Science Buddies: "Ask an Expert"

I conducted the "Wily Waves" project, and am now analyzing my data.
I found the mean and standard deviation for my data at heights of 1, 2, 3, 4, and 5 feet. My hypothesis was that as the height increased, the voltage produced would be greater/ The voltage produced would be greater at 5 feet than it would be at one feet.

At 1 foot- the mean is 0.14221
- the std. dev is 0.035

At 2 feet - the mean is 0.4874
- the std. dev is 0.031

The difference between the means is 0.34519.

I analyzed it like this: Since the difference between the means is greater than the standard deviations, the hypothesis was supported.

Is this a correct way to analyze my data?

Hi claram1,

You are on the right track! It sounds like your experiment turned out quite nicely.

You are right that your experiment shows that you got more voltage at 5 feet than at 1 foot. But, your interpretation of the statistics is slightly incorrect. The mean of the voltages produced at 5 feet is larger than the mean of the voltages produced at 1 foot. (You gave data for 2 feet in your post, but I think you meant 5 feet . . . if I assumed incorrectly, then replace "5 feet" with "2 feet" in the rest of this post.) That is how you know that you got more voltage at 5 feet than at 1 foot. The difference between the means and the standard deviations isn't what tells you which experiment produced more voltage.

The standard deviation tells you how much spread you have in your data. You can think of the standard deviation as an error bar that you add or subtract to/from the mean. For example, if you subtract the standard deviation of the 1 foot data from the 1 foot mean, you get 0.11; if you add the standard deviation to the mean you get 0.18. Let's do the same thing for the 5 foot mean. If we subtract the standard deviation of the 5 foot data from the mean of the five foot data you get 0.46; if you add the standard deviation you get 0.52. Scientists might call this a "one standard deviation interval".

The critical thing to note is that these two intervals don't overlap. The interval from 0.11 to 0.18 doesn't overlap with the interval from 0.46 to 0.52. This makes you quite confident that the difference you measured is meaningful: 5 feet really did produce more voltage than 1 foot. Woohoo!

Now, what if the data turned out differently? If the standard deviation is really, really large, then it can be hard to be certain that a difference in the mean of two data sets is actually meaningful. For example, let's hypothetically say that you got the following results:

1 foot: mean = 0.14; std. dev. = 0.1
5 feet: mean = 0.49; std. dev = 0.3

If we do the same thing (add/subtract the standard deviation from the mean to create an interval), then the one standard deviation interval for the 1 foot experiment is 0.04 to 0.24; the one standard deviation interval for the 5 foot experiment is 0.19 to 0.79. These two intervals overlap (between 0.19 and 0.24). This would make you much less confident that the difference between the mean of the 1 foot and 5 foot experiments was truly meaningful.