Assumptions

In general terms, an assumption is something taken for granted or accepted as true without proof [1]. In statistics, an assumption is an underlying truth that affects the interpretation of data. In terms of data related to public policy, most often statistical assumptions are general assumptions about statistical populations. For example:
  • Data collected from a subset of a population cannot be considered representative of that population unless the subset of the population from which the data were gathered is a random sample of that population. For example, sometimes an opinion poll is given to the readers of particular magazine. The statistics developed from that opinion poll represent only the viewpoints of the readers of the magazine who chose to take the poll, not the entire population that has access to the magazine, or even the entire pool of readers of that magazine.

  • When a statistic is created from collected data (for example, the average salary of adult males in the European Union), a confidence interval is usually included in order to provide the reader with an understanding of the margin of error for that statistic. The confidence interval is typically found by multiplying the calculated standard error for the statistic by a constant determined by the level of confidence desired (e.g., for a 95% confidence interval that constant is 1.96). The statistical assumption made when such a confidence interval is calculated is that the data used to create the statistic have a relatively symmetric distribution. The more skew the distribution of the underlying data has, the less valid the statistical assumption of symmetry becomes and the less valid the confidence interval is.
The important lesson is that if the statistical assumptions underlying an analysis are wrong, that analysis may not be valid. Common causes of violations of statistical assumptions include bias, methodology errors, lack of random assignment in the design of an experiment, and lack of random sampling for a survey.

Further information on assumptions can be obtained as follows:

1. From www.thefreedictionary.com/assumption (19 December 2006).

2. Sources for this encyclopedia entry include Wikipedia (accessed 19 December 2006) [disclaimer]; and Helberg, Clay, "Pitfalls of data analysis," from Practical Assessment, Research & Evaluation (1996) and obtained from http://PAREonline.net/getvn.asp?v=5&n=5 (accessed 19 December 2006).