# ANOVA for S/N ratio gives different results

M

#### mrbhala

I am testing paint Film Adhesion. Measuring it in % of portions are peeled off in a test.

When I am saying the quality of paint in terms of Film adhesion, I have to say % of portions NOT peeled off. So % NOT peeled off = 100 - % of Peeled off.

While doing Taguchi analysis
For the first category (% peeled off) I am taking "Smaller is better"
Also I am trying it
for the Second (% NOT peeled off) I am taking "Larger is better"

The results of Analysis of variance
for Means both (peeled off, Not peeled off) gives same R sqr, Adj R sqr and F values
but for S/N Ratio both gives different R Sqr, Adj R Sqr, and F values

Can anyone please explain me Why it is so?

PS: I have attached the data and results.

Thanks

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#### Miner

##### Forum Moderator
Staff member
Although you have asked several questions, most can be boiled down to one simple reason. None of your factors are statistically significant (i.e., all p-values >> 0.05). This makes all other numbers irrelevant.

Also, a number of noted statisticians have identified major flaws with the use of S/N Ratios and recommend analyzing the mean and the Ln(StDev) separately. S/N Ratios behave in a non-linear fashion, which can cause the exact problem which you have seen. The Smaller the Better version increases rapidly at first then plateaus. The Larger the Better version increases slowly at first then rises rapidly.

M

#### mrbhala

Thank you Miner.
Yes the factors don't have significant influence on the response variables. Actually I am testing 4 variables, out of which 2 are being influenced.

I have question here. I am also done the Gray relational analysis in which for its grades, I did ANOVA. even though the P values are not < 0.05, my guide said I can interpret how much each factor influencing based on the F-Ratio. Is it right?

#### Miner

##### Forum Moderator
Staff member
You can do that PROVIDED that the factors being compared are statistically significant at your designated Alpha risk. I do not recommend doing that with factors that are not statistically significant because you have not disproved the null hypothesis of no effect.

Y

#### yasir ishraq

Although you have asked several questions, most can be boiled down to one simple reason. None of your factors are statistically significant (i.e., all p-values >> 0.05). This makes all other numbers irrelevant.

Also, a number of noted statisticians have identified major flaws with the use of S/N Ratios and recommend analyzing the mean and the Ln(StDev) separately. S/N Ratios behave in a non-linear fashion, which can cause the exact problem which you have seen. The Smaller the Better version increases rapidly at first then plateaus. The Larger the Better version increases slowly at first then rises rapidly.
Dear Miner
your post is help full. i have same issue but the mean and SNR give different ranking. i have same insignificant value issue. but my study purpose is to find percentage of contribution only. the two Graphs should be overlapping each other as done in most of the studies.

#### Miner

##### Forum Moderator
Staff member
If your factors are not significant, there is no contribution, it is 100% noise.

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