A research question that can be addressed by a two-way factorial ANOVA is as follows: Is there an interaction between a person’s gender and their level of education that results in differences in the levels of depression between different groups?
A factorial ANOVA would be an appropriate analytical method for this research question because it allows for comparing the means of different groups into which the sample is split by several independent variables (two variables, in this case), as well as by combinations of levels of these independent variables (Warner, 2013).
There will be two predictor variables. The first one, gender, will be nominal, will describe a participant’s gender, and will have two levels (e.g., 1 = male, 2 = female). The second one, education, will be ordinal and will reflect the level of education one has attained. It can have four levels:
- no high school diploma;
- a high school diploma, no college;
- a high school diploma and some college, no college degree;
- at least an undergraduate degree.
The outcome variable will assess the levels of depression. It needs to be quantitative (Warner, 2013). Its values can range, for instance, from 0 (no depression) to 100 (extremely high level of depression).
The null hypothesis for the first main effect will state that there is no statistically significant difference in the levels of depression between different gender groups. The null hypothesis for the second main effect will assert that there are no statistically significant differences in the levels of depression between different education groups. The null hypothesis for the interaction will state that there are no statistically significant differences in the levels of depression between different gender × education groups.
It is expected that females will have more severe depression than males (Parker & Brotchie, 2010); that people with higher levels of education will have lower levels of depression than those with lower levels of education (Bjelland et al., 2008); and that males with the highest levels of education will have the lowest levels of depression.
A question that can be addressed by a one-way repeated measures ANOVA is as follows: Does a psychological intervention aimed at lowering levels of depression has a significant, long-lasting effect?
The within-subject factor will be the time. The levels of this variable may be as follows: 1 = one day before the beginning of the intervention, 2 = one day after the end of the intervention, 3 = one month after the end of the intervention, 4 = three months after the end of the intervention.
The outcome variable will be the levels of depression of participants. It needs to be measured using a quantitative variable (Warner, 2013). It is possible to use e.g. a scale ranging from 0 to 100, where 0 indicates no signs of depression in a participant, and 100 reflects an extremely high level of depression.
It is expected that the levels of depression will be the highest one day after the end of the intervention, then they will become lower one month after the end of the intervention, and then will go down, even more, three months after the end of the intervention. However, it is also expected that the levels of depression as measured three months after the end of the intervention will be lower than those identified one day before the beginning of the intervention.
A one-way repeated measures ANOVA will be appropriate for such a research question because this test allows for comparing the means of a variable of the same sample when these means were measured in different situations (Field, 2013). In this example, the means of the same variable (levels of depression) will be measured in different situations (according to their temporal disposition concerning the psychological intervention) to assess whether the intervention had a long-lasting effect.
References
Field, A. (2013). Discovering statistics using IBM SPSS Statistics (4th ed.). Thousand Oaks, CA: SAGE Publications.
Warner, R. M. (2013). Applied statistics: From bivariate through multivariate techniques (2nd ed.). Thousand Oaks, CA: SAGE Publications.
Bjelland, I., Krokstad, S., Mykletun, A., Dahl, A. A., Tell, G. S., & Tambs, K. (2008). Does a higher educational level protect against anxiety and depression? The HUNT study. Social Science & Medicine, 66(6), 1334-1345. Web.
Parker, G., & Brotchie, H. (2010). Gender differences in depression. International Review of Psychiatry, 22(5), 429-436.
Warner, R. M. (2013). Applied statistics: From bivariate through multivariate techniques (2nd ed.). Thousand Oaks, CA: SAGE Publications.