ANOVA - discrepancy between main result and model parameters

#1
I am running a two-way ANOVA examining the influence of both school and gender on Likert scale answers.

The Type III SS results show school significant (p=0,001), but gender or gender*school not significant.

Type III Sum of Squares analysis (Variable 10.Based on your overall perception of your teacher, do you believe he/she reviews and adjusts the course material every year based on his/her course evaluations ?):

Source DF Sum of squares Mean squares F Pr > F
Gender 1 0,912 0,912 0,921 0,338
School 13 34,683 2,668 2,692 0,001
Gender*School 13 12,664 0,974 0,983 0,467

Type II SS results are nearly the same, but it being an unbalanced design, I believe Type III SS are the more important ones to consider, correct?

However, the resulting model parameters show no significance:

Source Value Standard error t Pr > |t| Lower bound (95%) Upper bound (95%)
School-1 -0,556 0,290 -1,918 0,056 -1,125 0,014
School-2 0,399 0,286 1,396 0,164 -0,163 0,961
...
...

This confuses me, because in the one-way ANOVA with only schools as the categorial variable, two schools show up as significant under model parameters (note: variances are not equal).

AND: conversely, I have results for other Likert questions where model parameters show up as significant, but neither of the categorial variables, e.g.:

Type III Sum of Squares analysis

Source DF Sum of squares Mean squares F Pr > F
Gender 1 0,024 0,024 0,027 0,869
School 13 17,089 1,315 1,488 0,118
Gender*School 13 11,232 0,864 0,978 0,472

Model parameters

Source Value Standard error t Pr > |t| Lower bound (95%) Upper bound (95%)
School-3 0,772 0,310 2,495 0,013 0,164 1,381
...

A one-way ANOVA with just schools shows no school significant (under model parameters), the overall significance of schools is likewise not present (p=0,08).

Can anyone please explain this to me - and I guess I don't really understand what "model parameters" are, and how that list differs from the overall Type I/II/III result. (Note: variances not equal)

Thanks so much!
 
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