How large is the MSR value compared to MS effects in your experiment ?, if MSR is unusually large it can imply two things, one, there are one or more significant uncontrolled factors which fluctuate in their levels drastically, thereby generating a large error variance, in that case you have to identify these factors and control them during the experimentation process, i suggest you repeat the experiment setup and compare the error variance you get in the new expt. with that of the old, if the new error variance is much smaller than that obtained in previous experiment, some deterministic errors may have crept into the first experiment process.

A high p value can occur simply because of low sample size, even if an effect exists, resulting in low power and inability to reject the null hypothesis. This is because a low sample size results in a large standard error and confidence interval, which give an imprecise estimate of the effect. But sample size is not a problem in ANOVA, so long as you meet the other assumptions, such as normality. But what do you mean by 'p values for all 3 effects'? You need to obtain one p value from the ANOVA and only if this is < 0.05 do you do pairwise tests to determine p values for each factor. But you might just need to trust your statistics, that there isn't an effect.

Hello Muralishwara,

If levels of an IV (independent variable) are chosen at random from a population of possible levels, then, yes, "unlucky" selection could help account for nonsignificant variance being attributable to that IV. It is for this reason that it is advisable to sample many, not a few, levels of a random effects factor/IV.

Just about every textbook example I've seen of variants of Latin square design have used minimal (typically, one per cell) sample sizes. While that is certainly economical with respect to data collection, it frequently results in: (a) poor statistical power (as Andrew Paul McKenzie Pegman suggests); and (b) having to ignore possible interaction effects (because of insufficient data points to estimate). Hence, unless you know that your IVs are in fact potent with respect to their influence on the DV of interest, and that ignoring interaction won't add to the (otherwise) unexplained variance estimate (this is what Debopam Ghosh implies by having you look explicitly at MSerror), then these designs aren't necessarily optimal.

Good luck with your work!

Any time you use a saturated design, like a Taguchi design, the issue you have will be common. If you can go back and re-run the experiment, that will help a lot.

Another thing you could do is use coded levels for your factors (0, 1, 2 assuming that the distance between levels is equal) and run your analysis again. Then you can look at your coefficients for each term. The largest magnitude coefficients are the most "important" factors.

Thanks everyone, I conducted Taguchi Analysis first and got the main effects of SN ratios. Then I went to ANOVA - General Linear Model, where we get to know the level of significance of each factor, if they are significant at all. If the factors have to be significant, then P must be less than 0.05. But in my case they are all above 0.05. Like David Morse said may be the levels selected might be improper. I haven't conducted proper pilot studies before selecting the levels.