Using Statistics in Psychology

Scientists aim to accomplish two goals with their data. First, they want to organize and describe the data in meaningful ways. Second, they want to use the data to make inferences, or predictions, about a population of interest. To achieve the first goal, scientists rely on descriptive statistics. Descriptive statistics summarize a data set.

Descriptive statistics most often involve a measure of central tendency, one value representing the entire set of values. The most commonly used measure of central tendency is the mean, commonly referred to as the average. The mean is calculated by adding all values in a data set and dividing the sum by the total number of values. With a set of five exam scores (67, 72, 72, 91, 77), the mean would be Another measure of central tendency is the median, the value in the data set where half the values fall below that value and half are above it. To calculate the median, values need to be put in order from highest to lowest: 91, 77, 72, 72, 67. In this data set, the median is 72 because there are two exam scores below this number and two above it. In a data set with an even number of values, the median is the mean of the two middle values (92, 91, 77, 72, 72, 67—the median is the mean of 77 and 72, or 74.5). The last measure of central tendency is the mode, the most frequently occurring value in the data set. In this case, the mode is 72 because it occurs twice in the data set. If a data set contains a value that occurs the same number of times as another value, then the set has more than one mode. If a data set has no repeated values, then it has no mode. It is also useful to examine the variance between values in a data set. Variance refers to how similar or different the values are to one another. The least sophisticated measure of variation is range, the numerical difference between the highest and lowest values in a data set. A more commonly used measure of variation is the standard deviation, a measure of how much values differ from the mean. Most naturally occurring phenomena have normally distributed values. A normal distribution is a symmetrical, bell-shaped distribution in which most values fall near the mean (about 68% are within one standard deviation of the mean). For example, grades generally follow a bell-shaped distribution: some grades are very high and others are very low, but most are around the middle of the range (i.e., mean). Graphical displays of data help researchers visualize the entire data set at once, including variability in scores, relationships between variables, and potential differences between groups.