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Given that the validity of any conclusion drawn from a statistical inference depends on the validity of the assumptions made, it is clearly important that those assumptions should be reviewed at some stage. Some instances—for example where data are lacking—may require that researchers judge whether an assumption is reasonable. Researchers ...
Assumptions, parametric and non-parametric: There are two groups of statistical tests, parametric and non-parametric. The choice between these two groups needs to be justified. The choice between these two groups needs to be justified.
For example, the angular momentum of the universe is zero. If not true, the theory of the early universe may need revision. Null hypotheses of homogeneity are used to verify that multiple experiments are producing consistent results. For example, the effect of a medication on the elderly is consistent with that of the general adult population.
For example, a new technology or theory might make the necessary experiments feasible. Scientific hypothesis A trial solution to a problem is commonly referred to as a hypothesis—or, often, as an " educated guess " [ 14 ] [ 2 ] —because it provides a suggested outcome based on the evidence.
Informally, a statistical model can be thought of as a statistical assumption (or set of statistical assumptions) with a certain property: that the assumption allows us to calculate the probability of any event. As an example, consider a pair of ordinary six-sided dice. We will study two different statistical assumptions about the dice.
However, as either the sample size or the number of cells increases, "the power curves seem to converge to that based on the normal distribution". Tiku (1971) found that "the non-normal theory power of F is found to differ from the normal theory power by a correction term which decreases sharply with increasing sample size."
Most two-sample t-tests are robust to all but large deviations from the assumptions. [ 22 ] For exactness , the t -test and Z -test require normality of the sample means, and the t -test additionally requires that the sample variance follows a scaled χ 2 distribution , and that the sample mean and sample variance be statistically independent .
For example, suppose the treatment is passing an exam, where a grade of 50% is required. In this case, this example is a valid regression discontinuity design so long as grades are somewhat random, due either to the randomness of grading or randomness of student performance.