Any qualitative or quantitative study may require the collection of data that will need statistical processing afterward. Generally speaking, the establishment of hypotheses is an essential feature of experimentation because it determines its foundation and sets the vector for development. Within the framework of the discussed topic of the project, hypotheses will be established in the next question, but now it is clear that it will be necessary to test them statistically with the help of existing tools of analysis. Thus, in general, the entire procedure of hypothesis examination comes down to testing their statistical significance.
In more detail, once the null and alternative hypotheses have been established, it is necessary to select the criterion used for the analysis. The criterion should be understood as a mathematical characteristic of the sample, based on which the decision to reject or accept the working hypothesis will be made later (Introduction to hypothesis testing, n.d.). It can be the Shapiro-Wilk criterion, Student’s t-criterion (or Fisher’s F-criterion), and, for example, Wilcoxon’s criterion. The choice of the criterion is replaced by the choice of the statistical significance level alpha, which is 0.05 by default: this is the so-called probability of error of the first kind (UU, 2021). The fourth step is essential to find the boundaries of the hypothesis acceptance area; for this purpose, the statistical calculations of the selected criterion for the data set are performed. If the initial level of significance fits the processing result, then a conclusion is made that there is no sufficient reason to disprove the null hypothesis.
The purpose of the paper is to determine the level of effective integration of Iraq War veterans into academic communities based on opioid use. The null hypothesis is that most veterans use opioid medication to integrate into academia. The alternative hypothesis is that most veterans do not use opioid medication to integrate into learning.
This should be a virtual survey of respondents administered via the Internet. The choice of a nonphysical survey is driven by the epidemiological difficulty of being present in person (Tuma et al., 2021). The survey should be structured so that participants choose pre-generated responses on satisfaction, efficiency, and mental health scales.
The population is all Iraq War veterans, and the sample will be randomly selected by assigning a number to each veteran from the (pre-generated) list. The number will be chosen using a random number generator (randomly), which will reduce sampling error or bias.
Levels of satisfaction with training, levels of calmness and mental health, levels of PTSD-related stress absence, and levels of personal well-being after military service are measured.
The independent variable is the amount (or frequency) of opioid medication taken, which will determine how well student veterans integrate into learning (dependent variable). The dependent variable is a composite of the individual metrics discussed in (4). The independent variable is subject to a simple calculation of the amount or frequency of pain medication and nootropic medication. The reliability of the quantitative hypothesis measure will lie within the participants’ responses or the provision of medication prescriptions. The reliability of the independent variable measurement should be determined by scientifically valid scales of satisfaction, stress, and others (Beidas et al., 2015).
The statistical analysis used is the ANOVA analysis of variance, which will assess the significance of the results for multiple groups. Analysis of the quantitative data collected will be done using MS Excel.
Since a set of dependent variables is being measured, the ANOVA test is preferable to the paired t-test. In addition, ANOVA can control for the incidence of false positives. Finally, because the general population is expected to have a normal distribution (mean number of opioid drugs), ANOVA as a type of parametric test would be most appropriate.
Four basic assumptions do need to be made to do a regression analysis. These mainly concern the nature of the mutual relationship between the independent variable and the dependent variable and the reliability of the measurements. First and foremost, it is crucial to assume that there is a linear relationship between the number of opioids taken and the effectiveness of integration in learning (Vidhya, 2016). This can be assessed by performing a linear regression separate analysis of the independent variable and the assessed satisfaction, stress, and so on. The second assumption concerns homoscedasticity, where in all individual groups, the variance remains constant. This can be checked visually: one has to plot the dependence of the values of random residuals on the aligned value of the resulting variable.
The third assumption will be the independence of observations from each other. This means that there is no overlap between the levels of stress, satisfaction, and mental health. Finally, the fourth assumption will be the assumption of a normal distribution of the dependent variable. By plotting the regression relationship, it will be possible to infer the extent to which inclusion effectiveness usually is distributed relative to the amount of medication used.
Many statistical tools can be used to evaluate a data set. One such tool that is highly popular among researchers is the ordinary least squares (OLS) regression method. Such a model aims to find a curve that fits the variance of the data with the minimum sum of the squares of error. In other words, the variance for a given data set should be minimal because the closer the curve describes the trend to each point on the existence interval of the entire scatter, the more accurate the OLS satisfies that set.
When using OLS, the regression coefficient is usually a statistical relationship between the two variables under study. In other words, it is the degree of dependence of one line on the other. Consequently, if the regression coefficient is negative, it is reliable evidence of the so-called negative relationship between the variables. Visually, as the independent variable, for example, increases, the values of the dependent variable decrease.
During the use of regression analysis, the specialist must take into account the interaction terms. These conditions arise if the relationship between the independent variable and the dependent variable — in other words, the effect of the independent on the dependent — can change when influenced by external, other independent variables. Using this concept allows us to consider more hypotheses and, in general, to expand our understanding of the mechanisms of the relationship in the measured variables by finding new patterns. However, the use of interaction terms can be problematic, so the researcher must be confident in the statistical apparatus. Finally, for binary studies that measure the binary (dichotomous) dependent variable, logistic regression should be used instead of OLS. In addition, logistic regression produces discrete results, whereas OLS produces continuous.
References
Beidas, R. S., Stewart, R. E., Walsh, L., Lucas, S., Downey, M. M., Jackson, K.,… & Mandell, D. S. (2015). Free, brief, and validated: Standardized instruments for low-resource mental health settings. Cognitive and Behavioral Practice, 22(1), 5-19
Introduction to hypothesis testing [PDF document]. (n.d.). Web.
Tuma, F., Nituica, C., Mansuri, O., Kamel, M. K., McKenna, J., & Blebea, J. (2021). The academic experience in distance (virtual) rounding and education of emergency surgery during COVID-19 pandemic. Surgery Open Science. Web.
Vidhya, A. (2016). Going deeper into regression analysis with assumptions, plots & solutions. AV. Web.
UU. (2021). Hypothesis testing. Sociology 3112. Web.