How to Evaluate the Skewness Considering Sample Size

Skewness becomes more understandable when we have a tool by which to compare it. Consider the normal curve on a graph, which looks like a bell, with equal tails on the left and right and a single elevated curve in the middle, hence the term "bell curve" or "bell-shaped curve." This bell curve graphically represents a distribution of data that is symmetric, with most of the values concentrated around the center of the curve. A skewed distribution, as opposed to the normal, shows that data values are concentrated either on the left or right of the graph, giving the curve a lopsided look.

Things You'll Need

• Data in number form
• Graph paper
• Pencil

Instructions

1. Tabulate the frequencies of each variable to determine the distribution of data. Frequencies are the number of responses by attribute and the percentage of each attribute to the total, according to Dr. Brintzenhofe Szoc in her paper "Clearing the Research Cobwebs: A Review of Research Methodology." For example, arrange the test scores of 100 people from the smallest to the biggest value and start marking one by one how many people scored that value.

2. Plot your data on graph paper, then connect the data points to make a histogram, or bar graph. In the test scores example, the x or horizontal axis of the histogram would be the test scores, marked off in intervals of 5, e.g. 0-5, 6-10, 11-15, etc. The y or vertical axis would be the number of people. A histogram is a set of vertical rectangles that describe a frequency distribution.

3. Draw a line through the highest points of the blocks in your histogram. By now you can see a pattern forming. Ask yourself if your distribution looks like a normal or bell curve, or if it is skewed to the left or the right.

4. Simplify your understanding of the skewness of the distribution. The key to determining whether it is skewed to the left or skewed to the right lies in the tail, not in the curve. The tails are the parts of the curve that slope downward on both edges. If the left tail is longer, then the distribution is said to be skewed to the left or negatively skewed. (Sample observation values: 1, 100, 101, 102, 103.) If the right tail is longer, then the distribution is said to be skewed to the right or positively skewed. (Sample observation values: 1, 2, 3, 4, 100.)

References

• "Clearing the Research Cobwebs: A Review of Research Methodology"; Karlynn Brintzenhofe Szoc; August 2006