Statistics for everyone: ch.8 ANCOVA

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ch.8 ANCOVA

Let’s call up the Burt data in the carData package. Let’s say you do an experiment that compares the results of IQfoster in three groups that have performed 3 different types of treatment. The ANOVA you learned earlier will come to mind first, but the IQfoster score is expected to be highly related to the IQbio score that each individual originally had before. Therefore, if these three groups were the same group with different IQbio scores in the first place, the results could affect their IQfoster scores. So let’s do ANCOVA in a controlled (considered, covariated, adjusted) method of controlling the difference in IQbio scores.

Select ANCOVA.

Specify each variable like this. If you specify only the above two variables, it will be ANOVA.

The relationship between the IQfoster score and the class as the result variable is not statistically significant (p = 0.05031). IQbio scores and IQfoster scores are statistically significant, but this is something we already know, and is not a topic of interest at ANCOVA.

The value of the p, which is also 0.444 for the work or interaction of the correspondence, has no statistical significance.

If you look at the picture, there is a lot to interpret. Overall, the center of blue (roughly average) is higher than the center of pink (roughly average). So if you just did it with ANAVO, blue would be rated a lot higher than pink. However, The blue IQbio is located further to the right, and as you can see from the slope of the bar, it gets higher as you go to the right. If it's not positioned right, let's move the blue bar slightly left and the pink bar slightly right (if we're modifying the right-shifted effect). At this time, it is not parallel movement, but it is moved to the extension line considering the inclination of the stick. This is the geometric meaning of ANCOVA. The blue bar moves to the lower left and the pink bar moves to the upper right, so the height difference between the two bars becomes smaller.

And the answer to the question of whether these straight lines are all parallel can be said to be an interaction.

Ignoring the effect of the disturbing variable IQbio is the figure on the right, and it just becomes ANOVA. Studies include expressions such as ‘IQbio adjusted’ or ‘IQbio was covariate.’