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1 Evaluation of Significance of Findings: Case Scenarios DrPh, Walden University RSCH-8210R: Quantitative Reasoning and Analysis Dr. Nancy Rea July, 2020

2 Evaluation of Significance of Findings: Case Scenarios The understanding of statistical significance and meaningfulness in research are vital elements for practitioners (Page, 2014). The ability to create and change policies as well as evoking social change requires the comprehension of hypothesis testing and its implications. Two scenarios will be evaluated based upon, sample size, meaningfulness, statistical significance, and implications for social change. The case scenarios assessment should provide insights to the ability to apply learned skills. Scenario 1 The p-value was slightly above conventional threshold but was described as “rapidly approaching significance” (i.e., p =.06). An independent samples t test was used to determine whether student satisfaction levels in a quantitative reasoning course differed between the traditional classroom and on-line environments. The samples consisted of students in four face- to-face classes at a traditional state university (n = 65) and four online classes offered at the same university (n = 69). Students reported their level of satisfaction on a five- point scale, with higher values indicating higher levels of satisfaction. Since the study was exploratory in nature, levels of significance were relaxed to the .10 level. The test was significant t (132) = 1.8, p = .074, wherein students in the face-to-face class reported lower levels of satisfaction (M = 3.39, SD = 1.8) than did those in the online sections (M = 3.89, SD = 1.4). We therefore conclude that on average, students in online quantitative reasoning classes have higher levels of satisfaction. The results of this study are significant because they provide educators with evidence of what medium works better in producing quantitatively knowledgeable practitioners. Sample Size The independent variable is student satisfaction relate to traditional classroom and online

3 environments. Kukull and Ganguli (2012) state, “sampling an entire population is not feasible; hence, fair samples must provide valid estimates of population characteristics being studied.” The sample size is an issue since it is not diverse because it comes from the same university. Therefore, sampling is not a representation of the general population. To infer something about a community requires a form of traditional research, which must use a representative sample (Page, 2014). Meaningfulness Meaningfulness is the ability to take statistical data and determining its appropriateness in the real world (Laureate Education, 2016f). In the noted case, the statistical information provided does not rise to the level of meaningfulness. Without an accurate representative sampling of the population, results cannot give evidence to have an appropriate effect on the real world (Kukull & Ganguli, 2012). Additionally, the research is exploratory. Exploratory research is used for preliminary findings to determine if further and more in-depth studies need to be conducted to answer a posed question that may have implications of social change (Hallingberg, 2018). Since exploratory studies are preliminary, alone, they do not help in making real-world decisions. Statistical Significance The p-value assists in informing statistical significance; the value of alpha is frequently set at .05 (Skill Builder, n.d.a). Traditional p values to show statistical significance is p<0.05 (Page, 2014). The scenario has a couple of flaws the do not support statistical significance. The first is moving the level of significance to .10. A level of .10 has no statistical significance (Warner, 2012). Statistical power is the probability of detecting the differences between groups if they exist and should be determined at the onset of the study (Schmidt et al., 2018). The

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4 researcher seems to force the significance by moving the significance level, which can be considered inappropriate since it should be chosen at the onset of the study. Secondly, the phrase “rapidly approaching significance” after a review of the literature, this phrase seems to be a misnomer as the study has either significance or no significance (Amrhein et al., 2017). The results should be to retain the null hypothesis instead of rejecting the null hypothesis. The retaining of the null hypothesis is a Type II error (Page, 2014). Social Implications The social implications of scenario one could be reflective in satisfaction for online or traditional classroom learning based on the student preference. However, without a true sampling the consequences of social implications seem to be limited. The study being exploratory only is an initial step and fact-finding effort in the feasibility of a more detailed review. Even though there was no statistical a significance, a more robust sampling size may reveal additional information, which may provide the statistical significance desired. Therefore, another thorough study will help determine the medium that works best in producing quantitatively, knowledgeable practitioners. Scenario 4 A study has results that seem fine, but there is no clear association to social change. What is missing? A correlation test was conducted to determine whether a relationship exists between level of income and job satisfaction. The sample consisted of 432 employees equally represented across public, private, and non-profit sectors. The results of the test demonstrate a strong positive correlation between the two variables, r =.87, p < .01, showing that as level of income increases, job satisfaction increases as well. Sample Size

5 A correlation test was done. Pearson correlation r test are bivariate analysis that measures the strength of the relationship between two variables and the variables are continuous (Skill Builder, n.d.b). In this study, the two variables are the level of income and job satisfaction; both variables can be classified as scale. The sample size is 432 employees from various backgrounds. An issue with the sample size is representation. The study states the representation is equally represented. However, when assessing a sample of employees from such diverse backgrounds, there is usually one group represented more than the other group. The study's equal distribution in the sample could imply selection bias, which brings to mind the subject enrollment influenced by the study (Kukull & Ganguli, 2012). Meaningfulness In the study, there is a correlation between the increase in the level of income and the increase in job satisfaction because of Pearson’s correlation coefficient results is close to +1. The concepts of correlation and causation are essential because it allows the researcher to comprehend the cause and effect of the variables studied; while these concepts are imperative correlation does not always imply causation (Akoglu, 2018). Correlation may help stakeholders make decisions about projecting for future preparations (Akoglu, 2018). In the study, the correlation is high, but the increase in income does not necessarily increase job satisfaction. Therefore, the significance is present with a high correlation. Still, there is a failure to achieve meaningfulness because it cannot be established the cause of one variable affected the other variable (Hung, 2017). Statistical Significance The p-value < .01 reveals significance because the p-value should be less than or equal to .05 (Page, 2014). According to the results of the p-value, this study has statistical significance,

6 and the null hypothesis should be rejected. The correlation is strong as it shows an r =.87 between the two variables (Akoglu, 2017). Pearson’s correlation varies between -1 and +1; the closer to 1, the stronger the relations between the variables (Akoglu, 2018). Social Implications The social associations for the study do not give a true assessment of findings to support social changes. The importance of making decisions for social change is the comprehension of the aspects of research to utilize better the evidence for support (Page, 2014). The sample size should be reassessed to obtain a better sampling of the various sectors. The analysis of the variables may influence evaluation of the association of employment and the effects of income on job satisfaction. Conclusion Scenarios 1 and 4 both have missteps in the overall research provided through the examples. Each scenario had issues with sample size, whether it was insufficient or lacked diversity to get a true representation of the population. Both scenarios fail to achieve meaningfulness. The first scenario statistical significance could be argued that it was reached; however, with the p-value being relaxed, my assessment is that there was no clinical significance. Scenario 4 reached statistical significance, and the variables had a strong correlation. Social change implications provide awareness into the problems facing society and the need to alleviate such issues by conducting research to support decision making and policy review and implementation.

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7 References Akoglu H. (2018). User's guide to correlation coefficients. Turkish journal of emergency medicine, 18 (3), 91–93. https://doi.org/10.1016/j.tjem.2018.08.001 Amrhein, V., Korner-Nievergelt, F., & Roth, T. (2017). The earth is flat (p > 0.05): significance thresholds and the crisis of unreplicable research. PeerJ, 5 , e3544. https://doi.org/10.7717/peerj.3544 Hallingberg, B., Turley, R., Segrott, J., Wight, D., Craig, P., Moore, L., Murphy, S., Robling, M., Simpson, S. A., & Moore, G. (2018). Exploratory studies to decide whether and how to proceed with full-scale evaluations of public health interventions: a systematic review of guidance. Pilot and feasibility studies, 4 , 104. https://doi.org/10.1186/s40814-018- 0290-8 Hung, M., Bounsanga, J., & Voss, M. W. (2017). Interpretation of correlations in clinical research. Postgraduate medicine, 129 (8), 902–906. https://doi.org/10.1080/00325481.2017.1383820 Kukull, W. A., & Ganguli, M. (2012). Generalizability: the trees, the forest, and the low- hanging fruit. Neurology , 78 (23), 1886–1891. https://doi.org/10.1212/WNL.0b013e318258f812 Laureate Education (Producer). (2016f). Meaningfulness vs. statistical significance [Video file]. Baltimore, MD: Author. Page P. (2014). Beyond statistical significance: clinical interpretation of rehabilitation research literature. International journal of sports physical therapy, 9( 5), 726–736.

8 Schmidt, S. A., Lo, S., & Hollestein, L. M. (2018). Research techniques made simple: Sample size estimation and power calculation. Journ al of Investigative Dermatology, 138 (8), 1678-1682. https://doi:10.1016/j.jid.2018.06.165 Skill Builder (n.d.a). Hypothesis testing. Retrieved https://laureate.acrobatiq.com/courseware/wal_oct16_Qual_reasoning_11/ week_5__evaluating_p-values_and_statistical_power/evaluating_p-values/ wbp_hypothesis_testing Skill Builder (n.d.b). Introduction to correlation. Retrieved https://laureate.acrobatiq.com/courseware/wal_oct16_Qual_reasoning_11/ week_6__research_design__statistical_design__and_hypothesis_testing/ interpreting_correlation_and_regression_coefficients/wbp_introduction_to_correlation Warner, R. M. (2012). Applied statistics from bivariate through multivariate techniques . Thousand Oaks, CA: SAGE Publications.

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