I was emailed a question recently by a student who wanted to know more about the difference between independent/dependent variables. Having watched the tutorial on independent and dependent variables, they were still a bit perplexed, mainly around “height depends on your weight…. weight depends on your height… both sound the same to me?”. Since this is a common question students have, I though I’d post my response here so anyone else wondering the same thing can benefit.
Don’t forget, I’ll be running through the answers to the Core Section of the 2007 Exam 1 in the next couple of days, so print yourself a copy and have a crack at them first!
Here’s my response:
“Your weight depends on your height, and it doesn’t really work the other way around. Let’s say your height is 170cm and as a result, your weight is 70kg. If you grew a bit, and were now 180cm tall, it would make sense that your weight would increase a bit too, let’s say you now weigh 75kg. It’s likely that the taller someone is, the more they will weigh. A child who is only 90cm tall would weigh a lot less than an adult who was 160cm tall. There are other factors that determine how much you weigh of course, like lifestyle, diet, exercise etc. but one of the basic ways we can predict what the average person will weigh is knowing how tall they are. So in this way, your weight depends on how tall you are, that is, it’s determined by how tall you are.
Putting those variables the other way around, it sounds a bit whacky. For example, let’s say I know you weigh 70kg and your height is 160cm. Then if you gained a bit of weight (you’re now 75kg, say) and as a result you grow a bit taller?? You don’t grow taller because you gained weight. But you DO gain weight whenever you grow taller. Do you see the difference there?
So weight is dependent upon height, because as your height increases, so must your weight. As you grow taller, you get heavier – that’s just nature. When you’re 8 years old and 100cm tall, you weigh a certain amount, and then when you’re 18 years old and you’re now 180cm tall, you way a lot more, accordingly. So your height has a large affect on how much you weigh. But how much you weigh has no bearing on how tall you are.
It’s about whether we can use one variable to predict what the value of the other one might be.
Another example, let’s say we’ve got some data on how many hours a group of students studied for a test, and the result that they got on the test. We would expect that how many hours they studied for would have some effect on the result they get on the test. In general, we would expect that the longer they study for, the better they’ll do on the test. So in this instance your test score depends on how long you study for. If you study a lot, you’ll probably do well. If you don’t study at all, you probably wont score as highly.
Looking at the example of AGE and SALARY. You would expect that your salary would depend on how old you are. We would expect that when you’re 15 you probably don’t earn very much because you don’t have a degree, or much experience or training yet, so you would earn less. When you’re 50 years old and you’ve been in the workforce for 30 years getting payrises and promotions year after year, we would expect that you would earn considerably more money than the 15 year old. So because of that, your salary probably has a lot to do with how old you are – it depends on your age.
We can then use a person’s age to predict how much money they might make. For example, a 15 year old maybe makes $6,000 per year. A 20 year old maybe makes $30,000 per year. A 40 year old maybe makes $70,000 per year.
But that doesn’t work the other way around… It doesn’t really make sense to say your age depends on how much money you make. If you make a bit more money, does that mean you grow older? If I gave you a payrise, would you automatically age by 5 years? No – because your salary doesn’t have any affect on your age. But your age does have an affect on your salary.
I hope that clarifies it a bit better!”