Statistics: You're Doing it Wrong.

A lot of people don't really understand statistics, and it leads to all sorts of trouble. I get very tired of people quoting numbers and percentages that they've read in the paper while clearly not having a clue as to what they're actually talking about. Papers won't actually explain things properly either because that would make the story a whole lot less dramatic.  I'm hoping to clear some of that up here with a couple of examples of commonly misunderstood statistical talk.

1) Taking drug x increases your risk of cancer by 80%

Hearing this, a lot of people will immediately stop taking drug x, thinking that their chances of getting cancer from this stuff is now hugely amplified.

The actual fact is that it might not be. Lets assume that your probability of getting cancer at some point in your life is 1%.

80% of 1% is 0.8%. So, an increase of 80% means your probability of getting cancer is now 1.8%. Proportionally, this is significant. If your probability is already high, then you're in strife. But in real terms, if you are not already in a high risk group, you don't have all that much to worry about.

It's also why I assume some people use the term "percentage points", so that if probability has gone from 20% to 30%, it has gone up by 10 percentage points. It has also gone up by 50%.

2) How "averages" work in general

The "mean" is the biggest problem where these are concerned, and is the one most people take as what is normal. It is calculated by adding up each bit of data and then dividing your answer by how many bits there are.

When it comes to averages, it is unwise to only look at this one average. For example:

10 people are in a room. 9 of them will earn a salary of $40k this year. The 10th person is a CEO who will earn $4million. The average salary of the room is $436k per year, which is more than 10 times what most of the people in the room earn.

The data is skewed, and therefore not an accurate representation. This is why it is important to note the median (middle value) and mode (most frequent value), and to also look at your minimum and maximum data points so that you have a better idea of how the data is actually spread out.

The useful thing about the median is that it divides the population into two equal halves. So if you had people getting scores ranging from 0 to 100 and your median was 10, this means that half the people got less than 10 as their score. That's not very good...

There are also things called "quartiles". So they show you the quarters of your data. So if the lower quartile for the above info was 7, it means that a quarter of your people scored less than 7 and a quarter scored between 7 and 10. If your upper quartile is 95, then a quarter of your test subjects scored 95 or more (which is actually pretty good) and a quarter got between 10 an 95 (which is a heck of a range).

Medians and quartiles are a really good way of showing how data is spread out.

As far as simple representations go, I really like box and whisker plots. As far as representing data goes, I find them extremely useful: When you line up all the scores in order from smallest to largest, they show you the highest value, the lowest value, the middle value, and two values in between.

Snooty McSmugbox. The Box with Whsikers!

For example, let's say I have test scores for a class of 31:

Highest score: 90%

Lowest score: 10%

6 kids got exactly 30%

3 kids got exactly 34%

7 kids got 62%

13 kids got 74%

Here is the BW plot:

 Each section represents a quarter of my class. Half my kids got 62% or more, which is pretty good. More than half my kids got 50% or over (remember that the median splits the class into two equal halves), which is also not bad.

I think that they're pretty cool :-)

Love: What it is, and when to know if it isn't

Having posted recently on how tumultuous my relationship with  my mother was (while we still had one; it’s been several months since we’ve spoken), I’d like to discuss abusive relationships in general.

From the Reach Out website, these are the signs of an abusive relationship:

Possessiveness

• Checking on you all the time to see where you are, what you're doing and who you're with.
• Trying to control where you can go and who they can see (this includes telling you they don't like/trust/are jealous of your friends for whatever reason; making feel you bad about hanging out with your friends/family)

Jealousy

• Accusing you without good reason of being unfaithful or flirting.
• Isolating you from family and friends, often by rude behaviour.

Put downs

• Putting you down, either publicly or privately by attacking how smart you are, your looks or capabilities.
• Constantly comparing you unfavourably with others.
• Blaming you for all the problems in the relationship and for their own behaviour toward you ("I only got mad because you kept perving at that other girl/guy!" - especially if you weren't actually perving)

Menace + threats

• Yelling, sulking and deliberately breaking things that you value.
• Threatening to use violence against you, your family, friends or even a pet.
• Saying things like 'no one else will want you'.

The key thing is that these behaviours are not present all the time. Generally speaking, in an abusive relationship, if it is good then it is very very good. There is joy and laughter, gifts, surprise dates in new places, strawberries covered in chocolate; the kind of stuff movies are made of. The other person is sweet and gentle and warm. When it is good, it can seem absolutely perfect. It seems like the most loving relationship in the world.


This can often cloud the bad things. 

"But he loves me... He just got angry because I was tactless and that's why he shouted and said nasty things. I'll just be more careful about how I say things next time."


"She loves me - I know she does because she's so wonderful all the time. She just gets frustrated when I do things wrong. She doesn't mean it when she puts me down, and she always apologises afterward..."

"She's just insecure because she's had a hard past. She's jealous of my friends now, but she'll get better when she realises that I do really love her and that she doesn't need to be jealous. Then she'll stop being angry when I want  a night out with 'the boys'. "

"He's just trying to look after me. He doesn't want me being felt up by strangers in a crowd, and that's fair enough I guess. Maybe I shouldn't go to that concert after all..."

I’d like to say this very clearly: If you are being treated in such a shameful way and it never changes; if the other person shows no sign of being willing to alter themselves and take steps to make themselves better as well (because it's always a two-person job), it is not love. To quote the above website:

When you are in a healthy relationship, both individuals support each other, sharing the good times and helping each other through the tough ones.  When someone matters deeply to you, and those feelings of trust and respect are returned, it enables us to face the world with confidence.

Building and maintaining a healthy relationship needs the commitment from both of sides in order to work at it. But it is worth it, because in a good relationship, you feel good about your boyfriend or girlfriend, and good about yourself.

To stay with someone if they treat you in ways that make you feel insecure and unhappy is not to stay with them out of love.

To put someone down, say horrible things to them, threaten them, and still stay with them is not staying with them out of love. 

To keep saying bad things and taking them back but not actively working to change the behaviour is not showing love.

“Love” is not just a feeling; it is a verb. Whether it is romantic love, familial love, or love for a pet, you can claim to  love all you want but if you do not consistently show it in your actions then you are not loving the person.

“Love” is a two-way street. If only one person is trying to change themselves while the other continues to lay the blame, then they are not in a loving relationship. 

“Compromise” is not one-sided. Compromise requires meeting half-way to get the best possible outcome for both parties, and sometimes there can be no compromise. If it is a difference that will affect one or more parties negatively; if it will have a negative impact on the wellbeing of either party in the long run, the relationship should end.



If you find yourself in a relationship where the characteristics above are ever on display, seek help from someone you trust. If you're not sure whether you're in one, talk to someone about it. Talk to a friend. A teacher. A family member. Your doctor. Anyone, just talk to them, as they may be able to see something you haven't. Don't be afraid that they'll judge you or that you'll look like a failure if your relationship isn't perfect or happy; appearances are a bad reason to be in a relationship anyway.

I hate the phrase “true love conquers all”. There are things love shouldn’t need to conquer. There are some things that, if it really were “true love”, wouldn’t exist to be conquered in the first place. Disney can get stuffed.

Our consumerist lives

Shopping is a pretty big part of our lives. Most often, when thinking of somewhere to go, places that come up as ideas are shopping strips and shopping centres. I've heard a lot of grumbling in the past about how people really should find something else to do. See a film. Read a book. Have a picnic. Go bowling. Etc etc.

But I had a think, and I realised something: Window shopping is probably the cheapest and simplest form of entertainment you can get.

There are no entry fees, like for cinemas or bowling alleys. If you're going to a large centre, there's no worry about the weather going wrong and spoiling your lunch. You don't need to plan ahead a great deal, and if you don't actually buy anything you've only paid for getting there and maybe some food and drink (though nothing stops you bringing  your own to those places, either).

Now, the weather thing may well be a HTFU scenario, but in reality no one wants to be out in unpleasant conditions if there is another option, even if that option is your lounge room floor. But that is still not ideal, as you're back in the house which you wanted to escape in the first place.

To conclude: I don't t hink that shopping as entertainment is such a bad thing, as long as one is aware of their spending and why they went shopping in the first place.

Answers to Friday's quiz!

Flat surfaces:

• 6 bookshelves
• 1 floor
• 2 levels of the TV stand
• 2 levels of coffee table
• The top of my pile of papers
• 1 foot stool
• 1 piano stool
• 1 piano
• The top of the DVD shelves
• The top of each box next to the cabinet (3 surfaces)
• 2 levels of cabinet

Total = 19

There are seven which ones I had already taken advantage of :-)

Pop Quiz!

Question: How many flat surfaces can YOU see?
Bonus Question: How many have I already taken advantage of?
Answers at the bottom of Monday's blog!

What I've been doing!

So, I'm back from my break :-) I have not been sitting idle! Here's a brief rundown of what's been happening:

1) Writing reports.

Report-writing is boring and painful business. It's as bad as marking, quite frankly. The worst part is when you think you're finished and then discover that you have to read through all the reports you've written because the comment bank you used included stuff about topics you haven't actually covered...

2) Marking.

Kind of has to happen before you can write reports... Also painful and boring.

3) Weekend away with my sweetheart

We went to Bendigo in country Victoria for a weekend :-) It was lovely. Totally unstructured, so we did as we pleased. Read books, walked around the town, relaxed in the spa. Pure romance :-)

We also stopped in a smaller town called Malmsbury to see a village market. There were jams and preserves, wines, beers, hand-crafted jewellery. The gardens were also amazingly beautiful.

It was a fantastic weekend, and just what we both needed.

I'm now back in the real world and hopefully blogging regularly again!