How would you explain the analysis of variance?
It is a calculation that defines the amount of randomness in a set of data.
“Variance” is the observed deviation from an expected value. All measurement have variance from a variety of sources. In statistics the main concern is to identify causal relationships by the degree to which observed data “varies” from the distribution of values expected from a “normal” occurrence.
We see variations, or “variance” in everything! So, how can we tell whether a variation signifies a possible causality or not? The Analysis of Variance (ANOVA) gives us one important clue, although many users abuse its intent horribly!
The use is in showing that while variations are observed, they are really not of significant quantity or value in assigning a causative relationship to two events. The abuse comes when the probability of significance is mistaken for an empirical degree of connection.
It is VERY important to understand and use Levels of Confidence in conjunction with ANOVA to avoid being misled by our own biases into wishful results.