Inferential statistics deal with inferences about populations based on the results of samples. Most social science research deals with samples drawn from larger populations. Thus, inferential statistics are data analysis procedures for determining the likelihood that results obtained from a sample are the same results that would have been obtained for the entire population.
To illustrate: You have randomly selected a sample of ninth grade students. Based on a pretest in mathematics and other criteria, you have created two closely matched samples of students. Group A will be taught mathematics using a computer, and Group B will be taught mathematics using a traditional method. You want to know if the mean scores for Group A are significantly different from the mean scores of Group B. Results of the posttest in mathematics reveals that Group A has a mean score of 93, and the mean score for Group B is 85.
You have to make a decision as to whether the difference between the two means represents a true, significant difference in the treatment (in this case, method of instruction) or simply sampling error. A true difference is one caused by the treatment (the independent variable) and not by chance. Thus, an observed difference is either caused by the treatment, as stated in the research question (or research hypothesis), or is the result of chance, sampling error.
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