Introduction
The research is typically based on the research questions. Punch (1998) identifies the main reasons for setting a research question. The research questions help to organize and direct a study, and keep the researcher focused; they set the boundaries and framework for the project, and designate the data necessary for the project.
The research has to provide the reliable results and conclusions, irrespective of the area. Therefore, scientific and social research have to be based on the real-life data and the appropriate data processing methods. The data should be obtained using the procedure of statistical sampling and tested for normality. The research hypothesis have to be set and tested. Since the research areas are different, the data and the statistical methods are also different. There are data originally gathered as numerical values, for example, temperature, the number of study hours, the volume, etc. In social sciences, numerous factors require qualitative characteristics, which are categorical or ordinal data. When these data are processed with the statistical methods, they need to be cyphered in numerical form. Therefore, the different tests are applied. For the relations between the categorical or ordinal data, the χ-square test is used. The numerical data are processed with t-tests, when the means of two data sets are compared; z-test is applied when the probability of the certain value appearance need to be tested.
The paper presents the application of analysis of variance, commonly referred as ANOVA, for data processing in applied and social sciences research. Three peer-reviewed articles will be used to present the concept and real-life application of the analysis. The articles are chosen to represent different areas of the science.
ANOVA is a used for the complex statistical analysis of several data groups means. The procedure of the analysis is rather complex, thus it is performed by the application of statistical tools in the software, either specialized statistical packages, or MS Excel data analysis tool. Nowadays, the main task of the researcher is the correct interpretation of the data. The test results processing includes interpretation of the statistical figures with acceptance of the appropriate hypothesis and interpretation of the results in terms of the real-life problem, or narration of the test meaning. The interpretation of the statistical figures is presented with tables and/or graphs to illustrate the data or findings. The narrative part should be presented so that the person unfamiliar with the statistics would be able to understand it. In this section, it is important not to use the specialized terms, but a moderate scientific language, which is understandable for people with no mathematical or statistical background.
Literature Review
The data processing starts with the hypothesis setting (Daniels, 2015). The hypothesis is developed basing on the research questions and aims to find the relationship between the data. The null hypothesis typically states that there is no significance difference between the groups means. This is indicated by the p-value in the results output, p < 0.05. The alternate hypothesis is opposite to the null, namely there is a significant difference between the means, or at least one mean is different. In this case, p > 0.05. The statistical interpretation of the ANOVA results is based on the hypothesis testing.
P-value indicates the probability of the particular conclusion in the research is observed due to chance (Daniels, 2015). Therefore, p < 0.05 indicates that there is 5% or less chance that the observed effect appeared accidentally, and 95% of guarantee that the effect is due to consistent effect; when p > 0.05, the researcher has to be aware that the chance of the accidental effect is great. The choice of the threshold p-value depends on the researcher and his or her consent to accept an error. Sometimes, greater p-values are used.
Mechanical Engineering Application
The research of Atlan (2009) presents the application of statistical methods in experimental research in applied sciences. The author presents the experimental data processing with Taguchi, ANOVA and neural network methods. The shrinkage of polypropylene and polystyrene was measured at various conditions. The significance of each parameter influence on molding was studied. The parameters were melt temperature, packing pressure and time, and they influenced the shrinkage of polypropylene and polystyrene. The shrinkage parameters were measured at different conditions, and the results were analyzed with application of ANOVA. The author presented the results in a table and provided the reader with the interpretation. The format of the tables is exemplified by Table 1.
The table format in the article is the original way of presenting the results. It differs from the statistical software packages layouts, yet it includes all the necessary characteristics for data interpretation. The author notes the critical F-value in the text, and the table data present the values for each factor. Basing on the F-values (F-value < F-ratio), the author concludes the influence of factors A, C, and D on shrinkage. The alternate way to interpret the statistical results is the p-value. If the p-value < 0.05, the factor has significant influence on shrinkage at 95% confidence level. Either P- or F-value can be used for interpretation.
The ANOVA results from polypropylene and polystyrene testing follow the same pattern, namely indicate that B factor does not have the significant influence on molding. Therefore, the results are consistent. The ANOVA tables present the numerical results, while the narrative interpretation explains the reader the meaning of the statistical tests. The research also designated the order of factors influence, and these were packing pressure, time and melting temperature. Atlan (2009) used the effective way of presentation of the results.
ANOVA for Concept of Fit in Management
The research of the specialist in quantitative social research, Venkatraman (1989) presents a concept of fit in strategy research. The correspondence between a concept and its testing schemes is studied. The author emphasizes the issue of misusage of the fit perspectives in theoretical discussions and empirical researches. ANOVA is used as analytical scheme to test the fit in matching perspective, along with the deviation score analysis and the residual analysis. Despite of the typical use for interaction effect, the tests for fit reflection and matching prospective has been developed. The ANOVA allowed distinguishing the various types of fit: general, effect and functional, within the interaction effects. It emphasizes the similarity and matching of independent variables. The author reports that ANOVA can ‘test competing perspectives of fit within the analytical framework’ (Venkatraman, 1989).
The paper Venkatraman (1989) only mentions the ANOVA as one of the statistical tools, therefore there are no details of its application to fit in matching perspective. The presentation is narrative, there are no tables or graphs.
Clinical Research Analysis
Wallman et al. (2015) performed a clinical research of non-radiographic axial spondyloarthritis and ankylosing at anti-tumor necrosis therapy. The aim was to explore the influence of inflammatory activity measured by the specific protein at treatment. There were 86 and 238 patients involved for non-radiographic axial spondyloarthritis and ankylosing therapy, respectively. The research lasted three years. The ANOVA method was applied to identify the difference in the development of clinical effect during three years of therapy. The study was adjusted for sex, age, presence of arthritis, duration of the disease. The data for the missing values were approximated using the linear regression methods. The repeated ANOVA procedure was applied with the sensitivity analysis.
Wallman et al. (2015) presented the summarized table with the results, and there is no specific table for ANOVA test. The conclusions are made basing on the p-values. The between-group differences were not observed at p > 0.1. The C-reactive protein test results showed the significant between-group difference (p = 0.004), while the erythrocyte sedimentation rate was similar (p > 0.1).
The paper illustrates the application of ANOVA in clinical research. The peculiarity of the article is the minimum statistical details and emphasis on medical interpretation of the results. The comparison of the treatment method does not require the graphical illustration, therefore the figures for ANOVA results are absent. For the correct results, all the data in the data set should be present; in case of absence it is necessary to perform the approximation and correction. The authors (Wallman, 2015) use the p-value as the test significance indicator; if p > 0.05, the results are not significant, if p < 0.05, the results are significant.
The application of the statistical methods in clinical research provides a scientific basis for the decisions of treatment efficiency, clinical and therapeutic effects.
Conclusions
ANOVA is an essential part of the contemporary research in applied and social sciences, as well as in clinical research. It is used in confirmatory and exploratory data analysis and provides simplified method for comparison of numerous groups of data, which becomes routine analysis with the application of software procedures. The method allows comparison of the several groups means, and there are alternate ways for results interpretation, namely the F-values and p-values. Thus, a researcher has a choice of the results presentation. Since various groups are analyzed, illustration with the figures is inappropriate and is rarely used. In some cases, the table with the software output is presented, which includes all characteristics of the ANOVA results; this method was used by (Altan, 2010). Other researchers, as in clinical research by Wallman et al. (2015), use only p-values for interpretation and explanation. This is sufficient for the statistical significance proof. Hence, ANOVA provides a wide variety of methods for the outcomes presentation.
The ANOVA allows designating the significant influences of the factors, thus it is necessary for industrial testing of the items, the efficiency of the novel drugs, and the changes in the economical situation or psychology areas.
References
Altan, M. (2010). Reducing shrinkage in injection moldings via the Taguchi, ANOVA and neural network methods. Materials & Design, 31(1), 599604.
Daniels, W. (2015). Alzheimer Europe Research Understanding dementia research Types of research The four main approaches. Alzheimereurope.org. Retrieved from http://www.alzheimereurope.org/Research/Understandingdementiaresearch/Typesofresearch/Thefourmainapproaches.
Punch, K. (1998). Introduction to social research. London: SAGE Publications.
Venkatraman, N. (1989). The Concept of Fit in Strategy Research: Toward Verbal and Statistical Correspondence. The Academy Of Management Review, 14(3), 423.
Wallman, J. K., Kapetanovic1, M. C., Petersson, I. F., Geborek, P., & Kristensen, L. E. (2015). Comparison of non-radiographic axial spondyloarthritis and ankylosing spondylitis patients – baseline characteristics, treatment adherence, and development of clinical variables during three years of anti-TNF therapy in clinical practice. Arthritis Research & Therapy, 17, 378-388.
