Models with ordered and unordered factors

Hello;

I am having a problems with the interpretation of models using ordered or
unordered predictors.
I am running models in lmer but I will try to give a simplified example
data set using lm.
Both in the example and in my real data set I use a predictor variable
referring to 3 consecutive days of an experiment. It is a factor, and I
thought it would be more correct to consider it ordered.
Below is my example code with my comments/ideas along it.
Can someone help me to understand what is happening?

Thanks a lot in advance;

Catarina Miranda


y<-c(72,25,24,2,18,38,62,30,78,34,67,21,97,79,64,53,27,81)

Day<-c(rep("Day 1",6),rep("Day 2",6),rep("Day 3",6))

dataf<-data.frame(y,Day)

str(dataf) #Day is not ordered
#'data.frame': ? 18 obs. of ?2 variables:
# $ y ?: num ?72 25 24 2 18 38 62 30 78 34 ...
# $ Day: Factor w/ 3 levels "Day 1","Day 2",..: 1 1 1 1 1 1 2 2 2 2 ...

summary(lm(y~Day,data=dataf)) ?#Day 2 is not significantly different from
Day 1, but Day 3 is.
#
#Call:
#lm(formula = y ~ Day, data = dataf)
#
#Residuals:
# ? ?Min ? ? ?1Q ?Median ? ? ?3Q ? ? Max
#-39.833 -14.458 ?-3.833 ?13.958 ?42.167
#
#Coefficients:
# ? ? ? ? ? ?Estimate Std. Error t value Pr(>|t|)
#(Intercept) ? 29.833 ? ? ?9.755 ? 3.058 0.00797 **
#DayDay 2 ? ? ?18.833 ? ? 13.796 ? 1.365 ?0.19234
#DayDay 3 ? ? ?37.000 ? ? 13.796 ? 2.682 ?0.01707 *
#---
#Signif. codes: ?0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1
#
#Residual standard error: 23.9 on 15 degrees of freedom
#Multiple R-squared: 0.3241, ? ? Adjusted R-squared: 0.234
#F-statistic: 3.597 on 2 and 15 DF, ?p-value: 0.05297
#

dataf$Day<-ordered(dataf$Day)

str(dataf) # "Day 1"<"Day 2"<"Day 3"
#'data.frame': ? 18 obs. of ?2 variables:
# $ y ?: num ?72 25 24 2 18 38 62 30 78 34 ...
# $ Day: Ord.factor w/ 3 levels "Day 1"<"Day 2"<..: 1 1 1 1 1 1 2 2 2 2 ...

summary(lm(y~Day,data=dataf)) #Significances reversed (or "Day.L" and
"Day.Q" are not sinonimous "Day 2" and "Day 3"?): Day 2 (".L") is
significantly different from Day 1, but Day 3 (.Q) isn't.

#Call:
#lm(formula = y ~ Day, data = dataf)
#
#Residuals:
# ? ?Min ? ? ?1Q ?Median ? ? ?3Q ? ? Max
#-39.833 -14.458 ?-3.833 ?13.958 ?42.167
#
#Coefficients:
# ? ? ? ? ? ?Estimate Std. Error t value Pr(>|t|)
#(Intercept) ?48.4444 ? ? 5.6322 ? 8.601 3.49e-07 ***
#Day.L ? ? ? ?26.1630 ? ? 9.7553 ? 2.682 ? 0.0171 *
#Day.Q ? ? ? ?-0.2722 ? ? 9.7553 ?-0.028 ? 0.9781
#---
#Signif. codes: ?0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1
#
#Residual standard error: 23.9 on 15 degrees of freedom
#Multiple R-squared: 0.3241, ? ? Adjusted R-squared: 0.234
#F-statistic: 3.597 on 2 and 15 DF, ?p-value: 0.05297

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