Here's my situation, I have 3 possible methods to measure my variable of interest. I need to recommend the method that gives the lowest variability with the least amount of effort.
The more complicated/resource consuming methods have "lower" standard deviations of course but how do I know if this slightly lower std deviation is worth the time?. Can I just use ANOVA to compare the standard deviations?
Should I use Levene's test for this? (I have 8 values of the standard deviation for each method so I dont know if the data set is too small to have a reliable answer from Levene's)
Thank you in advance for your help guys :)
Identifying the method that has the lowest variability is not done with ANOVA, but by sorting the results (variances). This is not different to identifying the method associated with the least amount of effort. If both selections are the same method, you are done.
Your main problem starts when the method with the least variance is not the one with the least effort. Then you will have to weigh "variance" against "effort". If you can do this, then you can calculate a "variance/effort coefficient" and select the method giving the best coefficient.
Since comparing two methods is involved, Bland Altman plots might help to understand variability and agreement. Agreement seems not to be your main concern though.
your question doesn’t seem to be variance (or dispersion or reproducibility or ...) comparison but power comparison. If a method gives a large difference between different "treatments" it may be quite variable without impairing too much the comparisons' power. On the other side suppose a method which permanently gives a response equal to 1, its variance will be zero but its sensibility (power) also. You should have both variance estimations and a "treatment" difference estimations for each method and then compute the numbers of subjects needed with each method to achieve a given power - the lower the better of course. Be aware that a "sensible" method is very often (if not always) a variable one.
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