# OnPoint by Keith Ng

86

### Re: Education

Hey Herald. So "children in bigger classes and bigger schools get better grades", hur?

"Children in bigger classes and bigger schools get better grades" implies a relationship between these two things. This kind of relationship, if it's strong, might look something this:

On the other hand, if it's a weak relationship, it might look something like this:

This is what your relationship actually looks like (courtesy of DimPost):

Note the R^2 value. What does it mean?

The closer the R^2 value is to 0, the poorer the fit. Your R^2 value is 0.137. If we take out the special schools, that goes down to 0.0738. This is what we would call a "poor" fit.

Also:

I don't know what this "NCEA" thing is, but I hope that, one day, they'll start teaching it in schools.

### 86 responses to this post

First ←Older Page 1 2 3 4 Newer→ Last

• Ziiiiiiiiing

Suburbia, Wellington • Since Nov 2006 • 216 posts Report Reply

• Ouch.

Palmerston North • Since Nov 2006 • 1578 posts Report Reply

• The link at the top of the article is stuffed ;)

Why does the "Goodness of Fit" explanation talk about "R^2" but the table above it talks about the "r value" - or are these unrelated?

Wellington • Since Feb 2012 • 3 posts Report Reply

• In a simple linear regression (like in the pictures) R^2 is the proportion of the observed variability in the y-axis which is explained by the observations in the x-axis. In that setting R^2 is also the squared correlation (r) which measures the association between the variables x and y.

Christchurch • Since Sep 2012 • 1 posts Report Reply

• Didn't they have a system at high decile schools like Auckland Grammar whereby if you were in the rugby team or whatever, the teachers signed you off as passing university entrance without actually needing to do any exams?

Back in Wellington • Since Nov 2006 • 4095 posts Report Reply

• I'm not convinced that R^2 is a useful measure of goodness of fit in this case, especially with the ridiculously prescriptive interpretations given by this textbook.

The real problem here is confounding variables.

Dunedin • Since Nov 2011 • 8 posts Report Reply

• Are the values clustered to the bottom left the special schools?

The A.K. • Since Nov 2006 • 144 posts Report Reply

• Brilliant article! Thanks!!!

Auckland • Since Nov 2006 • 115 posts Report Reply

• Sacha, in reply to Hamish,

apparently

Ak • Since May 2008 • 15288 posts Report Reply

• Bart Janssen, in reply to PeterLynch,

Why does the "Goodness of Fit" explanation talk about "R^2" but the table above it talks about the "r value" - or are these unrelated?

I'm pretty sure "r value" is slang for R^2. They are the same thing.

Auckland • Since Nov 2006 • 2916 posts Report Reply

• Bart Janssen, in reply to Hamish,

Are the values clustered to the bottom left the special schools?

They probably are but it's worth looking, outliers are often very informative.

Auckland • Since Nov 2006 • 2916 posts Report Reply

• A shot to the heart, if the Harold actually had a heart...

Waikanae • Since Nov 2006 • 1636 posts Report Reply

• Are the values clustered to the bottom left the special schools?

Yep. I have no idea why they're in the data set.

Most of the other low scoring, high ratio schools are remote rural low decile schools with, like one teacher and eleven students. Amazingly they aren't delivering a comprehensive education.

Wellington • Since Nov 2006 • 890 posts Report Reply

• It's also worth noting that the value on the X axis is probably real.

But the value on the y axis is probably a lot of shit.

Not really much point in plotting shit vs real.

Auckland • Since Nov 2006 • 2916 posts Report Reply

• Graeme Edgeler, in reply to Danyl Mclauchlan,

Most of the other low scoring, high ratio schools are remote rural low decile schools with, like one teacher and eleven students. Amazingly they aren't delivering a comprehensive education.

National Standards don't address a comprehensive education.

Wellington, New Zealand • Since Nov 2006 • 2908 posts Report Reply

• Keith Ng, in reply to Peter Green,

The real problem here is confounding variables.

Agreed.

Auckland • Since Nov 2006 • 522 posts Report Reply

• Keith Ng, in reply to Hamish,

Are the values clustered to the bottom left the special schools?

Auckland • Since Nov 2006 • 522 posts Report Reply

• Is this "data" file available somewhere for constructing other spurious correlations?

Dunedin • Since May 2007 • 745 posts Report Reply

• Nathaniel Wilson, in reply to Bart Janssen,

I'm pretty sure "r value" is slang for R^2. They are the same thing

They're really not. Very roughly speaking, r gives you an indication of whether the two variables have a relationship, r^2 provides an indication of how much variance in the data can be explained. r^2 =1 means the line explains all the variance, r^2 of 0.074 means the line explains 7.4 % of the variance; sweet FA in other words. You could probably plot number of cars per household or number of badminton players per school on the x-axis and get just as good results.

Auckland, New Zealand • Since May 2009 • 35 posts Report Reply

• I can't even tell if the HoS is trying to make a meta-joke by channelling Helen Lovejoy from the Simpsons with their editorial Won't someone please think of the children?.

Still, it states:

In fact, buried within the national standards dross is valuable information about how boys are struggling, the decline in writing skills, and Pacific children getting lost at the back of the classroom.
If the idealogues on either side would stop to think, they might realise it is better to intelligently discuss pupils' results than try to hide them.

OK, even if we, for the sake of argument, accept that the raw data is ‘correct’, how would the HoS (or any of the main papers) manage to sift through the ‘dross’ to find this ‘valuable information’?

As shown by Keith above, this is high-school statistics and the National Standards shock: Big classes work article completely fails at even this basic level.

I don't expect everyone to have a working knowledge of statistics, but if you actually attempt to do some analysis and then publish your 'findings', I would expect the analysis to be given at least a 5-minute check by someone with that basic knowledge.

Lower Grey Lynn • Since Jul 2009 • 764 posts Report Reply

• Ray Gilbert, in reply to nzlemming,

A shot to the heart, if the Harold actually had a heart...

Wouldn't that be an arrow to through the eye?

Since Nov 2006 • 72 posts Report Reply

• Russell Brown, in reply to Graeme Edgeler,

National Standards don’t address a comprehensive education.

No – and they don’t measure performance against the primary school curriculum either. But the level of resourcing available at tiny rural schools is extremely likely to have an impact on national standards scores. A single-teacher country school will not, for example, have a reading recovery specialist on staff.

BTW, it seems to me that the HoS story isn't actually based on class size as such -- that information is not collected by the Ministry of Education -- but on pupil-teacher ratios across schools. Which isn't the same thing.

Auckland • Since Nov 2006 • 17276 posts Report Reply

• Bart Janssen, in reply to Nathaniel Wilson,

r gives you an indication of whether the two variables have a relationship

But in statistics a relationship is defined by the probability of the occurance of that relationship by pure chance. A relationship has no meaning unless there is a probability. While we are probably wrong to do so we do tend to use "r value" when we are referring to the probability that the relationship could have occured by chance. But we are mere molecular biologists in this lab :).

Auckland • Since Nov 2006 • 2916 posts Report Reply

• Does anyone know why the Funding per Student figures vary so much between schools of the same decile ?

Auckland • Since Feb 2007 • 324 posts Report Reply

• Bart Janssen, in reply to Russell Brown,

BTW, it seems to me that the HoS story isn’t actually based on class size as such – that information is not collected by the Ministry of Education – but on pupil-teacher ratios across schools. Which isn’t the same thing.

So not only is the y axis full of shit but so is the x axis?!?!?

Auckland • Since Nov 2006 • 2916 posts Report Reply

First ←Older Page 1 2 3 4 Newer→ Last