Compare your to α. Support or reject null hypothesis? If the is less, reject the null hypothesis. If the P-value is more, keep the null hypothesis.
This procedure of ANOVA through regression is actually using planned contrasts. When k=2, the omnibus and planned contrast tests are equivalent. However, when k;3, the contrast variables defined in the first step of this procedure provide opportunities to consider specific hypotheses concerning the treatment levels, or to further partition the explained variance. These contrast variables can be designed to test mean group differences, trend analyses, or other hypotheses of interest. To test the hypothesis of contrast i, compute
Would you reject the hypothesis H(0):MU = 69 versus the (one-sided) alternative H(1):MU > 69 on the basis of your observations, when testing at level ALPHA = .05?
Would you reject the hypothesis H(0):MU = 72 versus the alternative H(1):MU =/= 72 on the basis of the observations, when testing at level ALPHA = .05?
If you find yourself repeating lots of information about the experimental design when describing the data collection procedure(s), likely you can combine them and be more concise.
Compare your answer from step 4 with the α value given in the question. Should you support or reject the null hypothesis?
If step 7 is less than or equal to α, reject the null hypothesis, otherwise do not reject it.
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There are several ways to approach repeated measures analyses. Edwards (1985) presented two heuristic examples of repeated measures analysis performed through ANOVA and through regression. The following discussion will consider a one-way repeated measures design, but the concepts generalize to other designs. Table 1 represents a general data matrix for a one-way repeated measures design with n subjects and k treatments or repeated measures. Table 2 presents sample data from Edwards (1985). Tables 3 and 4 represent ANOVA summary tables for the general and example data matrices, respectively.
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Figure out the . The alternate hypothesis is the opposite of the null hypothesis. In other words, what happens if our experiment makes a difference?
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Though the benefits of repeated measures designs can be great, there are internal validity issues that must be addressed. "Carryover" effects are effects from one treatment that may extend into and affect the next treatment. They may be effects such as tracking memory over time or investigating practice or fatigue on a targeted behavior. However, carryover effects may be detrimental to a study, for example if a second drug treatment is administered without the previous drug passing out of the subject=s system (Edwards, 1985). This internal validity threat can be controlled through counterbalancing. By varying the presentation order of treatments, either randomly or systematically, interaction between treatment order and main effect can be investigated through data analysis (Huck & Cormier, 1996). However, even with couterbalancing, carryover effects can raise issues involving external validity.
Sometimes, you’ll be given a proportion of the population or a percentage and asked to support or reject null hypothesis. In this case you can’t compute a test value by calculating a (you need actual numbers for that), so we use a slightly different technique.