Day 49 – Introduction to ANOVA

Parametric tests have common operations:

  • Calculations on interval data
  • Ratios of variance (predicted variance divided by total variance)
  • Calculations of variance (squaring scores and summing the squares in different ways)


Sources of variance

There are two sources of variance in ANOVA: between-conditions variance (i.e. predicted variance) and error variance (i.e. variance due to unpredicted variables). Between-condition variance plus error variance make up the total variance. In ANOVA, test of significance are based on the ratio of variance.


Degrees of freedom

The importance of df in parametric tests come from the idea that parametric tests calculate variance based on variability in scores. It is considered essential that all scores can vary “freely”. See below:

Participants Scores
1 12
2 13
3 10
4 11
5 14
6 ??
 –  –
Total 75


We can calculate Participant 6’s score by substracting the a) total score (75) from the b) other 5 participants’ scores (60). This give us 15 as the score of Participant 6. The idea is that Participant 6 score is “pre-determined” from a and b. Since it is predetermined, it has no “freedom” to vary. Df take this into account and removes this predetermined participant in the following way: N (number of participants) – 1. In our case, this means that only the scores of the 5 participants can vary.

The use of ANOVA requires us to fulfill 3 requirements:

  • Measurement of the data: data type must be interval.
  • Data should be normally distributed.
  • Homogeneity of variance: the variability of the scores in every condition should be similar.



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