Relax, you will probably never have to use it. It’s the equation for the Normal distribution. If it is, a z-test or a t-test would be in order. Then, you need to assess whether it’s safe to assume that the frequency distribution of the measurements is similar to a Normal distributed. These measurements need to be independent of each other and representative of the population. Meaningfulness is assessed by considering the difference detected by the test to what magnitude of difference would be important in reality.Īfter defining the population, the phenomena, and the test hypotheses, you measure the phenomenon on an appropriate number of individuals in the population. Significance refers to the result of a statistical test in which the null hypothesis is rejected. Effect size can be too small, leading to false negatives, or too large, leading to false positives. Effect size is influenced by the variance, the sample size, and the confidence. The smallest difference the test could have detected. For a t-test, the degrees of freedom is equal to the number of samples minus 1.
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The number of values in the final calculation of a statistic that are free to vary. Power is based on sample size, confidence, and population variance and is NOT set by the person doing the test, but instead, calculated after a significant test result. Power is the ability of a test to avoid false-negative errors (1-β).
Usually, an error rate of 0.05 (5%) is selected but sometimes 0.1 (10%) or 0.01 (1%) are used, corresponding to confidences of 95%, 90%, and 99%. The confidence is set by the person doing the test before testing as the maximum false-positive error rate they will accept. For nonparametric tests, this usually involves the median and range.Ĭonfidence is 1 minus the false-positive error rate. For F-tests in ANOVA, this involves the variance. For t-tests using the Normal distribution, this involves the mean and the standard deviation. Test parameters are the statistics used in the test. Parametric tests tend to be more powerful. Statistical tests can be based on a theoretical frequency distribution (parametric) or based on some imposed ordering (nonparametric). They also assume that errors are normally distributed and the variances of populations are equal. Statistical tests assume that the measurements of the phenomenon are independent (not correlated) and are representative of the population. They can also be nondirectional or one-sided (i.e., ц0), in which only one tail of the distribution is assessed. Null hypotheses can be non-directional or two-sided (i.e., ц=0), in which both tails of the distribution are assessed. If the distribution is different from the tails of a Normal distribution, the results of the test may be in error. Parametric statistical tests assume that the measurements are Normally distributed. These extreme measurements occur in the tails of the frequency distribution. Statistical tests examine chance occurrences of measurements on a phenomenon. If you do not reject the null hypothesis, you adopt the alternative hypothesis. You then create a null hypothesis that translates the research hypothesis into a mathematical statement that is the opposite of the research hypothesis, usually written in term of no change or no difference. The research hypothesis is about the differences between the categories of the variable representing the population. You start statistical comparisons with a research hypothesis of what you expect to find about the phenomenon in the population.
The sample size contributes to the determinations of the type of test to be used, the size of the difference that can be detected, the power of the test, and the meaningfulness of the results. The number of observations of the phenomenon used to characterize the population. The number of phenomenon determines whether a comparison will be a relatively simple univariate test or a complex multivariate test.Ī relatively small portion of all the possible measurements of the phenomenon on the population selected in such a way as to be a true depiction of the phenomenon. It is usually measured as a continuous-scale attribute of a representative sample of the population. The characteristic of the population being tested. The number of populations determines whether a comparison can be a relatively simple 1- or 2-population test or a complex ANOVA test. Populations must be definable and readily reproducible so that results can be applied to other situations. Groups of individuals or items having some fundamental commonalities relative to the phenomenon being tested. The importance of these concept are highlighted in the following table. Part 3 shows how those concepts play a role in conducting statistical tests. Parts 1 and 2 of Dare to Compare summarized fundamental topics about simple statistical comparisons.
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