School deciles are often conflated with the wealth of the area surrounding the school. It commonly presents in the form of assumptions such as "That school in [suburb x] is decile 10, therefore [suburb x] is really well off." This assumption isn't necessarily unfounded or wrong. Public schools are zoned, meaning that each school has a surrounding geographic area where the majority of students come from. Parents generally want their kids to have the best education possible, pushing up demand (and therefore prices) for property in zones with schools that are perceived to be good. The people who can afford the more expensive homes tend to have more wealth and higher incomes. Deciles for schools are based on the socio-economic status of the area surrounding the school. Therefore, high deciles = wealthier families in the area, and statements like "All the kids that go to [good school] are rich" seem reasonable.
This common chain of logic is almost correct except for when it comes to how the deciles are calculated - the Ministry of Education explains here that the process of assigning deciles is a lot more complicated than just figuring out how rich the area surrounding each school is.
Firstly, the decile isn't based on the immediate geographic area surrounding the school - schools are required to provide the MoE with a list of addresses of their students, which makes sense since we probably want the decile calculation to be based on the students who are actually attending the school, whether they are in-zone or not. Since data on individual houses cannot be provided by Statistics NZ for privacy reasons, the MoE uses the finest data granularity possible - the meshblock, which is a group of roughly 50 households.
Secondly, the socio-economic indicator used by the Ministry of Education is based on more than just household income - there are actually five factors, including the occupation of the parents, household crowding, educational qualifications of adults, and percentage of adults on government income support such as unemployment or sickness benefits. While some of these factors influence each other (leading to co-correlation), these other factors play a part in influencing school deciles.
Thirdly, the definition of deciles means that they're relative - each decile from 1 to 10 represents 10% of the schools in the country. The MoE ranks all of the schools based on the socio-economic indicator from before, and divides it into 10 groups to assign the deciles. This means that the bottom of decile 10 is not all that dissimilar to the top of decile 9. The discrete levels used in deciles subconsciously imply step changes between the deciles, but the schools actually exist on a spectrum rather that at individual steps. I should note here that the MoE does divide the deciles even further into smaller steps when determining the funding per student for each school.
What does this all mean? Well it begins to suggest that the assumption of "high decile = wealthy geographical area" may not be true. The data that is used to build the deciles is much broader than that, and the discrete nature of deciles makes them poor measures of something as continuous as wealth anyway. But how bad is this assumption? To find out, I pulled school decile data for 2014 and census data for 2013, and tried to analyse how well school decile predicts median household income of the surrounding area. A different way of stating this hypothesis would be "given the decile for a particular school, how likely is it that the area surrounding that school is rich or poor?"
I did this for three different granularities of geographic area - Territorial Local Authority or Local Board (TLA), Ward, and Census Area Unit (CAU). Each of these areas is smaller (and thus a finer granularity) than the previous one. I used a regression analysis to determine how much the income variation was explained by the decile variation.
In all three cases, the decile only explains a relatively small amount of the variation in the household median income. There certainly is a statistical relationship at each granularity, but it is weakly positive. Since there's only one variable on each axis the strength of relationship would be the same if we flipped the axes around. We can therefore also say that household median income only explains a small amount of the variation in the school deciles. The rest of the variation is explained by the other factors used by the Ministry of Education as well as some contribution from the discrete nature of deciles.
Even just a cursory look at the graphs without the statistical analysis shows that there is a lot of overlap in median household income inbetween the deciles. While outliers are to be expected, the wide spread of median household income within each decile surprised me a little, and without the statistical analysis it would be easy to conclude that the household income makeup of each decile is the same.
So what does this all mean? The upshot is that school deciles are a poor indicator of the wealth or richness of the people who live in the geographic vicinity of the school. Just because a school is decile 10 does not mean that the people living near it are rich, and just because a school is decile 1 does not mean that the people living near it are poor.
Of course, median household income itself cannot 100% accurately predict overall socio-economic status of the area, and when people say "rich" or "poor" they may not just be meaning income. Median is also probably a bad measure of the overall rich/poor-ness of an area given the potential income spread/range, but it's what Statistics NZ provided. However, this analysis gives a brief insight into just how bad some of our assumptions around school deciles are. That's all I really wanted to know - can we say with confidence that a high decile school has high income families around it? No.
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