Illustration of Doubly MANOVA
A researcher is interested in improving reading skills of elementary school children. There are two traditional reading programs used in the schools: (1) traditional reading comprehension and (2) traditional reading comprehension + phonemic awareness. The researcher believes a new type of reading curriculum that includes traditional reading comprehension + phonemic awareness + segmentation would be a much better method of teaching reading.
The researcher randomly assigns students into one of three
1. traditional reading comprehension
2. traditional reading comprehension + phonemic awareness
3. traditional reading comprehension + phonemic awareness + segmentation
The researcher measures (a) reading skills and (b) reading motivation level across three time periods: (1) at the beginning and (2) end of the academic year and at the (3) beginning of the next year (after the summer vacation).
A doubly-multivariate analysis of variance was performed on reading skills and motivation to read over three time periods. Type of reading curriculum was the between subjects factor: (a) traditional reading comprehension, (b) traditional reading comprehension + phonemic awareness, and (c) traditional reading comprehension + phonemic awareness + segmentation. The within subjects factor was time periods: (a) at the beginning and (b) end of the academic year and at the (c) beginning of the next year (after the summer vacation). The sample size for each group was 6. No data were missing and no outliers were found. Cell means and standards deviations for the two DVs across all time periods are reported in Table 1 (see above).
The type of reading curriculum by time period interaction was statistically significant F(8, 24) = 3.35, p =.01, partial η2 = .52. There was also a statistically significant within subjects effect for time F(8, 12) = 16.98, p <.001, partial η2 = .85. There was not a statistically significant between subjects effect F(4, 28) = 1.46, p =.25, partial η2 = .17.
[For the class, you can simply follow up with univariate results using Bonferroni corrections. There are much better methods of conducting follow up procedures; for example, Roy-Bargmann Stepdown and trend analysis, or even simple contrast. These follow up procedures need to be planned a priori.]
Two follow up univariate mixed ANOVAs, one for each dependent variable, were calculated and a Bonerroni correction was used (ά=.025) . For reading skills, univariate mix ANOVA results indicated that there was not a statistically significant interaction effect, F(4, 9) = .78, p =.57, partial η2 = .09, but there was a significant within subjects effect for reading skills F(2, 227) = 318.71, p <.001, partial η2 = .82. There was not a significant differences between subjects effect, F(2, 6) = .74. Results of Helmert [look under the contrast option] contrast indicated that the reading skills mean was significantly lower than those of both the post and follow up reading skills means (F=37.73, p<.001, partial η2 = .09).
For motivation, mix ANOVA results indicated that there was a statistically significant interaction effect, F(4, 12) = 10.07, p <.001, partial η2 = .57. There was also a significant within subjects effect, F(2, 12) = 31.90, p <.001, partial η2 = .68. There was not a significant differences between subjects effect, F(2, 15) = 2.65, p=.10), partial η2 = .61. An illustration of the interaction is provided in the figure below. Simple effects across the three time periods were examined. There was not a statistically significant differences between the treatment groups for the first two time periods, but there was a significant difference between the groups at the third time period (return after summer vacation), F (2, 15)=10.86, p=.001. Group 2 (traditional and phonemic awareness) was significantly higher than group 1 (traditional).
There did not appear to be any differences in reading skills among the three different reading methods. The results suggest that group 2 reading methods (traditional + phonemic) were more motivated after summer vacation. The researchers new reading method (group 3) does not appear to demonstrate any improvement over the other reading methods.