ANOVA and MANOVA in Dissertation & Thesis Research
In dissertation or thesis research, an analysis of variance (ANOVA) is an inferential statistic used to analyze data from an experiment that has either multiple factors or more than two levels of the independent variable. In dissertation data, the value of any score on a variable may be due to one or more of these three factors: your independent variable, the individual differences of your subjects, and experimental error. Within even the best-designed experiments, scores on a measure will vary because your subjects are different from one another. Measurement error, too, will vary, even if all your subjects are exposed to the same treatment conditions.
Determining Statistical Significance with ANOVA
Total variability in experiment scores can be split into "between-groups" and "within groups" variability. Between-groups variability in research may be caused by the variation in your independent variable, individual differences in your subjects, experimental error, or a combination of any of these. Within-groups variability in research is often referred to as random or error variance. This variability is caused by individual differences between subjects that are treated alike within groups and/or experimental error.
The ANOVA statistic uses an F-ratio to determine the statistical significance of your results. The F-ratio is simply the ratio of your between-groups variability to your within-groups variability. Once you have obtained your F-ratio, you just compare it to a table of critical values in any statistics book to determine the statistical significance of your results. Even better, most statistical software packages will provide the p-value for you, so based on your dissertation's preset alpha level, you can determine at a glance whether your results are significant!
A one-factor between-subjects ANOVA is used when your research involves only one factor with more than two levels and different subjects in each of your experimental conditions. For example, say your question asks how much light a subject needs to read a sentence out of a book with 12-point font. You have three experimental conditions. One group of subjects is to read the sentence in a room with no light at all. Another group of subjects is to read the sentence in a room with a tealight candle 4 feet away. The third group of subjects is asked to read the sentence in a room with a 60-watt light bulb placed 4 feet away.
After collecting the data, you run an analysis using an ANOVA and find that your F-ratio has a p-value of .03. As you have set your alpha level at .05, this result is significant! However, this only supports your hypothesis that light is better than no light. For meaningful findings, you must see if your experimental manipulations were significantly different from each other.
To do this, comparisons must be made between your experimental conditions. These comparisons can be planned in advance or unplanned. After the ANOVA analysis, you would run a t-test for each pair of means for your three groups. Doing this, you may find that there is a big difference in the ability to read the sentence between the subjects who were in a dark room versus the subjects who were in the room with the 60-watt light bulb, but no difference between the subjects who were in the room with a tealight and those subjects who were in the room with the 60-watt lightbulb. The third possible comparison between groups is not needed, because you can safely assume that there is a big difference in the ability to read the sentence between the group in a dark room and the subjects who had a tealight.
Determining Statistical Significance with MANOVA
Let's say that your research involves an independent variable with more than one level, and your dissertation is using more than one dependent variable. In this case, your analysis would most likely use a multivariate analysis of variance, a MANOVA statistic. In dissertation research, the MANOVA statistic tests whether the mean differences between your groups on a combination of your dependent variables are likely to have happened by chance. Just as is the case for the ANOVA, a MANOVA tests the means by comparing the variances.
Continuing with the previous example, let's say that your dissertation had different levels of light for the independent variable, but you wanted to see whether the subjects in each experimental condition could tell the difference between red and green circles and determine the number of dots on a page 6 feet away. You still have one independent variable, but now your dissertation examines three dependent variables.
MANOVA vs. ANOVA
A dissertation using a MANOVA is better than a dissertation using an ANOVA in some ways. First, since your dissertation is looking at several dependent variables, you have a better chance of figuring out what it is that changes as your independent variable changes. For example, does your subjects' spatial perception improve with minimal light but not subjects' color perception? This question is best answered with a MANOVA. Secondly, a dissertation that uses a MANOVA is better than a dissertation that uses a series of ANOVAs in that it protects against a higher likelihood of committing a Type I error in your dissertation.