Final answer:
The one-group, posttest only research design involves measuring outcomes after a group experiences an intervention. In the provided scenario of evaluating a new math textbook, the groups are matched, not independent, as it involves the same students at different times.
Step-by-step explanation:
Understanding One-Group, Posttest Only Research Design Function
The one-group, posttest only research design function is commonly utilized in scenarios where a group of individuals is exposed to a certain condition or treatment, and then measured for outcomes after the completion of the intervention. In the context of investigating the effectiveness of a new math textbook for high school students, such research design would involve administering a posttest at the end of the year's instruction to gauge academic progress. If one were to administer both a pretest at the beginning and a posttest at the end of the year, it would be a pretest-posttest design rather than a posttest only design. Given this approach, the groups in the study would be considered matched as the same students who took the pretest are being compared after taking the posttest.
When we talk about one-way ANOVA, the aim is to see if there is a statistically significant difference between group means. For this test to be valid, the groups must be independent and meet additional assumptions such as normality and equal variances among populations. However, in the described scenario where a pretest and posttest are involved, the study design would not align with independent groups required for one-way ANOVA since it compares the same group of students at two different points in time.
Experimental design and ethics are critical in ensuring that the research data is reliable and that the only difference between treatment groups is the one imposed by the researcher. Therefore, in a well-designed study, any difference observed between treatment groups should be attributable to the effect of the explanatory variable. This is essential for the integrity and validity of the research outcomes.