Variance
Variance is a characteristic of a set of of data, or a series of answers. From a statistical perspective it is a measures of how cases are distributed within a range, of how much responses differ. If every case has the same value on some measure, then the variance is 0, otherwise there will be some level of variance. Variance is the sum of the squared differences between each score and the mean average of all scores.
V = [ ∑ ( Xi - MA)2 ]/
N
Where: V is variance,
Xi is each of the scores,
MA is the mean average, and
N is the number of scores.
There are other formulas that can be used to make the calculation in fewer steps, and there are specialized formulas for calculating an estimate of the population parameter when using samples drawn for a population. But since this is not a statistics course, we can leave all that for another day.
Standard deviation is the square root of variance. Many statistical processes use variance. Variance is frequently partitioned into that which can be be attributed to a specific condition and that which is assigned to other unmeasured conditions.
This division is frequently referred to as "explained variance" and "unexplained variance." The higher the explained variance relative to the total variance, the stronger a measure.Now we need to look at the "unexplained variance."
The unexplained variance can be further portioned into two parts. Some part of the unexplained variance is due to random, everyday, normal, free will differences in a population or sample. There is nothing we can do about it, and that's OK because among any aggregation of data these conditions equal out.
Then there is the variance that comes from some condition that has not be identified, but that is systematic. This variance, since it is consistent with some specific condition, introduces a bias.
When we examine cause and effect such a bias can lead to a false conclusion because it is not identified. For more information about this see the section on cause and effect.
The proportions of variance explained as compared with either the total variance or the portion of the variance unexplained are valuable tools in many statistics including regression, ANOVA, and t-tests
