Repeated-measures ANOVA is quite sensitive to violations of the assumption of circularity. It is closely related to another term you may encounter, compound symmetry. This assumption is called circularity or sphericity. A random factor that causes a measurement in one subject to be a bit high (or low) should have no affect on the next measurement in the same subject. Repeated-measures ANOVA assumes that the random error truly is random. Can you accept the assumption of circularity or sphericity? But it assumes the factor that defines which column each value is entered into is fixed. This model assumes the differences among subjects (or litters.) is random. WIth repeated measures, Prism can fit a mixed effects model. Type II random-effects ANOVA is rarely used, and Prism does not perform it. Type II ANOVA, also known as random-effect ANOVA, assumes that you have randomly selected groups from an infinite (or at least large) number of possible groups, and that you want to reach conclusions about differences among ALL the groups, even the ones you didn't include in this experiment. This tests for differences among the means of the particular groups you have collected data from. Prism performs Type I ANOVA, also known as fixed-effect ANOVA. Is the factor “fixed” rather than “random”? These data need to be analyzed by two-way ANOVA, also called two-factor ANOVA. Similarly, there are two factors if you wish to compare the effect of drug treatment at several time points. There are two factors in that experiment: drug treatment and gender. For example, you might compare three different drugs in men and women. Some experiments involve more than one factor. Or you might compare a control group with five different drug treatments.
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For example, you might compare a control group, with a drug treatment group and a group treated with drug plus antagonist. One-way ANOVA compares three or more groups defined by one factor. Prism does not test for violations of this assumption. While this assumption is not too important with large samples, it can be important with small sample sizes. Furthermore, it assumes that the random component follows a Gaussian distribution and that the standard deviation does not vary between individuals (rows) or treatments (columns). Repeated-measures ANOVA assumes that each measurement is the sum of an overall mean, a treatment effect (the average difference between subjects given a particular treatment and the overall mean), an individual effect (the average difference between measurements made in a certain subject and the overall mean) and a random component. Is the random variability distributed according to a Gaussian distribution? Since this factor would affect data in two (but not all) rows, the rows (subjects) are not independent. In this case, some factor may affect the measurements from one animal. For example, the errors are not independent if you have six rows of data, but these were obtained from three animals, with duplicate measurements in each animal. You must think about the experimental design. The results of repeated-measures ANOVA only make sense when the subjects are independent. Ideally, your choice of whether to use a repeated-measures test should be based not only on this one P value, but also on the experimental design and the results you have seen in other similar experiments. If the P value for matching is large (say larger than 0.05), you should question whether it made sense to use a repeated-measures test. Prism tests the effectiveness of matching with an F test (distinct from the main F test of differences between columns). The matching should be part of the experimental design and not something you do after collecting data. By analyzing only the differences, therefore, a matched test controls for some of the sources of scatter. Some factors you don't control in the experiment will affect all the measurements from one subject equally, so will not affect the difference between the measurements in that subject. The whole point of using a repeated-measures test is to control for experimental variability. Read elsewhere to learn about choosing a test, and interpreting the results. Repeated measures one-way ANOVA compares the means of three or more matched groups.