Summary

Representation of Data

Data are often represented in frequency distributions, which indicate the frequency of each score in a set of scores. Psychologists also use graphs to represent data. These include pie graphs, frequency histograms, frequency polygons, and line graphs. Line graphs are important in representing the results of experiments, because they are used to illustrate the relationship between independent and dependent variables.

Descriptive Statistics

Descriptive statistics summarize and organize research data. Measures of central tendency represent the typical score in a set of scores. The mode is the most frequently occurring score, the median is the middle score, and the mean is the arithmetic average of the set of scores. Measures of variability represent the degree of dispersion of scores. The range is the difference between the highest and lowest scores. The variance is the average of the squared deviations from the mean of the set of scores. And the standard deviation is the square root of the variance.

Many kinds of measurements fall on a normal, or bell-shaped, curve. A certain percentage of scores fall below each point on the abscissa of the normal curve. Percentiles identify the percentage of scores that fall below a particular score.

Correlational Statistics

Correlational statistics assess the relationship between two or more sets of scores. A correlation may be positive or negative and vary from 0.00 to plus or minus 1.00. The existence of a correlation does not necessarily mean that one of the correlated variables causes changes in the other. Nor does the existence of a correlation preclude that possibility. Correlations are commonly graphed on scatter plots. Perhaps the most common correlational technique is the Pearson’s product-moment correlation. You square the Pearson’s product-moment correlation to get the coefficient of determination, which will indicate the amount of variance in one variable accounted for by another variable.

Inferential Statistics

Inferential statistics permit experimenters to determine whether their findings can be generalized from their samples to the populations they represent. Consider a simple experiment in which an experimental group that is exposed to a condition is compared to a control group that is not. For the difference between the means of the two groups to be statistically significant, the difference must have a low probability (usually less than 5 percent) of occurring by normal random variation.