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One of the central goals of quantitative social science research is to establish relationships or associations between variables of interest as a means of providing empirical support for a theoretical proposition. Due to logistical constraints, researchers are usually unable to examine every single case in the population of interest and have to rely on a representative sample which is used to draw inferences about the population of interest. The adequacy of statistical inferences depends to a large extent on the representativeness of the sample.
Due to the necessity to work with samples rather than populations, tests of statistical significance, otherwise termed hypothesis testing or inferential statistics, are extremely important for dealing with the possibility that relationships derived from a sample data are based on chance. The goal of statistical inference is to be able to infer something about the truth of a hypothesis without collecting data from the entire population.
In hypothesis testing, the statistical hypothesis identifies an assumed value or relationship about a population — null hypothesis — which is assumed true until the sample data provide contradictory evidence. The null is rejected if an event can be shown to be highly unlikely to occur if the hypothesis is assumed true and the alternative hypothesis is affirmed. That is, if the sample result is contrary to what is expected when the hypothesis is assumed true, then the null hypothesis is rejected as a possibility.
The alternative hypothesis can be stated as a one-tailed or two-tailed test. If the researcher is unsure about the direction of the difference between and sample statistic and population parameter, then a 2-tailed test is specified. In this case, the researcher is most interested in whether there is difference between the sample and population but not the direction of the difference. In a 1-tailed test, on the other hand, the researcher can explicitly state whether the sample statistic is expected to be greater or smaller than the population parameter.
The decision to reject the null hypothesis in favor of an alternative hypothesis depends on the alpha level which is chosen prior to data analysis. For example, if the difference between the sample statistic and the hypothesized parameter is due to random chance, fewer than 5 times in 100 (i.e., a < 0.05, or a 5 percent level of significance), then the results are deemed statistically significant. As decisions based on probabilities will not be correct 100 percent of the time, it is always possible that an error has been made in the statistical inference resulting from the decision on whether to reject null hypothesis.
- Levin, J. & Fox, J. A. (2007). Elementary Statistics in Social Research, 10th edn. Allyn & Bacon, Needham Heights, MA.
- Healey, J. F. & Prus, S. (2009). Statistics: A Tool for Social Research, 1st Canadian edn. Nelson, Toronto.