# What constitutes non-trivial analysis of available data?

If a question asks whether `A` is bigger than `B`, and someone posts reliable sources that provide the size of `A` and the size of `B`, and says that since the source for `A` provides a larger number than the source for `B`, then `A` is bigger than `B`, that is obvious trivial.

However, what if the question asks whether the ratio of `A` to `B` is greater than the ratio of `C` to `D`, and four sources are provided to give the values of `A`, `B`, `C`, and `D`, but no source is provided giving the ratio of `A` to `B` or the ratio of `C` to `D`. If the answer than calculates the ratios and says which one is larger, is that still trivial? I would assume so, but I'm no longer certain if that's what the `FAQ` answer meant.

What if you have to calculate `A` / `B` - `C` and compare to `D` / `E` - `F`, where you provide sources for each of the items but can not find sources that perform the calculation? Assume that the question pretty much asks for those calculations explicitly. I would assume this is still trivial (we're talking about 4th grade math), but that seems just a step below an answer I gave to the question of whether doctors earn more per hour than teachers over their career after taking into account how much time they spent in school, where I was directed to look at this FAQ.

I know this question might sound combative, but that's not its intent. I truly want to understand best practices at this StackExchange site. Would my answer be better if I just provided the values of `A`, `B`, `C`, `D`, `E`, and `F` and let the readers draw their own conclusions? It doesn't seem that way to me, but that seems to be the message I'm receiving. Could someone clarify that for me? (Again, this is a sincere, non-combative question.)

There are various examples I can give

# The "obvious maths" fallacy

The discriminating factor is certainly not the level of mathematics, but the level of expertise needed to determine that a particular formula or method is fit to answer.

Canonical example: Pyramid schemes rely on assuming simple calculations are enough.

Logical fallacy: appeal to common sense

# The "back seat economist" fallacy

Another example is analyzing statistical or economical data. People are tempted to do simple calculations where an appropriate analysis would be much more complex.

Canonical example: assuming that a locally valid statistics can be scaled up (if 50% of men in London are bankers, then 50% of men in England are bankers) or that a general statistics has local validity (if 50% of men in England like beer, then 50% of men in Liverpool like beer). Or, many answers related to climate change also suffer from this.

Logical fallacies: fallacy of division, ecological fallacy, fallacy of composition

# The "calculator" fallacy

Furthermore: error analysis. Just calculating numbers without estimating the errors is meaningless.

Canonical example: "climate change models predicted a 0.3 degrees increase in temperature but we had a 0.2 degrees change". What was the margin of error claimed in the model? What is the margin of error in the measurement? What is the likelihood that the two measures are in agreement?

Logical error: false precision, also argument from ignorance/incredulity

# The "I know what I am doing" fallacy

Someone uses an arbitrary calculation which is not clearly reliable, but adds "I am a PhD in <relevant subject> so trust me on this". Anyone can claim any level of competence here.

Logical fallacy: appeal from personal authority

Honestly, I could go on, but the point is: this is not a place to show your research or novel ideas. This is a place to report the best available evidence on things, assuming there is evidence available.

• Very good answer. Would you say then that my answer would be better off without any math, or just deleted altogether? – Ben Hocking Aug 9 '15 at 15:10
• @BenHocking Not sure: the math seems incorrect to me (e.g. assuming that an average 170k salary is meaningful for comparison, or that you can simply multiply it by 20 to get the 20 year earnings), so unless you can find some reputable source making it for you, that has to go. I am not sure if the answer makes any sense without it, though. – Sklivvz Aug 9 '15 at 22:18