# The End -- for now...

Later, we'll talk about how to determine whether two groups are SIGNIFICANTLY DIFFERENT even though their distributions overlap. 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 all influence a single measurement.

An IDEAL normal distribution can be completely summarized by two measurements: **mean and standard deviation (SD)**.

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

Also, **68% 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 summarize 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.

*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.*

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