# 9: Summary: The End for now…

## The End — for now…

The take-home concepts are:

Many measurements in nature follow a normal distribution, because this is the kind of distribution
you get when lots of factors influence a single measurement.

An exactly normal distribution can be completely summarised by two measurements: mean and standard deviation (SD).

In an exactly normal distribution, half of the measurements fall below the mean, half above.

Also, 68% of measurements fall within 1 SD of the mean, 95% within 2 SDs, and 99% within 3 SDs.

## And for hypotheses…

A good scientific procedure requires a way to MEASURE, something to COMPARE your treatment to,
and REPLICATION to avoid random effects.

You can summarise many measurements by taking the mean AND standard deviation of the group of
measurements (assuming that your measurements are at least somewhat normally distributed).

A lot of overlap between two normal distributions makes it difficult (but not necessarily impossible)
to show that the means of the two groups are different.

When comparing two sets of data:

IF the means of two sets of measurement are far apart AND their standard deviations are
relatively small, THEN the two sets are (probably) significantly different.

IF the standard deviations are big compared to the difference between the mean, THEN the
data is too “sloppy” to draw any conclusions about significant differences.

## Learning outcomes

Now that you have worked through this module, you should be able to:

• Outline the three steps that describe good scientific procedure.
• Name the parameters that describe a normal distribution and explain how the distribution of a variable changes in response to changes of these parameters
• Indicate where the middle 68%, 95% and 99% of a normal distribution lies relative to the mean of the distribution.
• Indicate how the values of the mean and standard deviation of one normal distribution need to change in order to increase or decrease the overlap it has with a second normal distribution.

If you want a printer-friendly version of this module, you can find it here in a Microsoft Word document. This printer-friendly version should be used only to review, as it does not contain any of the interactive material, and only a skeletal version of problems solved in the module.