 # PSY 2060- Week 8 Project ANOVA and Repeated Measure ANOVA Designs

Aug 25, 2023

Use Online Resources to find two peer-reviewed articles in which the authors used ANOVA designs and two peer-reviewed articles in which the authors used repeated measures ANOVA designs. Summarize each article and evaluate whether the design used was logical. Explain your reasoning. Do you think that the design influenced the statistical significance observed? Why or why not? Could this influence the validity of the work?

#### Week 8 Project ANOVA and Repeated Measure ANOVA Designs

The statistical test known as ANOVA, or Analysis of Variance, is used to examine how the means of different groups differ from one another. In contrast to a two-way ANOVA, which employs two independent variables, a one-way ANOVA only uses one independent variable. ANOVA is frequently used to compare variation across groups against variance within groups to assess the equality of various means (random error).

ANOVA was created by Sir Ronald Fisher as a pioneering tool for examining the outcomes of agricultural experimentation. Researchers in all experimental sciences can use ANOVA because it is now available in practically every statistical software. It is simple and clear to enter a data set and do a basic ANOVA, but it might be difficult to select the best ANOVA for various experimental designs, check that the data correspond to the assumptions of the model, and accurately interpret the findings. This study, along with the following two pieces in the Statistical Primer for Cardiovascular Research series, aims to improve knowledge of ANVOA and encourage its successful application in experimental cardiovascular research (Siregar et al. 2019,335).  Along with limiting the weight of notation, technical speak, and mathematical equations within reasonable bounds, I and my partners try to achieve those aims through examples and explanations.

We can compare the means of multiple independent samples at once using the first model, a one-way fixed-effects ANOVA, which is an extension of the Student 2-independent-samples T-test. The second model, a two-way fixed-effects ANOVA, contains 2 components, A and B, and each level of factor A co-occurs with each level of factor B. With the use of this model, we can compare the means between levels of factor A and factor B. In addition, we can check to see if the combined impacts of the components have a positive or negative impact on the response.

In the second ANOVA article, the author discusses several multiple-comparison to concludetoconcludemultiple-comparison to conclude techniques for analyzing differences between means, including contrasts between the means of two groups and broader contrasts between group means. Multiple-comparison techniques are frequently used to regulate type I error rates across a variety of hypothesis testing. In the third article report, the author presents repeated-measures ANOVA, which is used when each experimental unit provides response data at each level of a fixed factor. Readers can find more technical information about the same themes in statistical textbooks and digital papers, as well as larger coverage of subjects not covered in these pages.

We need to understand the relationships between the components and the experimental units in order to choose the best ANOVA model. In experimental design and ANOVA, “fixed factors” and “random factors” are two different sorts of factors that analysts identify (Potvin, 2020, p.59). One for which the precise amounts are important is referred to as a “fixed factor”. If the experiment was repeated, different levels of the factors would be selected at random. The ANOVA’s goal when dealing with random factors is to draw conclusions about population-level random variation (Lakens & Caldwell, 2021, p.33). The entire experiment might be repeated with the same factor values on both occasions by the researcher. In theory, every level of a fixed factor corresponds to a different population with a different response mean. We refer to those levels as treatments when an investigator consciously sets or changes the levels of a fixed element.

The main goal of an ANOVA is to determine if response values are consistent across factor levels. The term “replication” refers to the process of applying a factor level to two or more separate experimental units.  The experimental design is considered to be “balanced” if there is an equal distribution of replicates for each factor level. These ideas apply to different levels of factor combinations. Both “crossed” and “nested” combinations of two or more factors are permitted in an experiment. Each level of factor A as well as each level of factor B are present when factors are crossed (Choi & Wilson, 2018, p.70). For example, each of the two treatments (drugs X and Y, factor A levels) may be given in either of the two doses (low or high, factor B levels), with each experimental unit receiving one drug at one dose. Every level of a nested factor only occurs in 1 level of the factor it is nested within, as opposed to several levels in the case of crossing factors. In a study to compare the duration of hospitalization for patients after bypass surgery for coronary arteries between for-profit and nonprofit establishments, organizational status is a fixed factor (for-profit/nonprofit), “hospital” is a random factor (specific hospitals are its levels), enclosed within the fixed factor levels, and individual patients are the experimental units.

The words “fixed effects” and “random effects” are frequently used to describe ANOVA designs. To avoid confusion, random factors directly correlate to random effects among levels, while fixed factors relate to fixed effects among factor levels (between-population mean differences). We employ a “mixed-effects” ANOVA model when the experimental setup incorporates both fixed and random factors.

#### References

Choi, J., & Wilson, M. R. (2018). Modeling rater effects using a combination of generalizability theory and IRT. Psychological Test and Assessment Modeling60(1), 53-80.

Lakens, D., & Caldwell, A. R. (2021). Simulation-based power analysis for factorial analysis of variance designs. Advances in Methods and Practices in Psychological Science4(1), 2515245920951503.

Potvin, C. (2020). ANOVA: experiments in controlled environments. In Design and analysis of ecological experiments (pp. 46-68). Chapman and Hall/CRC.

Siregar, S., Nieboer, D., Versteegh, M. I., Steyerberg, E. W., & Takkenberg, J. J. (2019). Methods for updating a risk prediction model for cardiac surgery: a statistical primer. Interactive cardiovascular and thoracic surgery28(3), 333-338.