COVARIANCE example for bird damage in Sorghum Plots

You first need to collect data (score of 1 to 10, or 0 to 100, or some other scale that can take qualitative data to a quantitative scale).  X person needs to know what 1 means and what 10 means.  10 would for me mean significant damage.  We need to “gauge damage” but using individual people.  If you want to add x-person, you can then compare them, but both need to be first instructed as to what the agreed-upon-scale meant.

Also, and unfortunately, the individual scoring the damage has to have his/her values for all plots.  ALL 72 plots where an independent score was recorded by that person.

How can this data be used.  First, if we plan on using this as a covariate, we must first analyze our “bird-damage” data as a dependent variable in the model.  If for instance the independent effect of treatment in the model was significant for “bird-damage” , then “bird-damage” cannot be used as a covariate.  If “bird damage” is found to be independent of treatment, it can be used as a covariate to remove this source of variability, and that allows the researcher to better detect treatment differences using their dependent variable (e.g., grain yield). 

Covariance can be viewed as  a linear regression adjustment, within an analysis of variance model.

We cover all of this in the Experimental Methods class that will be taught in the spring of 2019.  For this data, I will work with those interested to properly employ the covariate.

But, you have to remember, that “bird-damage” could actually be influenced by treatment.  Maybe the birds preferred the high N plots.  You just don’t know.  Also, this bird-damage data may not be normally distributed which throws and additional wrench into the mix, since non-parametric statistics would then be in order.

For taking scores, or ranks, you just have to apply the “score” number to the exact same area that would be harvested.  If I am going to harvest all of the center 2 rows, then the score has to be my “view” or my “rank” of that very same area.  These areas (harvest and rating) have to be the same, and that makes sense.  If the score and harvested area are different, how could I match final values up?  Obviously you cant. 

So, give those 2 center rows that you will harvest, your “mental average” score.  '

Should I generate scores from two different individuals on damage?  Run them separately as covariates?

EXAMPLE:  

Would these values work? With 2-4 and 6-9 being in between values?

1 - no damage
5 - 50% loss of grain
10 - complete loss of grain 

For me this is not appropriate because I seriously doubt you have plots that have 100% damage (a total loss).   Ten has to be the plot with the most damage of all plots.  A score of 1 has to be a plot that has the least amount of damage. 

You have to remember that you are entering a “score” for bird damage.  Nothing else.  If a plot is going to yield zero-grain, but where the reason for that damage score of 10 has nothing to do with “bird damage” then that plot’s bird damage score has to be zero.

These things happen overnight.  What can I do to ensure that I will have data for my trial or an estimate of yield?  or treatment effects?

Rule:  You have to run anova using preplant P as a dependent variable FIRST.  Why? Because you have to establish that "treatment" was not significant when using your potential covariate as a dependent variable. In essence the covariate has to be "RANDOM".   Your potential covariate has to be independent of treatment and the only way to establish this is to use as a dependent variable in your model.  Once you establish that your covariate is independent of treatment, you can legitimately use it. 

data one;
input rep nrate tillage yield preP;
cards;
1 0 0 20 16
1 50 0 25 13
1 100 0 29 13
1 150 0 35 14
1 0 1 35 18
1 50 1 35 16
1 100 1 38 11
1 150 1 39 19
2 0 0 20 22
2 50 0 26 23
2 100 0 30 21
2 150 0 32 25
2 0 1 36 19
2 50 1 36 11
2 100 1 37 18
2 150 1 40 16
3 0 0 17 28
3 50 0 22 19
3 100 0 25 28
3 150 0 29 22
3 0 1 29 23
3 50 1 34 25
3 100 1 38 24
3 150 1 40 18
proc print;
proc glm;
class tillage nrate;
model preP = nrate tillage nrate*tillage;
means nrate tillage nrate*tillage;
run;
proc glm;
class tillage nrate;
model yield = nrate tillage nrate*tillage;
means nrate tillage nrate*tillage;
run;
proc glm;
class tillage nrate;
model yield = nrate tillage nrate*tillage preP;
lsmeans nrate tillage nrate*tillage;
run;