Interpreting Median Absolute Deviation

chocksaway

Hi folks

just wondering if someone could help me out interpreting median absolute deviations (MAD)?

Basically, under one experimental condition (A), the median result is 29.6 with the MAD being 3.2. Under the other (B), the median is 32.4 with MAD being 2.5.

What I am taking from this is that under condition B, the dispersal of the data points is closer to the median than under A, improving the quality and accuracy of the data?

Or am I way off?

Thanks for any tips or suggestison

MathsManiac

chocksaway wrote: »

What I am taking from this is that under condition B, the dispersal of the data points is closer to the median than under A,...

Yes.

chocksaway wrote: »

...improving the quality and accuracy of the data?

That's not necessarily the correct interpretation. It depends on the context.

If all of these data are repeated attempts to measure a quantity that is known to be fixed, then this does suggest that condition B is producing measurements of greater consistency.

The measurement process with greater consistency might also be of greater accuracy, but that does not necessarily follow. Consider two sharp-shooters. One has a telescopic sight that is slightly off line; the other has no telescopic sight at all. If both are aiming repeatedly at a target but cannot see whether or not they have hit it, the first is likely to have tightly clustered shots that are not centred on the target; the second is likely to have more dispersed shots, but their "average location" might well be closer to the target than that of the first shooter.

chocksaway

That's perfect cheers!