Using a Two-Way ANOVA for the Second Dependent Variable, and Assessing the Results of the Test

As for the impact of the independent variables on the variable measuring the days of delay, the dependent variable is quantitative, so the means for groups resulting from combinations of levels of the independent variables can be compared with a two-way ANOVA (Forthofer, Lee, & Hernandez, 2007). However, the claim of absence of statistically significant interaction between the variables might be doubted. Indeed, the mean for both interventions was nearly 90.33% of that for the outreach only; therefore, using both interventions decreased the mean roughly by 10% compared to the outreach only. (The mean for both interventions was nearly two times smaller than that for prompting only, so no comparison of interaction to prompting only is made; it is only needed to investigate whether prompting further improved the results of the outreach.) It seems that such a difference should be judged statistically significant, especially given the quite large sample sizes, for the latter tend to increase the statistical significance of results (Field, 2005, pp. 2-3). In fact, without knowing the effect size estimates or the standard deviations of the groups, it is hard to be sure if such a difference is large/important or not, and whether or not it should be deemed statistically significant (Coe, 2002, p. 2). Nevertheless, it still appears likely that the difference ought to be at least marginally significant (George & Mallery, 2016, p. 113) in this case.

Possible Problems Resulting From a Differential Loss of Participants

The differential loss of participants may adversely affect the results of the study by causing selection bias, which is “the constant divergence of a sample value… from the corresponding population value” (Forthofer et al., 2007, p. 139). If selection bias occurred, then the means of the compared groups might have changed, so the results of the test might have changed as well. However, the difference between the sample means might have become either larger or smaller, and it is not known which occurred. Finally, selection bias does not always result from differential loss (Carter, Imlach-Gunasekara, McKenzie, & Blakely, 2012), so it is possible that the differential loss did not influence the outcome considerably.

Conclusion

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Therefore, it was inappropriate to use a two-way ANOVA to test the influence of the independent variables on the variable reflecting the percentage of the immunized people, which was categorical; nevertheless, this test was appropriate for the dependent variable measuring the days of delay, which was quantitative. However, the claim that no statistical difference was found for the interaction of variables in the second case appears doubtful. It is also possible that due to the differential loss of the subjects, the sample statistics diverged from the population parameters, but it is not necessary that this occurred.

References

Carter, E. N., Imlach-Gunasekara, F., McKenzie, S. K., & Blakely, T. (2012). Differential loss of participants does not necessarily cause selection bias. Australian and New Zealand Journal of Public Health, 36(3), 218-222. Web.