Statistics and Environment in an Urban Studies Program

A graduate student in an urban planning program asked me to tutor her for statistics and physics material she has to cover. She sent me guidlines, assignment instructions, and her completed assignments from the first two weeks of class.

The documents basically covered two concepts: confidence intervals (in statistics) and impact of human-influenced environmental factors (think carbon emissions, climate change).

Confidence Intervals

The assigned video says this a bunch of times, but I will say it again here because it is important. A 95% confidence interval is interpreted as: if we drew a large number of independent random samples from a population, and constructed a 95% confidence interval each time, then 95% of those confidence intervals would contain the true population parameter (e.g. the population mean). In other words, if you generated a large number of confidence intervals from a large number of samples, and then selected one of those confidence intervals at random, there is a 95% probability that the selected interval would contain the true population parameter. Note that technically, this is not the same as saying that there is a 95% probability that the population mean is inside any particular confidence interval. This is a common misinterpretation.

I had to slow down and read that a few times over.

The document also mentions the t-distribution.

[The professor] outlines the assumptions we need to construct a confidence interval. Among them is #3: population standard deviation is known. She notes that this is not a good assumption; in most cases we will be estimating the standard deviation using the same sample we are using to estimate the mean. When we estimate the standard deviation from our sample (which is the case in virtually all practical applications) we will want to rely on the t distribution rather than the normal distribution for calculating the confidence interval. You should watch the video, then review the slide deck for how to calculate confidence intervals based on the t distribution.

Considering things like this is important. Statistics classes aren’t just about tallying values and plugging in numbers into formulas. It helps to understand when to use what and adjust accordingly before you start making calculations or using statistical software packages.

Bulletpoints of note from the two slideshows in this unit included:

• The 𝑡 distribution shape is similar to a normal distribution, except that it is broader and has higher tails

• The exact shape of the 𝑡 distribution depends on the “degrees of freedom”, df = 𝑛−1

• As the sample size 𝑛 increases, the 𝑡 distribution gets closer and closer to the standard normal distribution.

• You use t-distribution when the population standard deviation is not known.

• Try to rember how to calculate sample size

Environment

Two successive assignments ask students to “practice applying the social cost of carbon to monetize the climate impacts of transportation activities, and to gain an understanding of how the discounting of future climate damages informs the selection of a time horizon for measuring global warming potential.” The assignments asks students to use theoretical assumptions to calculate theoretical estimates for levels of CO2 concentration in the atmosphere, energy used by AI-supported technology, external cost of transportation (emissions), public transporation, and occupancy, among other things.

Some of these calculations feel grounded in something that can be traced and tested against. Others feel very arbitrary. The big thing here is that all the quantified cost and benefit is calculated in terms of dollar amounts. They even apply a discount rate to compare present and future values.

It feels a little bit weird when talking about something that can impact an entire planet and lives within any given (or every single) municipality to not have other considerations. It reminded me of the big controversy by the shift by the federal EPA. The government agency decided to stop considering any costs that weren’t financial when making policy decisions. It feels like another way of choosing billionaires and mega-corporations over the people at large that the government is supposed to serve.

There are a few things I get through reading through materials like this though:

• It’s another general way to talk to students at various levels of math about how conversion rates and dimensional analysis are applied in the real world. Want to argue for decisions, resources, or policy as an engineer, local resident, city official, businessperson, or scientist? Learn to multiply those ratios.

• It shows how important it is to try to get an understanding of what assumptions sit behind the ratios that are used to come up with final numbers.

• Truly understanding what sits behnd those ratios would require understanding of other things. This includes science, engineering, and social science. No man understands everything. But it sort of reemphasizes why I’ve extended out from math to trying to learn a little bit more about other disciplines.

• I have to think other municipalities and countries consider more than direct and implied financial costs when thinking about things like carbon emssions. The biggest deal is conditions for organic life and the planet that supports it.