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Intuitive understanding of ANOVA.

S

srinivasaniyengar13

Made first post
I'm not sure if my understanding of ANOVA is correct,so please guide me-
What I have understood is-
1. If the null hypothesis (all treatment effects)=0 is rejected, most of the variability is caused by the variance between treatments,and the fitted model does not 'explain' the total variance.
Therefore,there is a difference between the treatment means.

2. If the null hypothesis is accepted, most of the variability is caused by variance among the treatments ,and the fitted model 'explains' the total variance.
Therefore, there is no difference between the treatment means.

Am I correct?
 
srinivasaniyengar13 said:
I'm not sure if my understanding of ANOVA is correct,so please guide me-
What I have understood is-
1. If the null hypothesis (all treatment effects)=0 is rejected, most of the variability is caused by the variance between treatments,and the fitted model does not 'explain' the total variance.
Therefore,there is a difference between the treatment means.

2. If the null hypothesis is accepted, most of the variability is caused by variance among the treatments ,and the fitted model 'explains' the total variance.
Therefore, there is no difference between the treatment means.

Am I correct?
Click to expand...

Good! Just take care for two points.
Each fitted model explain total variance, but sometimes very low.
While starting test we assume Null hypothesis is true, you can't accept it, you just reject it or don't reject it.
 
Dear both

I have doubt regarding the conclusion that whether fitted model explain the total variance or not or model is good fit or not

As per my understanding if most of the variability is caused by the variance between treatments this mean "fitted model explain the total variance or model is good fit" and if most of the variability is caused by variance among the treatments not by the variance between treatments this means fitted model does not 'explains' the total variance and model is not good fit.

Please correct if I am wrong.
 
Last edited by a moderator:
suresh bishnoi said:
Dear both

I have doubt regarding the conclusion that whether fitted model explain the total variance or not or model is good fit or not

As per my understanding if most of the variability is caused by the variance between treatments this mean "fitted model explain the total variance or model is good fit" and if most of the variability is caused by variance among the treatments not by the variance between treatments this means fitted model does not 'explains' the total variance and model is not good fit.

Please correct if I am wrong.
Click to expand...

Suresh - it's the other way round. ANOVA is testing if the means are the same. If there is variability between the treatment means then this indicates that they are NOT the same. Hence the model "means the same" does not explain what we see.
 
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