Statistics

Our goal is to record statistics that can be used to estimate standard deviation or standard error. Many different methods can be used to summarize data, and this is reflected in the diversity of statistics that are reported. An overview of these methods is given in tab:statname and a description below.

Where available, direct estimates of variance are preferred, including Standard Error (SE), sample Standard Deviation (SD), or Mean Squared Error (MSE). SE is usually presented in the format of mean$ (\pm$   SE$ )$. MSE is usually presented in a table. When extracting SE or SD from a figure, measure from the mean to the upper or lower bound. This is different than confindence intervals and range statistics (described below), for which the entire range is collected.

If MSE, SD, or SE are not provided, it is possible that LSD, MSD, HSD, or CI will be provided. These are range statistics and the most frequently found range statistics include a Confidence Interval (95%CI), Fisher's Least Significant Difference (LSD), Tukey's Honestly Significant Difference (HSD), and Minimum Significant Difference (MSD). Fundamentally, these methods calculate a range that indicates whether two means are diffent or not, and this range uses different approaches to penalize multiple comparisons. The important point is that these are ranges and that we record the entire range.

Another type of statistic is a ``test statistic''; most frequently there will be an F-value that can be useful, but this should not be recorded if MSE is available. Only if there is no other information available, record the P-value.


List of the statistics that can be entered into the statname field of traits and yields tables. Please see David (or Mike) if you have questions about statistics that do not appear in this list. If you have P, or LSD in a study with $ n\neq b$ (e.g. not a RCBD, see tab:statconversions), please convert these values prior to entering the data, and add a note that stat was transformed to the table. Note: These are listed in order of preference, e.g., if SD, SE, or MSE are provided then use these values
Table 5: List of statistical summaries
statname name definition notes
SD Standard Deviation, $ s$ $ \sqrt{\frac{1}{N} \sum{(x_i - \bar{x})^2}}$ $ \bar{x}$ is the mean
SE Standard Error $ \frac{s}{\sqrt{n}}$  
MSE Mean Squared Error   like SD, but with multiple treatments. in R: $ \frac{mean(aov(y x)\$residuals^2}{aov(y x)\$df}$
95%CI 95% Confidence Interval $ t_{1-^{\alpha}/_2,n}*s$ measure the 95% CI from the mean, this is actually $ ^1/_2$ of the CI
LSD Least Significant Difference $ t_{1-\frac{\alpha}{2},n}\sqrt{2\text{MSE}/b}$ $ b$ is the number of blocks (Rosenberg 2004)
MSD Minimum Significant Difference    

Figure 9: Form used to enter a new trait.
Image traits_new


Table 6: Table of traits to be entered. Notes: q: if only q is available, record this value, otherwise record either total root and total aboveground (for grasses) or fine root and leaf biomass (for trees) data when these are available. For calculating q, units may be per area or per plant, but must be the same for both the aboveground/leaf and belowground/fine root components. q is calculated from fine root and leaf biomass that are associated with the same treatment, date, species, and site. root_respiration_rate: represents the total root respiration, root_respiration_factor is an ED parameter that represents the maintenance respiration, for which little (if any) data is available. Only if root maintenance respiration data is found, the root_respiration_factor variable should be used.
Variable units median (90%CI) or range definition
https://www.betydb.org/variables/4Vcmax $ \mu$mol CO$ _2$ m$ ^{2}$ s$ ^{-1}$ $ 44 (12, 125)$ maximum rubisco carboxylation capacity
https://www.betydb.org/variables/15SLA m$ ^2$ kg$ ^{-1}$ $ 15(4,27)$ Specific Leaf Area area of leaf per unit mass of leaf
https://www.betydb.org/variables/254LMA kg m$ ^{-2}$ $ 0.09 (0.03, 0.33)$ Leaf Mass Area (LMA = SLM = 1/SLA) mass of leaf per unit area of leaf
https://www.betydb.org/variables/10leafN % $ 2.2(0.8, 17)$ leaf percent nitrogen
https://www.betydb.org/variables/31c2n leaf leaf C:N ratio $ 39(21,79)$ use only if leafN not provided
https://www.betydb.org/variables/40leaf turnover rate 1/year $ 0.28(0.03,1.0) $  
https://www.betydb.org/variables/5Jmax $ \mu$mol photons m$ ^{-2}$ s$ ^{-1}$ $ 121(30, 262)$ maximum rate of electron transport
https://www.betydb.org/variables/26stomatal slope   $ 9(1, 20)$  
https://www.betydb.org/variables/9GS     stomatal conductance (= gs $ _{\textrm{max}}$
https://www.betydb.org/variables/21q*   0.2-5 ratio of fine root to leaf biomass
*grasses: ratio of root:leaf $ =$ below : above ground biomass    
aboveground biomass g m$ ^{-2}$ or g plant$ ^{-1}$    
root biomass g m$ ^{-2}$ or g plant$ ^{-1}$    
*trees: ratio of fine root:leaf biomass    
leaf biomass g m$ ^{-2}$ or g plant$ ^{-1}$    
fine root ($ <$2mm) biomass g m$ ^{-2}$ or g plant$ ^{-1}$    
https://www.betydb.org/variables/41root turnover rate 1/year 0.1-10 rate of fine root loss (temperature dependent) year$ ^{-1}$
https://www.betydb.org/variables/22leaf width mm 22(5,102)  
https://www.betydb.org/variables/27growth respiration factor % 0-1 Proportion of daily carbon gain lost to growth respiration
https://www.betydb.org/variables/7R $ _{\textrm{dark}}$   $ \mu$mol CO$ _2$ m$ ^{-2}$ s$ ^{-1}$ dark respiration
https://www.betydb.org/variables/39quantum efficiency % 0-1 efficiency of light conversion to carbon fixation, see Farqhuar model,
https://www.betydb.org/variables/29dark resp factor % 0-1 converts Vm to leaf respiration
https://www.betydb.org/variables/44seedling mortality % 0-1 proportion of seedlings that die
https://www.betydb.org/variables/192r fract % 0-1 fraction of storage to seed reproduction
https://www.betydb.org/variables/244root respiration rate* CO$ _2$ kg$ ^{-1}$ fine roots s$ ^{-1}$ 1-100 rate of fine root respiration at reference soil temperature
https://www.betydb.org/variables/49f labile % 0-1 fraction of litter that is goes into the labile carbon pool
https://www.betydb.org/variables/45water conductance      


David 2011-10-07