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Eliminate ambiguous or non-significant zeros by using Scientific Notation: For example, 1300 with three significant figures becomes 1.30 × 10 3. Likewise 0.0123 can be rewritten as 1.23 × 10 −2. The part of the representation that contains the significant figures (1.30 or 1.23) is known as the significand or mantissa.
Although the 30 samples were all simulated under the null, one of the resulting p-values is small enough to produce a false rejection at the typical level 0.05 in the absence of correction. Multiple comparisons arise when a statistical analysis involves multiple simultaneous statistical tests, each of which has a potential to produce a "discovery".
A probability sample is a sample in which every unit in the population has a chance (greater than zero) of being selected in the sample, and this probability can be accurately determined. The combination of these traits makes it possible to produce unbiased estimates of population totals, by weighting sampled units according to their ...
The sample extrema can be used for a simple normality test, specifically of kurtosis: one computes the t-statistic of the sample maximum and minimum (subtracts sample mean and divides by the sample standard deviation), and if they are unusually large for the sample size (as per the three sigma rule and table therein, or more precisely a Student ...
The sample size is an important feature of any empirical study in which the goal is to make inferences about a population from a sample. In practice, the sample size used in a study is usually determined based on the cost, time, or convenience of collecting the data, and the need for it to offer sufficient statistical power. In complex studies ...
Researchers focusing solely on whether their results are statistically significant might report findings that are not substantive [46] and not replicable. [47] [48] There is also a difference between statistical significance and practical significance. A study that is found to be statistically significant may not necessarily be practically ...
The term "Z-test" is often used to refer specifically to the one-sample location test comparing the mean of a set of measurements to a given constant when the sample variance is known. For example, if the observed data X 1 , ..., X n are (i) independent, (ii) have a common mean μ, and (iii) have a common variance σ 2 , then the sample average ...
The sample standard deviations for the two samples are approximately 0.05 and 0.11, respectively. For such small samples, a test of equality between the two population variances would not be very powerful. Since the sample sizes are equal, the two forms of the two-sample t-test will perform similarly in this example.