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I'm developing a participatory social environmental diagnostic. To do this, I'm using primary (qualitative data from interviews with stakeholders) and secondary data (local socioeconomic data).

From this data, I distribute the identified factors in a SWOT matrix - identifying opportunities, strengths, weaknesses and threats that could afftect the local community. After that, each factor is given a scale from 0 to 2, being:

0 - Null or small impact 1 - Medium impact 2 - High impact

In this way, I have this kind of data:

enter image description here

Ok. Now I build a scale with this formula:

= (((strengths + opportunities) - (weaknesses + threats)) / ((strengths + opportunities) + (weaknesses + threats)) * 2

OBS: basically opportunities and strengths are positive values and threats and weaknesses are negative, so I subtract the negative values from the positive ones. The division by the sum of all values are made to have the statistical universe (population, in this case the maximum value). The multiplication by 2 are made to have the possibility to create a range from -200% to 200%, but it could be -100% to 100% too ;)

Now I have a scale ranging from -200% to 200% that I interpret in this way:

enter image description here

Very unfavorable (-200% to -100%) Unfavorable (-100% to -29%) Balance (-30% to 30%) Favorable (31% to 99%) Very favorable (100% to 200%)

OBS: This scale was used at this website (https://en.luz.vc/template/swot-analysis-excel-tool-template/)

Now, what I need is to convert this to 0 to 10 scale so I apply this formula:

enter image description here

I've discover this formula here: (https://stats.stackexchange.com/questions/25894/changing-the-scale-of-a-variable-to-0-100)

Finally, my question is how can I achieve this score (from 0 to 10) right from the beginning, without the need to make the conversion from the first scale?

OBS: The first scale give a percentage (-200% to 200%) and the second one a decimal number (0 to 10).

Warm regards ;)

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    $\begingroup$ Hi, have a look at the formula you're using = (((strengths + opportunities) - (weaknesses + threats)) / ((strengths + opportunities) + (weaknesses + threats)) * 2 and think about what this does and mean (particularly the *2 at the end) $\endgroup$ – Sammy Dec 12 '19 at 13:44
  • $\begingroup$ Hi @Sammy, basically opportunities and strengths are positive values and threats and weaknesses are negative, so I subtract the negative values from the positive ones. The division by the sum of all values are made to have the statistical universe (population, in this case the maximum value). The multiplication by 2 are made to have the possibility to create a range from -200% to 200%, but it could be -100% to 100% too ;) $\endgroup$ – Britto Dec 12 '19 at 14:41
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Let's suppose you have a variable $x_{old} \in [-1,1]$. If you would like to transform that to $ x_{new} \in [-2,2]$ then you could just apply the transformation formula you posted:

With $min_{old}=-1, max_{old}=1, min_{new}=-2, max_{new}=2$ you would get $$\frac{max_{new}-min_{new}}{max_{old}-min_{old}} (v-min_{old}) + min_{new} = \frac{2-(-2)}{1+1} (v+1) + (-2) = \frac{4}{2} (v+1) -2\\= 2v+2-2=2v$$

Now if you compare that to your formula

= (((strengths + opportunities) - (weaknesses + threats)) /
 ((strengths + opportunities) + (weaknesses + threats)) * 2

then you can see that it is exactly what you did here by multiplying with 2 at the very end. You transformed your first scale from $[-1,1]$ to $[-2,2]$. Therefore, if you want it to be in the interval $[0,10]$ just apply a different transformation at the very beginning when deriving the first scale:

$$\frac{max_{new}-min_{new}}{max_{old}-min_{old}} (v-min_{old}) + min_{new} = \frac{10-0}{1+1} (v+1) + 0 = 5v +5$$

Which means your calculation for the first scale needs to be

= (((strengths + opportunities) - (weaknesses + threats)) /
 ((strengths + opportunities) + (weaknesses + threats)) * 5 + 5

(instead of scaling it to $[-2,2]$).

Intuitively I like to think of it like this: you "stretch" the interval from $[-1,1]$ to $[-5,5]$ by multiplying with 5 ("making it 5 times larger"). And then, since you want it to be positive and start at $0$, you "shift" it "upwards" by adding 5.

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  • $\begingroup$ Hi @Sammy Thank you for your very precise answer. It really helped me a lot and explain things that I was doing intuitively. Warm regards. $\endgroup$ – Britto Dec 13 '19 at 12:02

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