A Madness for all Seasons

Our fourth post on the  2017 VCE exam madness will be similar to our previous post: a quick whack of a straight-out error. This error was flagged by a teacher friend, David. (No, not that David.)

The 11th multiple choice question on the first Further Mathematics Exam reads as follows:

Which one of the following statistics can never be negative? 

A. the maximum value in a data set

B. the value of a Pearson correlation coefficient

C. the value of a moving mean in a smoothed time series

D. the value of a seasonal index

E. the value of a slope of a least squares line fitted to a scatterplot

Before we get started, a quick word on the question’s repeated use of the redundant “the value of”.

Bleah!

Now, on with answering the question.

It is pretty obvious that the statistics in A, B, C and E can all be negative, so presumably the intended answer is D. However, D is also wrong: a seasonal index can also be negative. Unfortunately the explanation of “seasonal index” in the standard textbook is lost in a jungle of non-explanation, so to illustrate we’ll work through a very simple example.

Suppose a company’s profits and losses over the four quarters of a year are as follows:

    \[ \begin{tabular} {| c | c | c | c |}\hline {\bf\phantom{S}Summer \phantom{I}} &{\bf\phantom{S}Autumn \phantom{I}} &{\bf\phantom{S}Winter \phantom{I}} &{\bf\phantom{S}Spring \phantom{I}} \\  \hline {\bf \$6000} & {\bf -\$1000} & {\bf -\$2000} & {\bf \$5000}\\ \hline \end{tabular}\]

So, the total profit over the year is $8,000, and then the average quarterly profit is $2000. The seasonal index (SI) for each quarter is then that quarter’s profit (or loss) divided by the average quarterly profit:

    \[ \begin{tabular} {| c | c | c | c |}\hline {\bf Summer SI} &{\bf Autumn SI} &{\bf Winter SI} &{\bf Spring SI} \\  \hline {\bf 3} & {\bf -0.5} & {\bf -1.0} & {\bf 2.5}\\ \hline \end{tabular}\]

Clearly this example is general, in the sense that in any scenario where the seasonal data are both positive and negative, some of the seasonal indices will be negative. So, the exam question is not merely technically wrong, with a contrived example raising issues: the question is wrong wrong.

Now, to be fair, this time the VCAA has a defense. It appears to be more common to apply seasonal indices in contexts where all the data are one sign, or to use absolute values to then consider magnitudes of deviations. It also appears that most or all examples Further students would have studied included only positive data.

So, yes, the VCAA (and the Australian Curriculum) don’t bother to clarify the definition or permitted contexts for seasonal indices. And yes, the definition in the standard textbook implicitly permits negative seasonal indices. And yes, by this definition the exam question is plain wrong. But, hopefully most students weren’t paying sufficient attention to realise that the VCAA weren’t paying sufficient attention, and so all is ok.

Well, the defense is something like that. The VCAA can work on the wording.

 

Three Apples + Two Oranges = Infinite Nonsense

The key findings of Australia’s 2016 National Drug Strategy Household Survey were released earlier this year, and they made for sobering reading. The NDSHS reported that over 15% of Australians had used illicit drugs in the previous year, including such drugs as cannabis, ice and heroin. Shocking, right?

Wrong. Of course.

We’re being silly in a way that the NDSHS reporting was not. Yes, the NDSHS reported that 15% had used illicit drugs at least once (including the possibility of exactly once) in the previous year, but NDSHS also emphasised the composition of that 15%. By far the most commonly used drug was cannabis, at about 10% of the population. Ice use was around 1%, and heroin didn’t register in the summary.

Illicit drug use is a serious problem, and a problem exacerbated by idiotic drug laws. Nothing can be learned, however, and nothing can be solved if one focuses upon a meaningless 15% multicategory. Whatever the specific threats or the reasonableness of concerns over the broad use of cannabis, such concerns pale in comparison to the problems of ice and heroin. The NDSHS makes no such categorical mistake. Unfortunately, there are plenty of clowns who do.

Last week, the Federal Ministers for Social Services and Human Services announced the location of a drug testing trial for job seekers who receive federal benefits. The ironically named Christian Porter and the perfectly named Alan Tudge announced that receipients would be tested “for illicit substances including ice (methamphetamine), ecstasy (MDMA) and marijuana (THC) … People who test positive to drug tests will continue to receive their welfare payment but 80 per cent of their payment will only be accessible through Income Management.” The plan is deliberately nasty and monumentally stupid, and it has been widely reported as such. For all the critical reporting, however, we could find no instance of the media noting the categorical lunacy of effectively equating the use of ice and ecstasy and THC.

Still, one should be fair to Porter and Tudge. They are undeniably dickheads, but Porter and Tudge are hardly exceptional. They are members of a very large group of thuggish, victim-blaming politicians, which includes Malcolm Turnbull, and Peter Dutton, and Adolf Hitler.

It is also notable that this kind of multicategory crap is only practised by social conservatives. It’s not like a nationwide survey on sexual harrassment and sexual assault in universities would ever couch the results in broadly defined categories in such a clouded and deceptive manner. Nope, not a chance.