Category Archives: Statistics

Swine flu vaccination program – is it worth it?

One might ask oneself if the public vaccination program in Sweden (and in many other countries) is worth the costs of it. Of course, this is not an easy question, as many parameters plays a role in this decision. How important is the saving of lives, how severe is the side effects, how much is an individual person’s health worth, etc. On a global scale we have to wait a year or more until the pandemic is over, or at least until next Spring, before we can draw any conclusions on if the vaccination program has been effective enough, or if it was necessary at all. However, as the spreading of the disease has increased dramatically over the last weeks e.g. in Ukraine, but also in Sweden, the importance of the vaccination program and that the government has acted fast has been painfully underscored. However, my purpose of this article is not to discuss the vaccine itself, nor the side effects, or anything else related to the vaccine. Instead, I am aiming for if the costs of the program in real numbers will payback for the government, and thus the Swedish economy.

Simply put, I will just do my math homework using the swine flu statistics. I will make the following assumptions:

  • If nobody was vaccinated, 10% of the Swedish people would suffer from the swine flu. This seems to be a rather safe expectation, it is more likely that much more than 10% will be sick without any vaccinations, but let’s keep the numbers within safe margins.
  • None of these people will die or require more complicated medical care. We already know that this statement is untrue. However, this assumption makes the math much easier. Also, if people require more complicated care, the costs would go up, not down, so just keep in mind that my expectations are (again) set too low.
  • A typical influenza victim needs to stay home from work for two weeks, and is then fully recovered. Let’s just assume that people are smart and stay home until they don’t carry the disease anymore.
  • The estimated costs of the vaccination program are 3 billion swedish kronor (about 430 million USD). This is based on an estimation made in August by Sveriges Kommuner och Landsting (SKL). The real costs for the program will not be known until some time next year. Of these 3 billions, 1.3 billions is the actual cost of the vaccine – the rest is administrative costs, according to Göran Stiernstedt at SKL.

Given these assumptions, how much would it cost not to run a vaccination program in Sweden? Well, Sweden’s GDP (Gross domestic product) was estimated to be $348.6 billion in 2008, that is about 2,437 billion Swedish kronor. So, if 10% of the population gets sick and stays home from work for two weeks that means that the loss in GDP would be (approximately):

0.10 * 2/52 * 2,437,000,000,000 kronor ≈ 9,373,000,000 kronor

So, for these low expectations I made above, Sweden would still loss about 9 billion kronor just from people not coming to work. That’s a lot of money compared to the estimated cost of three billions. And still, we have not included the increased costs of medical care into our figures. As an additional note: Swedish tax revenue is almost 50%, which means that almost 4.5 of these 9 billions will end up in the government’s hands. In that perspective, the invested three billions seem to be well-used money.


Where are the Mac viruses?

Quite often I hear the explanation that Macs don’t get infected by viruses, because Apple’s market share is so small, it wouldn’t be worth the time and effort write a proper Mac OS X virus. This implies that once Mac OS X has reached a critical market share level, there will be a sudden outbreak of hundreds of viruses. My simple question is this: how come there has (to my knowledge) been no actual Mac virus affecting Mac OS X while there have been a couple of viruses affecting Linux, despite its even smaller market share? Wikipedia lists the following Linux viruses:

  • Alaeda – Virus.Linux.Alaeda
  • Bad Bunny – Perl.Badbunny
  • Binom – Linux/Binom
  • Bliss
  • Brundle
  • Bukowski
  • Diesel – Virus.Linux.Diesel.962
  • Kagob a – Virus.Linux.Kagob.a
  • Kagob b – Virus.Linux.Kagob.b
  • MetaPHOR (also known as Simile)
  • Nuxbee – Virus.Linux.Nuxbee.1403
  • OSF.8759
  • Podloso – Linux.Podloso (The iPod virus)
  • Rike – Virus.Linux.Rike.1627
  • RST – Virus.Linux.RST.a
  • Satyr – Virus.Linux.Satyr.a
  • Staog
  • Vit – Virus.Linux.Vit.4096
  • Winter – Virus.Linux.Winter.341
  • Winux (also known as Lindose and PEElf)
  • Wit virus
  • ZipWorm – Virus.Linux.ZipWorm

Can someone, please, explain to me in a rational way how this list can be so long, despite Linux being such a terribly small platform? I suppose, as I do not know for certain myself, that most of these viruses are rather harmless, and that most wouldn’t work on modern Linux systems, as they probably explore vulnerabilities that have been patched in revisions of the OS. I also am aware of that there have been proof-of-concept viruses for Mac, that utilize vulnerabilities that later have been fixed. Some of the viruses in the list above may be similar proof-of-concept examples for Linux.

Personally, I think OSX and Linux match up quite well when it comes to virus security, and that this has nothing to do with the size of the platform, but everything to do with the UNIX/UNIX-like foundation underneath. In both cases, the worst threat is the users themselves, who often allow to run malicious code without knowing what they are doing. This is a big threat to any computer platform, regardless of the security measures taken by programmers. As long as the user can install new software, this will be a potential threat (even though sandboxing and securely signing applications can decrease the risk of malware infection).

That being said, Mac OS X is incredibly easy to hack once you have access to the computer. This is a problem, and Apple really should be busy fixing that. But please aim your guns at the right issues. Mac viruses is not a real threat for the moment, just as Linux viruses is not really a big threat to Ubuntu users. That a Mac can be hacked to gain root access in a minute – that is a problem, which have everything to do with OS architecture. However, making the Mac market share smaller will not solve this problem, nor will it get worse as the platform expands. If we’re in luck, though, Apple may acknowledge the problem as its user base grows, and address it before it gets too late.

Young people don’t want to work?!

An article in the Gothenburg local news paper, GP (full article, Google translation) , indicates that young people are becoming increasingly comfortable with faking sickness to get away from work. However, it is likely that the journalist is wrong. Here’s why.

The conservative issue with young people and labor

Based on a statistical survey carried out by the Swedish opinion-measuring institute SIFO on behalf of the news paper (Göteborgsposten, GP, independent liberal) the journalist Anna Holmqvist draws the conclusion that young people don’t want to work, but rather stays at home pretending to be sick. However, she is obviously not very familiar with how statistics works, nor does she hide her political agenda. Let’s go through the article together while I point out some of the most obvious misunderstandings in it.

According to the article, six percent of the Swedish people thinks it is okay to tell authorities that you’re sick, when in fact you are not. Already here the problems arise. First, the method of the survey is not disclosed, so we’re left to guessing the importance of these results. Not publishing such numbers is often not a good sign, so let’s suppose that SIFO is not that confident in these results itself (and trust me, these people know their statistics). Probably the answering frequency was not brilliant, to say the least. Second, the survey says nothing about for how long these people think it is okay to stay home for “non-sickness” reasons, nor does it define what is meant with “faking disease”. This is also a serious problem for this survey.

The which-hunt for the young

In the next sentence, the article states that 15 percent in the ages 15 to 29 years thinks it is acceptable to fake sickness. It then refers to a similar survey made five years ago where only 12 percent in this group said this behaviour would be acceptable. Then Anna Holmqvist makes the claim that this is a significant increase, and thus inclines that the youth increasingly disobey the rules. While a populist statement, there is no significant data to support a such statement. In fact, going from 12 to 15 percent is a 3 percent increase. Given that this survey probably reached less than a thousand people (many people are unreachable when SIFO calls etc.) three percent represents 1000*0,03 ≈ 30 persons. Then, note that we’re only considering the group between 15 and 29 years old here, which statistically can’t make up more than a third of the people in the survey (probably less, since these surveys have problems reaching young people and thus are biased from the beginning). This leads to the conclusion that these three percents consist of less than 10 people! Less than ten! Hello uncertainty. When working with such small numbers of individuals, conclusions will be drawn from random events rather than statistical trends. Everyone working with statistics knows this. Anna Holmqvist either doesn’t, or hides this knowledge well to support her populist political agenda. I don’t know which, but obviously it’s not good journalism.

The next sentence supports that Anna does not know statistics, however, since it comes with a rather hilarious claim: “Something seems to happen with our morale when we turn 30.” Hopefully, this is a joke. Of course it could look like this to an untrained eye, but this is an issue with how the age groups are divided. Draw the line between the groups at 28 instead (15-27, 28-45, etc.) and you’ll suddenly see that something happens with our morale when we turn 28… This part is just bullshit.

Who is less educated?

Then the article goes on drawing similar conclusions related to education, saying that lower education leads to higher a degree of cheating. Once again without caring about statistical issues. Holmqvist does not even point out that less educated people are most likely over-represented in the 15-29 age group, and that these numbers thus influences each other in some way. Instead, she goes on to conclude that older people often are less educated (which is true, of course), and that this makes the results even more puzzling. Please, make the connection between young age and low education here…

At the end, the article points out that people living in the Gothenburg area are more likely to cheat with disease faking than other people in Sweden. However, once again we can use math to disprove the significance of this: 1000 people in the survey, the Gothenburg area holds about a million inhabitants, while Sweden have about 9 millions. Thus, Gothenburg have about 100 people answering to this survey, comparable to Stockholm. Smaller towns in Sweden will have too low answering frequency to be significant. Now the article claims that 14 percent of the people in Gothenburg accepts cheating. 14 percent – that’s about 14 people. Wow! What a significant number to compare. And the article don’t even give Stockholm’s numbers for us to compare.

Percents are not facts

Personally, I think that GP should send Anna Holmqvist on a 15 hec statistics course. To everyone else, please don’t accept when journalists throw percentage number around themselves. Percents are not facts. Percents are statistical measurements, and as such they should be taken with a huge grain of salt.