# Methods

This page contains how we got to the results.

## Research Question

We were interested in finding out, whether or not gentrification of a quarter has an influence on its population growth.

Three scenarios were coming to our mind, in context of that question:

To answer the above question about population growth and gentrification, we made the simplification of modeling gentrification as economic status change in a quarter. This seems plausible, since gentrification can be explained as the replacement of lower economic status households with high economic status households and a big increase in this economic status would be due to such a significant replacement.

This lead us to following H0 hypothesis: There is no significant causality between economic status growth (in gentrified quarters) and population growth.

## Used Data

We started with data of:

## Used Variables

All variables used are per statistical quarter. There are 34 quarters in Zurich.

We calculated two different values for each variable, in order for us to properly analyze and visualize the data, as further explained below.

### Variable "Population"

#### For visualization purposes

In order to effectively visualize population change in each quarter over the time period of 1999 to 2012, we have to overcome two challenges. Make the population change comparable between the quarters, and allow to observe a development over this time, rather than having just isolated visualizations, of how the population changed from one year to the next.

As for the first challenge, we normalized the data, to show increase in percent, rather than absolute values, which made for a good comparison between each quarter. To overcome the second challenge, we decided to use this percental increase in population, in relation to the population of 1999 in that quarter, rather than just visualizing the change from on year to the next. This way the changes from the previous year's get preserved while the change from one year to another still is visible by the changes in the map compared to last year's map.

This variable for the visualization of population is calculated as follows: the population from year YYYY minus population from year 1999. then divided by the population from year 1999 and multiplied by 100 in order to get the percental change in population.

**Cumulated vs. yearly changes:** Comparison of our cumulated variables, which were used for visualization purposes(blue), in relation to the isolated yearly changes, that were used for the statistical analysis (orange) for the Mühlebach quarter from 1999-2012. The blue line also allows for an assignment of the respective years.

#### For analysis purposes

In order for us to find a correlation between gentrification, respectively economic status and population, we cannot use the same “summed up” percentages of population increase since 1999, as we do for the visualization, since this would distort the results. (An increase in population by 10% in 2000 without increase in economy, followed by an increase by 10% in economy without increase in population in 2001, could, summed up, seem like a correlation between the two values, even if there is not.) To avoid this distortion, we used this time the also mentioned percental change from one year to the next, since those values are isolated and cannot lead to a false outcome, by adding themselves up to a perceived correlation.

This variable for the analysis of population is calculated as follows: the population from year YYYY minus population from year YYYY-1. then divided by the population from year YYYY-1 and multiplied by 100 in order to get the percental change in population.

#### How to interpret the maps in regard to the population?

This variable is represented in the choropleth map (the color). We chose five classes. A positive change means, that, since 1999, more people have moved in than out and a negative change means, that more people have moved out than in.

The classes boundaries are:

### Variable "Economic Status"

This variable shows how economically well a quarter's population is doing. It represents the amount of money the median inhabitant of that quarter has for one year. It is a combination of the median income per year and the median wealth per year.

#### How is the economic status index created?

To get a representative value for the economic status of a quarter we decided to use a combination of median wealth and median income, since these two variables should adequately describe the economic status in a small scale environment, like the city of Zurich, where there shouldn't be any distorting factors like different prices for goods, for example.

To combine wealth and income, a simple addition of those two would be too trivial and give the wealth to much meaning. Instead we decided to try to convert the wealth to a value that is more equivalent to income. The idea behind this conversion was, to find out how much the wealth increases the yearly income, and to do so we divided over the remaining years an average person of each quarter would still have left to live. For example, if the average person in a quarter is 50 years old and expected to become 80 years old, he/her can spend 1/30 of his/her wealth per year, resulting in an increase of the yearly income by 1/30 of the wealth.

The next paragraphs explain more detailed, how we got to the economic status.

The median wealth data consisted of three tax classes for people older than 18 and how many people per quarter where in one tax class. We used a weighed mean to calculate the median wealth per quarter, where the weight was the number people in that tax class. Same goes for the median income.

To calculate the mean age for each quarter and year, we used a weighed mean (where number of people in that age class was the weight). The mean age is different in each quarter and year. We found differences of 10 years or more.

For the average age per quarter we used all peoples age including children. We didn't exclude children since families with children will need more money than childless families. By including the children in the mean age, the mean age gets smaller, so the rest life gets bigger, so the wealth available per year gets smaller.

Then, we calculated the average life expectancy for Switzerland's inhabitants, which is assumed to be the same for all, since they roughly have got access to the same medical support. In Zurich live 49.7% men and 50.3% women, which is practically a 50-50 ratio. We therefore used the mean of the average life expectancy for men and women in Switzerland, leaving us with the life expectancy in Zurich of 82.3 years.

→ Now we've got the life expectancy, the mean age and the median wealth per quarter, per year. To calculate how much life is left to live, we subtract the mean age from the life expectancy and call this rest life. The median wealth per year is the median wealth divided by the rest life.

#### How did we use the resulting economic status for visualization and analysis purposes?

We pretty much used this economic status index the same as we used the population data. Meaning that we visualized the percental change from each year compared to the year 1999 and analyzed the individual percental differences in between years to find a causality between the economic status and the population.

#### How to interpret the maps in regard to the economic status?

The cartograms in the Maps section show the differences in economic status for a year YYYY relative to 1999. A negative change (the quarter got poorer) will lead to a disappearance of the quarter. Whereas quarters with a positive change (the quarter got richer) will become bigger in the cartogram.

→ A quarter with a big positive change in economic status is regarded gentrified.

To answer our research question, we're interested only in the gentrified quarters. Therefore, it is okay, that quarters disappear when they experience a decreasing economic status and quarters of interest become bigger.

## Which quarters are considered gentrified?

Based on our economic status index, we can distinguish between gentrified and non-gentrified quarters. To do so an adequate threshold is needed. As a reference we took the inflation into consideration, which is, according to the Bundesamt für Statistik (2004), 10.2% from 1999 to 2012. Doubling this value and only regarding quarters that had an economic growth of more than these resulting 20.4% since 1999 seems like a good way to insure, that only quarters with a big increase in economic status are taken for the evaluation of our research question.

The quarters that met this bar of 20.4% economic status growth since 1999 are: Mühlebach, Seefeld, Hottingen, Fluntern and Escher Wyss. Those are the quarters, which we will focus our analysis on in the results section.