3: Estimating averages

So, what is the first step for the amazing (but not super-powered) t-test? Well, if you’re going to compare averages, you first need to know what those averages are, right? I’ll assume that if you are with me so far, you know how to calculate an average (if you don’t, now is a great time to find out). There are a few different sorts of averages that statisticians use. The one we are using is the simplest and it’s called the mean. So, take a look at the data below, and then just click on the buttons below to have the module do the busy work for you:

Click to see average weight gain:

Control :
 Growth in grams:
131 156 162 163 170 175 212 215
 Growth in grams:
212 221 240 241 283 297 318 324


fish farm

OK, so the mean for the control group is 173 g and the mean for the treatment group (those fed with Fish-2-Whale) is 267 g. Before we can compare these two numbers we need to know how accurately we have estimated these means.

The accuracy of our estimates depends on two things:

  • the amount of variation in our population and
  • the size of our samples.

Aside:  What is a sample?  What is a population?  You might like to read about these two very important statistical terms here. (http://stattrek.com/sampling/populations-and-samples.aspx)

fish vs shark

If we have only used a small sample in our observations or experiments then we might expect that our results may not be very accurate and if there is a lot of variation within the population then we might also expect to have more difficulty getting accurate estimates of the means.

photo credits: fish farm | shark and fish