Section 2e - Project on the Normal Distribution

Exploration
The Fathom Workshop Guide that I used in my exploration of simulation suggests
that the distribution of the mean proportion of males in my samples follows a
Normal distribution.

Plan and Data
What I plan to do is to use the data generated from the simulation and to analyse the distribution through the tools supplied by Fathom.

Analysis

If the simulation data follows a Normal distribution I would expect the cumulative distribution to look like an S shaped curve very similar to the one I obtained. I can get better visual confirmation that the data follows a Normal distribution by looking at the Normal Quartile Plot provided by Fathom.

From the Fathom Help file - A Normal Quartile Plot shows the distribution
continuous (numeric) data. It plots the z-scores associated with the percentile of
each case if the data were normally distributed. Therefore, if the data are
Normal, the plot should show a straight line. My simulation data is very close to
the straight line shown on the plot.

Finally, I can do some checking whether the distribution of my simulation data
has the following properties of the Normal Probability distribution:
    50% of the data falls on each side of the mean
    About 68% of the data falls within one standard deviation of the mean
    About 95% of the data falls within two standard deviations of the mean
    About 99% of the data falls within three standard deviations of the mean
For my simulation data the mean proportion is 0.531, the standard deviation is 0.0497 and the Dot Plot is

where each dot represents two data. I counted the data in each interval and
divided by 200 hundred to get the percentage within each interval. I found the
percentage of data that falls on either side of the mean is 49.5% and 50.5%,
which is about 50% on each side of the mean.
The percentage of data that falls within one standard deviation (0.48 - 0.58) of
the mean is 73.5, which is larger than the predicted 68%.
The percentage of the data that falls within two standard deviations (0.43 - 0.63)
of the mean is 97%, which is larger than 95%.
The percentage of the data that falls within three standard deviations (0.38 -
0.68) of the mean is 100%.

I did not have time to explore whether the approximations that I did (rounding off
the mean and standard deviation, and counting from the Dot Plot rather than
using the raw data) biased these results.

Conclusion
The work that I did suggests that the distribution of the data I obtained from the
simulation could be modelled by the Normal probability distribution.

<<Section 2d | Project Conclusions>>