Indosearch Research Center [IRC]

Of major interest and concern to the educational research worker is the observed variation of naturally occurring events in human behavior and educational practice. Not only does variation occur naturally in human characteristics, but it also arises in response to different treatment conditions acting to influence learning and the consequent stability and change in those characteristics. In addition, variation arises as a result of what has come to be known appropriately as “error,” which is associated with the random fluctuations of observations about an expected value. Such error occurs as a consequence of variability involving the observer, the variability in the procedures or the instruments used for observation, and variability in the object being measured.
Statistics has been referred to by Fisher (1970) as the study of the variation observed in the investigation of populations: The conception of statistics as the study of variation is the natural outcome of viewing the subject as the study of populations: for a population of individuals in all respects identical is completely described by a description of any one individual, together with the number in the group. The populations which are the object of statistical study always display variation in one or more respects. (p. 3)
Thus the educational research worker and statistician are necessarily concerned not only with the individual within the population under investigation, but also with the different conditions and circumstances that have contributed to the variation in the observations and measurements that are made. This entry presents the different measures of variation that are widely used in educational research. First, consideration is given to measures that relate to variation about the mean value. Second, a less extensive treatment is provided regarding measures that refer to variation about the median value. The former set of measures are of greater interest in practical investigations since they are rigorously defined, easily calculated, and more readily amenable to algebraic treatment and to systematic analysis. Thus, the mean and its associated measures of variation are generally employed in situations where the variables may be considered to involve interval or ratio data. However, the use of the median and its measures of variation is preferred in some situations, where the data are essentially ordinal in nature or where outlying values may distort the location of the mean and spread of values recorded. Since statistics is the study of variation, it is not surprising that reference should be made in other entries in this Handbook to the analysis of variance (see Variance and Covariance, Analysis of) and to the procedures by means of which the variation in a set of data can be partitioned into different components that can be ascribed to different factors (see Multilevel Analysis). These different factors may be associated with treatment conditions, naturally occurring variation, or different sources of error. (J.P. Keeves) Full Reading ... PPT Download ...