Data Analysis: Parametric inferential tests will be preferred over non-parametric tests, unless data deviate strongly from assumptions of parametric procedure

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Data Analysis: Parametric inferential tests will be preferred over non-parametric tests, unless data deviate strongly from assumptions of parametric procedure. [Parametric tests are based on assumptions about the distribution of the underlying population from which the sample was taken. The most common parametric assumption is that data are approximately normally distributed.] Inferential analysis will be univariate (one predictor variable and one outcome variable). Inferential tests designed to assess groups that are unmatched/independent will be used. NB. Data are to be reviewed to make sure they meet the parametric and individual assumptions made by each statistical test. If determined that assumptions of the parametric procedure are not valid, use an analogous nonparametric procedure instead. [The reason we do statistics is to make inferences from samples to populations. To do this we have to assume that the populations have certain properties so that the theoretical statistical models we adopt are appropriate for making these kinds of inferences.] Assumptions of Confidence intervals:


Assumptions of one-way ANOVA for independent samples: 1. Scale on which the dependent variable is measured has the properties of an equal interval scale. 2. Group samples are independently and randomly drawn from the source population(s). 3. Source population(s) can be reasonably supposed to have a normal distribution. 4. Group samples have approximately equal variances. NB. Normal Distribution defined, explained, and method to determine provided: The Normal Distribution The Normal Distribution is a mathematical function that defines the distribution of scores in population with respect to two population parameters. The first parameter is the Greek letter ( , mu). This represents the population mean. The second parameter is the Greek letter ( , sigma) which represents the population standard deviation (the standard deviation is equal to the square root of the variance, so the variance is represented as ). Different normal distributions are generated whenever the population mean or the population standard deviation are different. Hint: Most of the time that Greek letters are used to refer to means, standard deviations and variances they are referring to populations, not samples. Above: ANOVA assumes that the populations tested have the same variance. ANOVA tests to see if the central tendency (mean) difference between samples (middle diagram).