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Assumptions behind hypothesis tests

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					Assumptions Behind Hypothesis Tests
Test                Type of data                        Assumptions & Non-directional Null
One-sample Z        Quantitative – one variable         Known mean and SD for null hypothesis;
                                                        adequate sample size to meet central limit
                                                        theorem
                                                                          H0: 1 = null
One-sample t         Quantitative – one variable        Known mean for null hypothesis; adequate
                                                        sample size to meet central limit theorem
                                                        (estimate SD from sample)
                                                                          H0: 1 = null
One-way 2           Qualitative – one variable         Known pattern of proportions for null
                                                        hypothesis; adequate sample size to make
                                                        minimum expected frequency of 5 per cell
                                                             H0: a1 = anull ; b1 = bnull ; c1 = cnull
Two-way 2           Qualitative – two variables        Adequate sample size to make minimum
                     Note: can have two DVs (like       expected frequency of 5 per cell
                     a qualitative correlation) or        H0: the two variables are independent / not-
                     one IV and one DV (like a                        related to each other
                     qualitative independent t)
Dependent t          Quantitative – same variable       Known mean for null hypothesis; adequate
(two-dependent       measured twice (same person        sample size (of difference scores) to meet
samples)             measured under two conditions      central limit theorem; Note null hypothesis is
                     or matched subjects measured       about the mean difference score
                     under different conditions)                          H0: diff = 0
                     Note: this test is like a one-
                     sample t-test conducted on a
                     sample of difference scores
Independent t        Quantitative (DV) and              Known mean for null hypothesis; adequate
(two independent     Qualitative (true IV or            sample size to meet central limit theorem;
samples)             grouping variable) with only       Note null hypothesis is a about the difference
                     two possible values for the        between two independent sample means
                     qualitative variable                    H0: 1 = 2 or H0: (1 - 2) = 0
One-way F            Quantitative (DV) and              Known mean for null hypothesis; adequate
(ANOVA)              Qualitative (true IV or            sample size to meet central limit theorem;
                     grouping variable) with three      Note null hypothesis is about the difference
                     or more possible values for the    between a set of independent sample means
                     qualitative variable. Note: this              H0: 1 = 2 = 4 = 4 …
                     test is an extension of the
                     independent t-test to compare
                     3 or more groups.
Correlation          Quantitative – two variables       Both variables are reasonably normally
(Pearson r)                                             distributed, the relationship between them is
                                                        linear and homoscedastic, the range of both
                                                        variables is appropriate to the research
                                                        question
                                                                            H0:  = 0

				
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