3.4 Distribution shapes

The Normal Curve

When we administer a psychological test to a group of individuals, we obtain a distribution of real scores from real people. Unlike this real distribution of scores (or what we call the obtained distribution of scores), normal probability distributions (also referred to as normal curves) are theoretical distributions. These theoretical distributions exist in our imagination as perfect and symmetrical and actually consist of a family of distributions that have the same general bell shape-high in the middle and tapered to the ends. Figure 3.2 shows some examples of normal distributions.

3.4 Distribution shapes

Notice how each distribution in Figure 3.2 is symmetrical, with scores more concentrated in the middle of the distribution than in the tails of the distribution. Although the area under each distribution is the same, the distributions differ in terms of how spread out they are or how tall or short the shape is.

The normal probability distribution has a number of characteristics that are important for the interpretation of test scores. These characteristics are displayed in the distribution pictured in Figure 3.3 and include the following:

Most test scores cluster or fall near the middle of the distribution, forming what we refer to as the

average or the central tendency. The farther to the right or left you move from the average, the fewer the

number of scores there are.

Most people will score near the middle of the distribution, making the center of the distribution the

highest point.

The curve can continue to infinity, and therefore the right and left tails of the curve will never touch the baseline. Approximately 34.1% of the population will score between the mean and 1 standard deviation (we explain this term later in this chapter) above the mean, and approximately 34.1% will score between the mean and 1 standard deviation below the mean. Approximately 13.6% of the population will score between 1 and 2 standard deviations above the mean, and approximately 13.6% will score between 1 and 2 standard deviations below the mean.

3.4 Distribution shapes

Approximately'2.1% of the population will score between 2 and 3 standard deviations above the mean, and approximately 2.1% will score between 2 and 3 standard deviations below the mean. This curve will capture most of the scores in a population.

The curve is convex at its highest point and changes to concave at 1 standard deviation above the mean and 1 standard deviation below the mean.

3.4 Distribution shapes

Most distributions of human traits, from height and weight to aptitudes and persons characteristics, would form a normal curve if we gathered data from the entire population. For example, although some people are as short as 4 feet and some are as tall as 6 feet 5 inches, most people are between 5 feet 2 inches and 5 feet 9 inches. Most psychological tests, when administered to large groups of individuals, approximate the normal curve.

Not all psychological measurements, however, yield normal or bell-shaped curves .Some are negatively skewed (there are many high scores). Some are positively skewed (there many low scores). Some are peaked (most individuals have the same score). Finally, some are bimodal (there are many low scores and many high scores).

Evenly Distributed Distributions

In evenly distributed distributions, most test scores cluster or fall near the middle of the distribution, forming what we refer to as the average or central tendency. The farther a point is to the right or left from the central tendency, the fewer the number of individuals represented at that point.

Positively Skewed Distributions

Positively skewed distributions have one high point and are skewed to the right. In positively skewed distributions, there are more low scores than high scores.

3.4 Distribution shapes

Negatively Skewed Distributions

Negatively skewed distributions have one high point and are skewed to the left. In negatively skewed distributions, there are more high scores than low scores.

Peaked Distributions

Peaked distributions have one high point and result when man individuals score near the center of the distribution.

3.4 Distribution shapes