WK5Assgn_Beal_R (5) (2)

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Feb 20, 2024

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1 Statistical Significance in Scenarios One and Four Roswell Beal PhD of Science in Public Policy and Administration, Walden University Quantitative Reasoning and Analysis Professor Olivia Yu December 31 St, 2023

2 Scenario One The first scenario sought to identify which medium was preferred among students in a quantitative reasoning course based on student satisfaction levels of traditional classrooms and online environments. In both cases, four classes of each type were observed at the same university where n=65 students of in person students and n=69 of online students. The sample size used for this study is adequately sized for statistical hypothesis testing because the sample size in both in person students and online students is over 50 (Frankfort-Nachmias & Leon- Guerrero, 2020). The effect size of the sample is concerned with the confidence level of the study or in other words the strength of the relationship between the sample mean and the population mean (Frankfort-Nachmias & Leon-Guerrero, 2020 and Warner, 2012). This study focuses on the statistical significance as a meaningful level of measurement by the effect being denoted by the p-value (Bhandari, 2023). The research utilizes the inferential statistic t test that evaluates the difference of significance between online students and in person students' respective preferred medium for the class by identifying the difference in the means between both groups (Hayes, 2023). The t test shows the significance as t(132)= 1.8, p=0.74 with students in traditional classes having a mean of M=3.39 and SD=1.8 showing lower levels of satisfaction than online students with a mean of M=3.89 and SD=1.4. Since this research uses an inferential statistic t test, it can also be determined that the sampling method used is probability because nonprobability samples have a major limitation by not allowing the use of such statistics that generalize from the sample inferences of the population (Frankfort-Nachmias & Leon-Guerrero, 2020). This study includes a relaxed level of significance of .10 which is the alpha level, since the author notes that the study is exploratory in nature. This level stands as the researcher's willingness of a 10% chance that the result of supporting the hypothesis is untrue or does not

3 represent the total population of students preferred medium of the course (Serdar et. al., 2021). The P-Value is identified as “rapidly approaching significance” at p= .06 and can be interpreted as the probability of incorrectly rejecting the null hypothesis (Frankfort-Nachmias & Leon- Guerrero, 2020). When comparing the p-value and the alpha level, the researcher determined there is a statistically significant result because the p-value of .06 was lower than the alpha level of .10 (Frankfort-Nachmias & Leon-Guerrero, 2020). There is correlation between online students and traditional students because the variable of student satisfaction is associated with both (Frankfort-Nachmias & Leon-Guerrero, 2020). The research of online students' level of satisfaction being higher than traditional face to face students regarding the medium for the class show that there is statistical significance of the findings in the exploratory study that shows that online students more favorably preferred the class medium, while traditional students hd lower levels of satisfaction of in-person class. Based on this evaluation of the scenario, the implication for social change is determining how the in person class experience differs from the online medium and lead to lower satisfaction levels of students. Further research will be needed for devising strategies that combat dissatisfaction of in person students or to determine why the online medium is preferred and to better evaluate the different outcomes of students capabilities of both online and in person quantitative reasoning classes as a way to improve the outcomes. Scenario Four The second Scenario chosen for this assignment is number four where a correlation test was utilized to identify the relationship between the level of income and job satisfaction of respondents. The sample size consists of 432 employees spread out evenly across public, private and non profit sectors which provides useful representation of various types of employment. This would be considered a type of probability sampling method as a stratified random sample

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4 because the population is divided into subgroups of employment type and then a simple random sample is taken from these subgroups equally to the sum of 432 respondents (Frankfort- Nachmias & Leon-Guerrero, 2020). The correlation test found a meaningful relationship between the two variables of level of income and job satisfaction which is represented as r=.87 and p<.01. R represents the correlation coefficient which is useful in determining the measure of association of two interval-ratio variables such as job satisfaction and level of income (Frankfort- Nachmias & Leon-Guerrero, 2020). The degree of the relationship between the two variables is thus r=.87 and reflects a strong and positive linear correlated relationship which shows the meaningfulness of the research as being valuable to understand that the variables are associated with one another (Frankfort-Nachmias & Leon-Guerrero, 2020). It should be noted that is all a correlational test shows and the statistical significance of the findings only reflects that there is an association between the two variables without going into enough detail to identify any clear association with other important variables that could alter the findings such as employee or workplace relations or what implications there may be for social change (Frankfort-Nachmias & Leon-Guerrero, 2020). What this is to say, is that a correlation of two variables does not denote causation in the relationship and that other factors may be involved in job satisfaction and income level not addressed currently by this research and therefore the statistical significance of the variable should not be based solely on a correlation test alone (Frankfort-Nachmias & Leon- Guerrero, 2020). The practical significance is determined by the effect size which is categorized by small, medium or large and based on Pearson’s r, this study would be considered large since r=.87 and that the sample size was adequate to show the statistical power needed to identify the effect of the sample size (Bhandari, 2023). Thai study is missing the ability identify further information about the variables in a meaningful way that shows statistical significance such as

5 what the mean is for the subgroups of respondents and how they differ from one another, an ANOVA test would better frame the findings in a way that shows more than an association of two variables and aid research into the inferential statistics in analyzing the relationship between the subgroups (Frankfort-Nachmias & Leon-Guerrero, 2020). Implications for social change can not be highlighted or identified by merely saying these two variables are associated and requires different research techniques to identify them and evaluate the variations in the subgroups. References

6 Bhandari, P. (2023, June 22). What is effect size and why does it matter? (examples). Scribbr. https://www.scribbr.com/statistics/effect-size/ Frankfort-Nachmias, C., Leon-Guerrero, A., & Davis, G. (2020). Social statistics for a diverse society (9th ed.). Thousand Oaks, CA: Sage Publications. Hayes, A. (2023). T-test: What it is with multiple formulas and when to use them . Investopedia. https://www.investopedia.com/terms/t/t-test.asp Serdar, C. C., Cihan, M., Yücel, D., & Serdar, M. A. (2021). Sample size, power and effect size revisited: simplified and practical approaches in pre-clinical, clinical and laboratory studies. Biochemia medica, 31(1), 010502. https://doi.org/10.11613/BM.2021.010502 Warner, R. M. (2012). Applied statistics from bivariate through multivariate techniques (2nd ed.). Thousand Oaks, CA: Sage Publications.

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