MathBench > Statistics

Normal Distributions and the Scientific Method

The End -- for now...

shark imbedded in suburban roof 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...

fish with baby 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.

 

 

 

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