My end goal is a tool that I can use to help me select the best product of the ones that are available.

Whenever I set out to buy something that has a lot of “factors” that I need to consider, such as price, weight, resolution, response time, calories, capacity, noise level, power, efficiency, and ratings from one or more sources, I get frustrated trying to keep track of so any factors for so many products. They are all on different scales and the scales may go high-to-low or low-to-high.

I thought if I had a tool that would allow me to convert each product factor to a common scale, all going in the same direction (High to Low), I could then compute a composite value. I could even assign weighting factors to each factor to ensure that the ones that are the most important to me get an appropriate weight.

After playing around a bit and reading the opinions and references here and elsewhere, I believe that z scores (standard scores) will allow me to convert pretty much any factor to a common scale with mean=0 and std dev=1. That will eliminate a lot of the vagaries of many of the factors, especially the ratings. It not only arranges the values in order, but also indicates by how much they are above or below the mean

*for that sample*. This is critical for things like the ratings that tend to be bunched at one end of the scale. This should allow me to combine them and add weighting factors.

The table below is my latest attempt. It looks to me like it will do the job. Of course, I would be interested in any criticisms or suggestions.

In the main table, columns C & D contain the product ID and any comments about how I chose the values. These are all fictitious products. Once I get the underlying code working, I’ll test it on real products.

These 8 products are being evaluated on 4 factors: Price (E-G), Rtg (H-J), MPG (K-M), and dB (N-P). The ratings are an Amazon 5-star system. MPG is miles/gallon. dB is the noise level in decibels. In each section, the 1st column is the factor value, the 2nd column is the z score, and the 3rd is the rankings based on the z score.

The rows above the table contain the mean (3), std dev (4), order (5), and weight (6). The mean and stddev are for the z score calculation. The order specifies whether high (HiLo) or low (LoHi) values are favored, which determines the sign on the z scores. The weights allow me to give more or less weight to each factor.

Columns Q & R show the sum of the z scores and the rankings based on them.

Columns S & T do the same but with the mean of the z scores, rather than the sum. Since they both result in the exact same rankings, which is what I would expect, I see no benefit to using the averages, so I’ll probably just use the sums.

Column U contains the z score of the z score sums. I did this this just out of curiosity. As expected, the mean is close to zero. I don’t see any benefit to this, either.

Columns V & W show the weighted sums and the rankings based on them. If the weights are all 1 (or any other number), then this will be identical to columns Q & R. In this example, I assign a weight of zero to the price, indicating that I don’t care what it costs, leaving the composite rating to be based on the other factors. Column X contains the difference between the weighted ranking and the unweighted one. Most of the products only moved by 1 rank.

Product F moved up 5 levels to #1. It was the second most expensive product (rank 7), but that factor was eliminated. It got the lowest rating, but that factor has the lowest weight of the remaining 3. It was #2 on MPG and #1 on dB.

Thanks for the help.