## Friday, September 21, 2012

### Learning Statistics: Fundamentals and Lessons

This is the first guest post on CSI without Dead Bodies from Jane Collander.  Enjoy.

Many future statistics students sweat the ordeal of dealing with numbers and abstractions as it applies to real world scenarios. So what intimidates most beginning statistics students? Perhaps the textbook definition of statistics: the aggregation, organization, scrutiny, interpretation, and presentation of data. As much of a mouthful as this technical definition is, learning and implementing statistics is really as easy as appreciating a few basic concepts.

Levels of Measurement
There are four levels of measurement, or scales of measurement, employed in statistics: nominal scale, ordinal scale, interval scale, and ratio scale. The progression essentially follows an ascending order of difficulty from nominal to ratio scale arrangements. As the name would imply, a nominal scale merely assigns a name to data. An example of a nominal scale would be classifying individuals based on their male or female gender.

One level more progressive from a nominal scale is an ordinal scale. An ordinal scale is also intuitively named in that an ordinal scale classifies items both by name and rank order. For instance, suppose twelve high schoolers participate in the 100 meter dash. An ordinal scale would arrange each runner based on his finish time in rank order. An ordinal scale is slightly more sophisticated than a nominal scale because an ordinal scale includes rank.

Even more complex than nominal or ordinal scales are interval scales. An interval scale not only tells the reader about the order of the items, as an ordinal scale does, but it also includes the measurable distances between data points. For instance, with ordinal scales the reader might not know the time by which runner one beat runner two, but with an interval scale this information is known and presented.

Finally, a ratio scale is an interval scale with a true zero point. Whereas an interval scale, like conventional readings of temperature, can go below zero (e.g., minus eighteen degrees fahrenheit), a ratio scale cannot go below zero. For this reason, the measurement of height would be an example of a ratio scale in that zero inches does in fact denote zero height.

Mean, Median, and Mode
In statistics, measures of central tendency, or the manner in which data tends to cluster around one quantitative value, are denoted by mean, median, and mode. This concept isn't actually that hard to pin down: the mean or arithmetic mean for height among males in the United States is around five feet eight inches. The arithmetic mean is simply the average of all of the items in a group of data. The average is calculated by dividing the total number of something, say pounds, by the total number of items in the group. For instance, if three people collectively weighed three hundred points, the average weight would be one hundred pounds.

Median means the number found in the center of a data set. The median effectively separates the top half of the data set from the bottom half of the data set. The median can be less helpful as a measure of central tendency when there are many outliers, or statistical aberrations, that aren't accounted for by locating the number in the center of a data set. The mode can be helpful for alerting the reader to an often occurring event because the mode is the most frequently occurring number.

Summing Up
Statistics is frequently less intimidating than most beginning students realize. The field and study of statistics, however, requires a robust understanding of basic psychometrics, such as the ones presented in this article.

Jane Collander writes about parenting, education & more at http://www.healthinsurancequotes.org.
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