When more than two populations are given and we have to test the equality of means of these populations, we use analysis of variance. In analysis of variance populations are considered to be independent and samples are chosen randomly from these populations. There are three types of analysis of variance including randomize complete design, complete randomize block design and Latin square design. When more than one independent variable is involved in the testing, we use complete randomize block design and Latin square design. CRBD is used for two independent variables and LSD is used for three independent variables. Moreover, complete randomize block design and Latin square design are also known as two way classification and three way classification respectively.
An important point about the use of ANOVA with two or more independent variables is given by the fact that you can combine the analysis into one. Suppose I obtained the mean test scores for fifteen participants under different room temperatures and different humidity levels. The data is given in the table below. Room Temperature
Humidity Level
70 degrees
80 degrees
90 degrees
Low Humidity
Scores for 15 participants who are tested in a 70 degree room with low humidity
Scores for 15 participants who are tested in a 80 degree room with low humidity
Scores for 15 participants who are tested in a 90 degree room with low humidity
High Humidity
Scores for 15 participants who are tested in a 70 degree room with high humidity
Scores for 15 participants who are tested in a 80 degree room with high humidity
Scores for 15 participants who are tested in a 90 degree room with high humidity
For the preceding data, I can test three hypotheses about the populations from which the samples were obtained.
1. I can test the mean differences between the scores by humidity levels.
2. I can test the mean differences between the scores by room temperatures.
3. I can test the mean differences between the scores by the combinations of all humidity levels and room temperatures.
The test of the preceding will provide independent pieces of information about the differences by humidity levels, by temperature and both by temperature and humidity levels. For the preceding example, I would still need to conduct a posttest by temperature to examine pair-wise difference.
