Sociological research can have three distinct goals: description, explanation, and prediction. Description is always an important part of research, but most sociologists attempt to explain and predict what they observe. The three research methods most commonly used by sociologists are observational techniques, surveys, and experiments. In each case, measurement is involved that yields a set of numbers, which are the findings, or data, produced by the research study. Sociologists and other scientists summarize data, find relationships between sets of data, and determine whether experimental manipulations have had an effect on some variable of interest.
The word statistics has two meanings: (1) the field that applies mathematical techniques to the organizing, summarizing, and interpreting of data, and (2) the actual mathematical techniques themselves. Knowledge of statistics has many practical benefits. Even a rudimentary knowledge of statistics will make you better able to evaluate statistical claims made by reporters, weather forecasters, television advertisers, political candidates, government officials, and other persons who may use statistics in the information or arguments they present.
Representation of Data
Data are often represented in frequency distributions, which indicate the frequency of each score in a set of scores. Sociologists also use graphs to represent data. These include pie graphs, frequency histograms, 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 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 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 permit social researchers to determine whether their findings can be generalized from their samples to the populations they represent. Consider a simple investigation in which an experimental group that is exposed to a condition is compared with 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.
McGraw Hill. (2001). Statistics Primer for Sociology. http://www.mhhe.com/socscience/sociology/statistics/stat_intro.htm