# Assumptions

All statistical tests need to make various assumptions about your data when conducting the test. This is due to the algorithms at work assuming your data fits specific distributions, has equal variances and your replicates are independant of one another (not spatially autocorrelated). Any violations of these assumptions can cause the test to produce a false-positive, as an analysis of variance is sensitive to violations in the assumptions of normality and homogeneity of variance (also called homoscedasticity). These pages cover the basic ways to test these assumptions on your analysis of variance to ensure any statistical findings are correct and not confounded by violations in the basic assumptions.

### Content:

• Normality
• Normality can be tested in two basic ways. Through visual inspection of residuals in a normal quantile (QQ) plot and histogram, OR, through a mathematical test such as a shapiro-wilks test. To produce the two graphs for visual inspection of residuals we use the following commands: plot(weeds.aov, 2) # Normal quantile plot The normal qq plot should display the residuals along the dotted line in a straight manner. In this example, it is pretty straight :)

• Homogeneity of Variance
• Homogeneity of variance is the other main assumption we are concerned with when conducting an ANOVA. Homogeneity of variance is the assumption that the variance between groups is relatively even. That is to say, all groups have similar variation between them. Similar to the assumption of normality, there are two ways to test homogeneity, a visual inspection of residuals and a statistical test. To conduct a visual inspection of the residuals we simply use the following: