A Statistical Review

·
Review what has been covered

Introduction

Avoid these
common mistakes in statistical analysis:

·
Using non-representative data

·
Using the wrong tool or using the right tool
incorrectly

·
Using the right tool incorrectly

·
Misinterpreting results

Graphical Analysis

One of the best methods for
quickly assessing trends in data is to view data in a graphical representation.
The distribution of data is described statistically using two characteristics,
both of which are necessary in evaluating data. *Central
tendency* indicates the middle of the data distribution, whether that
refers to the mean, mode, or median of the distribution. The *dispersion* of the distribution of
data describes the amount of spread or variation in the data.

The Normal Distribution

The Normal Probability
Distribution allows us to put everything on the same scale. The Normal curve is a bell-shaped curve that peaks in the
middle at the mean. The Standard Normal curve has a mean of zero. Units on the
standard normal curve are measured in terms of the standard deviations; one
standard deviation in both directions from the mean captures 68% of the data,
two standard deviations in both directions captures 95% of the data, and three
standard deviations in both directions captures 99.7% of the data. As expected,
the bulk of the data is close to the mean

Words to Know

·
*Mean*
(population = m,
sample = ) – the
average value of the observations

·
*Median*
– the middle observation; the point that is greater than half the data and less
than the other half of the data

·
*Mode* –
the most frequently occurring value

·
*Range*
– the difference between the highest value and lowest value in a data set

·
*Standard*
*Deviation* – the average weighted
distance of data points from the mean

·
*Interquartile*
*Range* – the difference between the
upper quartile and the lower quartile

·
*Probability*
– Mathematically, probability equals the number of events meeting the specified
condition divided by the number of possibilities

Conclusion

It is important
not to blindly accept the results of a statistical analysis. Contradictions to
historically well-supported hypotheses need to be carefully considered and
investigated. Look at data intelligently. Identify the source of the data and
always ask if the data and the results of an analysis make sense. Follow some
basic thinking about statistical analysis: beware of incorrect analyses, do not
jump to conclusions, and perhaps most importantly, check the math!