[R] Ancova_non-normality of errors

[Tobias Erik Reiners]

Hello Helpers,

I have some problems with fitting the model for my data...
-->my Literatur says (crawley testbook)=
Non-normality of errors-->I get a banana shape Q-Q plot with opening  
of banana downwards

Structure of data:
      origin   wt   pes gender
1      wild 5.35 147.0   male
2      wild 5.90 148.0   male
3      wild 6.00 156.0   male
4      wild 7.50 157.0   male
5      wild 5.90 148.0   male
6      wild 5.95 148.0   male
7      wild 8.55 160.5   male
8      wild 5.90 148.0   male
9      wild 8.45 161.0   male
10     wild 4.90 147.0   male
11     wild 6.80 153.0   male
12     wild 5.75 146.0   male
13     wild 8.60 160.0   male
14  captive 6.85 159.0   male
15  captive 7.00 160.0   male
16  captive 6.80 155.0   male
..
...
283    site 4.10 130.4 female
284    site 3.55 131.1 female
285    site 4.20 135.7 female
286    site 3.45 128.0 female
287    site 3.65 125.3 female

The goal of my analysis is to work out what effect the categorial  
factors(origin, gender) on the relation between  
log(wt)~log(pes)(-->Condition, fett ressource), have.
Does the source(origin) of translocated animals have an affect on  
performance(condition)in the new area?
I have already a best fit model and it looks quite good (or not?see below).

two slopes(gender difference)and 6 intercepts(3origin levels*2gender levels)

lm(formula = log(wt) ~ log(pes) + origin + gender + gender:log(pes))

Residuals:
      Min       1Q   Median       3Q      Max
-0.54181 -0.07671  0.01520  0.09474  0.28818

Coefficients:
                     Estimate Std. Error t value Pr(>|t|)
(Intercept)         -7.39879    1.97605  -3.744 0.000219 ***
log(pes)             1.78020    0.40118   4.437 1.31e-05 ***
originsite           0.06572    0.01935   3.397 0.000781 ***
originwild           0.07655    0.03552   2.155 0.032011 *
gendermale          -9.32418    2.37476  -3.926 0.000109 ***
log(pes):gendermale  1.90393    0.47933   3.972 9.06e-05 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.1433 on 281 degrees of freedom
Multiple R-Squared: 0.7227,     Adjusted R-squared: 0.7177
F-statistic: 146.4 on 5 and 281 DF,  p-value: < 2.2e-16

When plot this model I get a banana-shape in Normal Q-Q Plot(with open  
site pointing downwards) , indicating non-normality of my data....how  
to handle this?

-->Do I have unbalanced data?
       captive    site    wild
n-->     119     149      19

My problem is that I see that my data is not as good as the  
modelsummary tells.
Should I include another term in my model formular?

I think I have to differenciate more, but I don't know  
how.(contrasts?, TukeyHSD?,Akaike Information Criterion? or lme())to  
many different ways out there.

Cheers,
Tobi