Descriptive statistis are used to summarize data under study. Some descriptive statistics summarize the distribution of attributes on a single variable; others summarize the associations between variables.
• Descriptive statistics summarizing the relationships between variables are called measures of association.
• Many measures of association are based on a proportionate reduction of error (PRE) model. This model is based on a comparison of 1. the numbers of errors we would make in attempting to guess the attributes of a given variable for each of the cases under study - if we knew nothing but the distribution of attributes on that variable - and 2. the number of errors we would make ...view middle of the document...
Some inferential statistics estimate the single-variable characteristics of the population; others - tests of statistical significance - estimate the relationships between variables in the population.
• Inferences about some characteristic of population must indicate a confidence interval and a confidence level. Computations of confidence levels and intervals are based on a probability theory and assume that conventional probability-sampling techniques have been employed in the study.
• Inferences about the generalizability, to a population, of the associations discovered between variables in a sample involve tests of statistical significance, which estimate the likelihood that an association as large as the observed one could result from normal sampling error if no such association exists between the variables in the larger population. Tests of statistical significance are also based on probability theory and assume that conventional probability-sampling techniques have been employed in the study.
• The level of significance of an observed association is reported in the form of the probability that the association could have been produced merely by sampling error. To say that an association is significant at the .05 level is to say that an association is large as the observed one could not be expected o result from sampling error more than 5 times our of 100.
• Social researchers tend to use a particular set of levels of significance in connection with tests of statistical significance: .05, .01 and .001. This is merely a convention,...