Unizor - Statistics - Normality Test Example

Notes to a video lecture on http://www.unizor.com


Normality Test - Example

As an example of an analysis on normality of statistical distribution consider the hourly sea level observed at Midway Island during a period from January 1st, 2012 to December 31st, 2014.
Raw data are taken from the official Web site Sea Level Center of University of Hawaii.

Based on these data certain analitical calculations were performed and are presented atSea Level at Midway Island 2012-2014 Analysis. The histogram as a picture is at Sea Level at Midway Island 2012-2014 Histogram.

The calculated statistical values are:
minimum 660 mm,
maximum 1859 mm,
average μ = 1125 mm and
standard deviation σ = 142 mm.
We also calculated the double and triple standard deviation.

We have built a histogram of sea level distribution by dividing the range of values into 30 bins and presenting frequencies for each bin in numerical and graphical (histogram) form. The histogram does resemble the bell curve, which is a good indication of normality.

Next we calculated how many data elements fall in σ, 2σ and3σ intervals around the mean values and the results are as follows.
Out of a total of 26304 data elements
26223 (99.69%) fall within 3σinterval around mean value μ,
25265 (96,05%) fall within 2σinterval around mean value μ,
17651 (67.10%) fall within σinterval around mean value μ.
These calculations correspond to theoretical numbers (99.7%, 95% and 68%) for Normal distribution quite well.

The bottom line - the distribution does correspond to Normal.