9: The same graph both ways

If you get confused between standard deviation and standard error, here are some suggestions:

1. Standard deviation is about how far members of an entire population deviate from the average. It is a
characteristic of the population, so it doesn’t depend on how many members you sample (except that
if you only sample a few members, you won’t get a good estimate of SD).

If you are trying to describe variability in a population, you probably want to use standard deviation.

2.Standard error is about how much error you, as an experimenter, cannot rule out from your results when predicting a population mean from a sample. SE falls steadily as you sample more and more members of the population. No matter how variable the population is, some TRUE mean exists, and SE tells you how accurately you can estimate this true mean using a sample of the population.

If you are trying to support or reject a hypothesis — in other words, when you are reporting on the
results of an experiment — you will most likely be using Standard Error for your error bars .

Which graph will be more useful for each question below?

SD or SE?

The Budget Fude people take exception to your results, and carry out a massive
experiment in an Olympic-size swimming pool divided in half, containing 10,000 fish. They claim
that under the right temperature conditions, Budget Fude is superior to Fish2Whale. Are they
interested in SD or SE?

SD or SE?

The University wants to choose a brand of fishfood to feed their fish during
experminents on critical temperature limits. It is important that the brand they choose produces
fish that are as similar as possible. Are they interested in SD or SE?

bar graph with SE bar graph with SD