Anova assumes which of the following

The variability within each group is represented by the vertical size of each box; i. The boxplot shows that the variability is roughly equal for each group.

This plot shows the residuals errors on the y-axis and the fitted values predicted values on the x-axis. If the variance of each group is equal, the plot should show no pattern; in other words, the points should look like a cloud of random points.

The plot shows that the variances are approximately homogenous since the residuals are distributed approximately equally above and below zero. If the red line is flat, then the relationship between the independent and dependent variables is linear. However, linearity is not an assumption of ANOVA so it will not be discussed here but it will be discussed in the linear regression tutorial. Another way we could have constructed the previous plot is to manually extract the residuals and the fitted values from the ANOVA result and plot them.

We can then plot them like so:. This time we will divide each residual by its standard deviation; that is, each residual is made to have a standard deviation of 1.

The standard deviation for residuals can vary a great deal from observation to observation so it is a good idea to standardise the residuals in order to allow easier comparisons. Standardised residuals are just scaled versions of the unstandardised residuals - and thus contain all the same information - so generally there is no reason to use unstandardised residuals in a diagnostic plot.

That is, values more than 2. However, this is just a rule of thumb. Can you provide the following information? Describe the scenario that you are looking at. Include the nature of the data. What hypotheses are you trying to test? How small depends on a number of things. I have non-normal data that I would have liked to analyze using a 2-way repeated measure ANOVA two groups with measurements at 2 time points.

I tried transformation sqrt, ln, log, box-cox , and data stay non-normal. What do you suggest? Also, my sample size is small, 15 per group. Is this true? Thank you!! This is much like the rule of thumb for equal variances for the test for independent means.

If the ratio of these two sample standard deviations falls within 0. Recall the application from the beginning of the lesson. We wanted to see whether the tar contents in milligrams for three different brands of cigarettes were different. Check the assumptions for this example. The smallest standard deviation is 0. The largest standard deviation is less than this value. Since the sample sizes are the same, it is safe to assume the standard deviations and thus the variances are equal.

The sample size is small.