Statistical notes for clinical researchers: Two-way analysis of variance (ANOVA)-exploring possible interaction between factors

When we have a continuous outcome e.g., bonding strength and two categorical explanatory variables such as 4 different resin types and 2 different curing light sources, usually we consider applying the two-way ANOVA for analyzing the relationships. However because implementing the two-way ANOVA is relatively complicated, some clinical researchers prefer to apply the one-way ANOVA for one factor on each level of the other factor, repeatedly. They often insist that they are interested only in one factor (e.g., manipulation methods) and are not interested in the other factor (e.g., brands), claiming that the one-way ANOVA is the more appropriate strategy. Even though the trial with a variety of brands may be considered as a simple way of generalization among various brand types, possible different effects of materials of different brands can never be detected by the one-way ANOVA. Actually materials of different brands may have slightly different ingredient compositions which may elicit different effects on the other factor. Application of the one-way ANOVA cannot detect the possible interaction between two explanatory categories. Table 1 shows a data of bonding strength of four types of resin (A, B, C and D) on the teeth surface with a simultaneous use of two different curing light sources (Halogen, LED). The highest overall bonding strength is found on resin D followed by resin C and resin B showing insignificant differences (see the superscript a, b, and c). Considering cases using the 'Halogen,' resin D is the strongest among four resin types, while resin C shows the highest value when the 'LED' was used. This explicitly shows that the effects of different resin types are not following a similar trend according to different levels of curing methods, 'Halogen' or 'LED'. Figure 1a shows that trend of (descriptive) mean bonding strengths for resin types are changing according to the levels of curing methods. Figure 1 Graphs for bonding strength by resin materials (A, B, C, and D) displayed as separated lines of different curing light sources (Halogen (b) Estimated means by the model with the interaction term; (c) Estimated means ... Table 1 Measurements of bonding strength (Mpa) according to four different types of resin and two curing methods