be really careful making conclusions when not significance as it is basically just by chance.

Can you do further analysis? Look at a multitude of factors?

In reply to AlexM:

Hi Alex,

I'm using Pearson's as my sward height was normally distributed. I've used Spearman's where a variable wasn't normally distributed.

I have another 13 independent variables e.g. pH, soil moisture and organic matter content, soil nitrate concentrations etc. and after running a multiple regression test to see if one or more are related it seems none are.

In reply to abseil:

I have read about squaring the r value if negative but don't understand why? I ran the test using SPSS (a computer programme) and whilst it provides an answer without thinking, I'd much prefer to hurt my brain working it out manually and actually understanding it all.

In reply to greylag:

if you have several variables, shouldn't you be using ANOVA or similar ?

In reply to Roadrunner5:

But the way I understand it is that a significant result assumes as one increases, so does the other, 2=2, 4=4, 6=6 etc etc.

Therefore if you plot sward height on the x axis, waxcap richness on the y axis, the downwards sloping trendline leads me to think that as sward height increases waxcap richness decreases e.g. 2cm sward height = 10 species, 4cm = 8 species , 6 cm= 4 species , 8 cm = 2 species until you get to a 'tall' sward height of 10 cm and 0 waxcaps.

In reply to Doug:
This was discussed with my lecturer Doug and he suggested a stepwise regression model which removes the least significant value at each 'step' until you are (hopefully) left with two / three significant results which are linked thus identifying the important factors in conserving a waxcap grassland.

I wasn't that fortunate.

Thanks for all of your responses..you're filling in for a lecturer who is working in Indonesia with limited or no internet! Excellent!

In reply to greylag:

Won't help with the stats but guess you've seen
Griffith, G. W., Roderick, K., Graham, A., & Causton, D. R. (2012). Sward management influences fruiting of grassland basidiomycete fungi. Biological Conservation, 145(1), 234-240.
Halbwachs, H., Karasch, P., & Griffith, G. W. (2013). The diverse habitats of Hygrocybe–peeking into an enigmatic lifestyle. Mycosphere, 4(4), 773-792.
?

In reply to greylag:


About "squaring the r value if negative but don't understand why" my understanding [as taught by a maths professor in advanced statistics class] is, squaring the r value [an exercise unconnected to whether it is a negative or positive correlation] shows you [as I said before] the actual and measured meaningfulness of the relationship between the two variables. What I learned was e.g. if the correlation is .9, squaring that [result = .81] shows the actual/real connection/correlation between variable A and variable B: .81 rather than .9.

I'm really sorry I can't explain this point any better.....

About "I'd much prefer to hurt my brain working it out manually and actually understanding it all", too right, and I believe it really pays users to understand statistics results and what they mean rather than just feeding in numbers and pressing buttons and quoting the statistical significance.

In reply to Doug:

Cheers Doug, yes I have both of those. Griffith in particular is the Lord of the Waxcaps.

Thanks all for your help, I'll look further in to your suggestions.

Enjoy your Saturday evenings!

In reply to greylag:

Ahh ok. Regression is a field in itself. I don't know enough about it or about what SPSS is doing to say anything specific.

Best bet is to find a friendly statistician at your institution and ask for help. Professional input is the best way to decide whether your results support XYZ, support the opposite, or you are just looking at noise. And in the case of the former two, how strong the evidence is for either, whether it's worth going away and collecting more data, etc...



Don't be concerned about trying to find a positive result. What you're doing is still science, even if you find a non-result.

In reply to AlexM:


I remember getting advice from the head of stats when designing the field work for my PhD, 3 years later I went back for some further advice on how best to analyse the data to find the old head of dept had retired. The new guy took one look at my experimental design & suggested that I should have had advice before setting up the experiment & then spent a long time telling me that I'd be lucky to get anything out of such a poorly designed experiment. In some ways he was right, but luckily it seems neither of my examiners knew much about stats & were more interested in the results.

In reply to Doug:

Never trust a statistician you have not made up yourself, or something along these lines...

CB

In reply to Doug:

Yeap, sounds like statisticians.

Another option is to hit the stats books and cram up oneself.