# The difference between percentage and percentage points

Note: This is a repost from my old blog. It appears as it originally did, except for the correction of an embarrassing math error and the addition of one note.It was originally written as part of the basic concept concept thought out by MarkCC at Good Math, Bad Math. The blog post is the single most visited blog post at my old blog, with daily visits ever since it came up.

Quite often I’ve come across situations where it’s unclear if someone knew the difference between percentage and percentage points, so I thought I’d write a post where I would try to explain the difference.

Simply put, percentage is relative, while percentage points are absolute.

For example, if we say that the number of female CEOs increase by 3%, we mean that the number increase with 3% of the current number of female CEOs.

If we say the number increases with 3 percentage points, we mean that the number of female CEOs increase with 3% of the total number of CEOs.

So if 5% of all CEOs are female (the current situation in Denmark, according to today’s newspapers [note: 2007 numbers]), a 3% increase would not be noticeable, since it increased the number of female CEOs to 5.15% of the total number of CEOs.

On the other hand, if we say that the number of female CEOs increases with 3 percentage points, it would mean that 8% of all CEOs would be female. Quite a difference.

Generally speaking, percentage points should be used to measure the difference between two percentages, since it gives a more clear view of the differences than when percentages are used.

Let me give an example of how it gives a clearer view.

Let’s say that a poll in year 1 shows that 10% of the population supports slavery (to take a, hopefully absurd example). In year 2 the poll shows a 20% decrease in the support compared to year 1. However, in year 3, the same number has gone up by 25% compared to year 2.

Many people would get the impression that the number of slavery supporters in year 3 is higher than in year 1, but that’s actually not the case.

In year one 10% supported slavery. The next year, the number fell by 20%. 20% of 10% is 2%, which means that 8% supports slavery. Then the number of supporters increased with 25%. 25% of 8% is 2%, so the total is back up to 10%.

If we have used percentage points, we could just say that in year 2, the number of supporters fell by 2 percentage points, and that the number of supporters increased by the same amount of percentage points in year 3. Thus making it much clearer that the amount of supporters was the same in year 1 and year 3.

# Nothing in Medicine Makes Sense in the Light of Homeopathy

Note: This is a repost from my old blog. It appears at it originally appeared on my old blog.

I am not the first person to state this, but I think that it’s important that we all keep up saying this: Testing of homeopathic medicine should end.

Why do I say this? Well, for a very simple reason: There is no evidence that homeopathy works. And what’s more, the whole concept of homeopathy flies against everything we know about chemistry, physics, and physiology.

This blog post is triggered by a truly abysmal study where homeopathic medicine was compared to proper medicine used for treating moderate to severe depressions – there were numerous flaws in the study (which I plan to address in a later post), but the fundamental problem was that it was comparing medicine with remedies based on nonsense.

There is a famous essay by Theodosius Dobzhansky called “Nothing in Biology Makes Sense Except in the Light of Evolution“, which goes on to explain how our knowledge of biology wouldn’t make sense except if evolution is true. One could write a similar essay, called say “Nothing in Medicine Makes Sense in the Light of Homeopathy”, in which one explains how all our knowledge of medicine and physiology doesn’t make sense if homeopathy is true.

I don’t think this can be stressed enough.

It’s not just a matter of science not understanding homeopathy. If homeopathy was true, it would mean that the basic building blocks upon which our knowledge is built would be wrong.

Given we know that this is not the case, homeopathy must be wrong. No, that’s too mild; homeopathy must be absolute nonsense.

The basic concepts of homeopathy are things like “like cures like”, miasms, and and the concept of “memory” in water, all of which is nonsense.

“Like cures like” (or law of similars) is the idea that medicine should be based upon things which gives the same symptoms as the original disease. This was perhaps plausible back when Hahnemann first proposed it two hundred years ago, but we now know that there is no truth to this idea. Sometimes the medicine will be based upon substances which gives similar symptoms, but mostly it won’t.

Miasms are an old concept, in which diseases are caused by pollution or bad air. This idea was replaced by the germ theory of diseases, and is not taken serious by anyone except for certain branches of alternative “medicine” such as homeopathy, where they have added their own twists to the concept, but still stay largely true to the old Medieval concept.

The “memory” of water (or sugar for that matter) is the explanation used to explain how homeopathic medicine can have any effect. Homeopathic remedies are based upon the concept of diluting, in which the remedies are diluted to a degree where none of the original molecules are left (see this rather poor Wikipedia article for the numbers).

Oh, and the homeopaths also claim that the more diluted a remedy is, the more potent it is. Yes, this is really what they claim. No, it doesn’t make any sense.

So, all in all, we know that homeopathy doesn’t work. So, why the hell are we continuing to test it against proper medicine?

There are a lot of alternative “medicines” which might work, even if the concepts they are based upon are nonsense (e.g. acupuncture), and it makes sense to test these (so far, the effect of acupuncture seems to be placebo), but this is most certainly not the case with homeopathy. There is no way in which that can work.

Homeopaths might claim otherwise, but then it’s up to them to explain how our basic understanding of chemistry, physics, physiology, and medicine is wrong in this matter, and yet works in every other case. In other words, it’s up to the homeopaths to propose new theories in which homeopathy works, and which still supports our current state of knowledge, and until then, they should be ignored.

Not shunned, but ignored. Like we ignore perpetual motion machine builders, flat-earthers, and other weirdos.

Conventional medicine is not perfect, and our knowledge is expanding all the time, but theories like the germ theory of diseases are well established through science. We understand the mechanisms at play, and this knowledge enables us to fight diseases more efficiently. Much like our understanding of vira has helped us fighting other diseases more efficiently.

Why does claims of memory in water and strength through dilution bring to the table? In what ways are they expanding our knowledge? What diseases are we able to cure because of them? Nothing, none, and none are the answers. So stop bringing them to the table. Instead focus on the many valid ideas, which don’t fly in the face of all the collective knowledge of the sciences.

Woos like to bring up Nobel Laureates Barry Marshall and Robin Warren, and their discovery that ulcers were caused by the bacterium Helicobacter pylori as an example of how outsiders can turn conventional knowledge on its head.

This is of course pure wishful thinking from their side. Marshall and Warren were very much part of the established scientific community, and while their proposal was received skeptically at first, it was not dismissed out of hand for some very simple reasons:

• It was built upon evidence.
• The mechanisms etc. all worked within conventional science and the mechanisms known at the time.
• There seemed to be some problems with the prevalent hypothesis at the time.

In other words, not only did they work within the established science, they actually addressed some known issues and presented evidence for their claims.

Yes, it took some time (and a very drastic demonstration) to convince people, but the scientific and medical community was very willing to be convinced, and as soon as there were sufficient evidence, the new explanation was universally accepted in quite a short time.

This is how it is done.

So, in what way has proponents of homeopathy done any of this?

The truth is that most people with a basic understanding of science understands that homeopathy is nonsense of the worst order, yet money is still spent on testing this nonsense, demonstrating again and again that it doesn’t work. Why? We know that it doesn’t work, since we understand the fundamental flaws in the premises behind homeopathy, and we know that homeopathic remedies are nothing but water, alcohol, or sugar (depending on whether they are liquid or in pill form), so they cannot work any better than placebo – they ARE placebo.

Let’s put an end to this.

All it does is to lend credibility to homeopathy in the eyes of observers who don’t know any better. They think that since homeopathic remedies are continuously being tested, there must be something to them. Why do we let this misconception continue? Science wins nothing from these sham studies, and it only lends cranks an aura of respectability. Stop it.

Yes, I am very passionate about this – we are allowing a lie to continue perpetually. That’s wrong. Homeopathy has been around for 200 years, providing no value to society as a whole, and generally decreasing the general level of health, and it’s time to stand up and say so.

It goes without saying that I have only contempt for hospitals and doctors who provide homeopathic remedies to their patients. Homeopathic practitioners are usually acting in good faith, believing in their nonsense, but doctors and nurses should know better – they have an education behind them, which provides them with the knowledge necessary to understand what nonsense homeopathy is.