Inferential Research and Statistics
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Introduction
Inferential statistics is a sub-branch of statistical analysis that investigates differences and similarities among factors in a research study. Statistical analysis is widely used in various aspects of life, ranging from health, agriculture, education, social life, economic life, etc. Researchers and scholars employ statistical analysis and techniques to investigate and support hypotheses under study. Inferential statistics, therefore, deals with measurable factors in a research study. The central concept under statistical inference is measuring two or more population parameters and investigating a significant difference.
Hypothesis testing forms the basics of inferential statistics. In statistical analysis, there exist two hypotheses, the null hypothesis, and the alternative hypothesis. The null hypothesis denotes as (H0) tests the existence of no difference in the population under study. The alternative hypothesis (H1) tests a statistically significant difference in the population under study. The p-value scores are used to decide whether a statistical test is statistically significant. Statistically, a p-value score of <0.05 implies that the statistical test is significant, while a p-value score of >0.05 indicated that the test is not statistically significant.
Statement of the problem
A new treatment method has been introduced in a new clinic to treat clients veterans with PSTD. Exist research suggests that virtual reality is highly effective in treating PSTD. The current treatment method employed in the clinic is the cognitive processing therapy method. The clinicians are in the process of finding out whether the VR method differs from the CPT method in treatment effectiveness. While measuring PSTD symptoms, the clinicians used the combat scale. The two methods require to be applied for a period of twelve weeks for effectiveness.
Research Design
Research design in a research study describes the processes and techniques applied in the study to construct meaningful information from data. Research design depends on the nature of the research study, the data present, and the objectives of the study. The goal of this research report is to investigate whether the two treatment methods, VR and CPT, differ in treatment results. Two groups will be randomly chosen from the population and treated with different treatment methods. The groups should then be exposed to the respective treatment for 12 months ad final results investigated. The treatment outcome will be accessed base on the symptoms of PSTD. A sample size of 15 participants in each group will be utilized, adding up to a sample size of 30 participants. The null hypothesis in this research report states that;
H0: There is no difference in treatment between VR and CPT
H1: There is a difference in treatment results between the two methods.
The independent variable in this research study is the treatment method, and the response variable is the PSTD symptoms measure by the combat scale. Randomization is a technique employed in a research study to minimize the presence of errors. In order to ensure each participant had an equal chance of being selected in the study, a simple random sampling method was used.
Data Analysis
Data analysis involves breaking down the information collected from research into useful insights that can be understood and presented to the wider consumers. Generally, it involves establishing correlation and association between variables and modeling the association in terms of functions. Investigating differences among two populations is conducted using the independence t-test. The independence t-test makes several assumptions concerning the data that have to be met to achieve correct results. Some of these assumptions include the normality of the two populations, continuous data, randomly elected sample, and the sample should be a representative of the wider populations.
Histograms are visual plots for investigating the data distribution of a variable. Additionally, they also depict whether the variable is normally distributed. The histograms for the two groups were plotted, and their distribution averagely matched the normal distribution curve. Box plots can also be used to access the distribution of the data in cases where the data is consisting of outliers is the reliability of the means would not be logical due to outliers.
Fig 1.0: Histogram plots for the two groups of treatment
Microsoft Excel was used to conduct a t-test for the two populations. The hypothesis under test is rendered the test to be two-tailed since the hypothesis was non-directional. The p-value score was set at 0.05, representing the significance score. If the t-test yields a p-value less 0.05, then there exists a difference in treatment between the two methods; otherwise, there is no significant difference between the two methods at alpha level 0.05. The alpha level was also set at 0.05, indicating the accepted error the researcher is willing to accept from the result. The t-test with unequal variance assumed was fitted for the two treatment data represented by group 1 and group 2. Table 1.0 below represents the output results.
Table 1.0: T-test analysis
| t-Test: Two-Sample Assuming Unequal Variances | ||
| GROUP 1 | GROUP 2 | |
| Mean | 5.61 | 7.326666667 |
| Variance | 4.798172 | 1.855816092 |
| Observations | 30 | 30 |
| Hypothesized Mean Difference | 0 | |
| df | 49 | |
| t Stat | -3.64507 | |
| P(T<=t) one-tail | 0.000323 | |
| t Critical one-tail | 1.676551 | |
| P(T<=t) two-tail | 0.000646 | |
| t Critical two-tail | 2.009575 | |
The mean for group one was 5.61, and Group 2 was 7.33. the variance for group one was 4.798 and for group two was 1.856. The variance of a dataset represents the variability in the data. The bigger the variance, the more spread is the data. When the variance score is less, it indicates that there is less spread in the data. The independent t-tests produce both one-tailed and two-tailed tests. One-tailed tests consider on none side of the hypothesis, while a two-sided hypothesis considers both sides of the hypothesis (greater and fewer sides). The one-tailed t-test score p-value was 0.0003232 less than 0.05, indicating statistically significant results. Upon investigating the two-tailed test, the results were also significant, with a p-value score of 0.000646. the results of the t-test imply that there is a statically significant difference in the two treatment methods. For instance, let us consider group 1 results to represent the VR treatment method and group two to represent the CPT method. We would therefore conclude that the CPT treatment method is more effective than the VR treatment methods at alpha value 0.05.
Another method to access the significance of statistical results is to employ the concept of the computed statistic and the table value. The critical value, in this case, represents the table value, and the score is 2.009, the computed t statistic is -3.645. Statistically, we would reject the null hypothesis as |computed t statistic= -3.645| is greater than the |table value = 2.009|. Likewise, since the computed t value is greater than the critical value, we reject the null hypothesis and conclude that the two treatment methods are not the same.
Since the results indicate that the existing treatment method is more effective in treating PSTD, there is no need to change the treatment method from CPT to VR since the new suggested treatment method does not improve the treatment process and the treatment results. Additionally, collection of other information concerning the patients would also be of use in order to access the existing association between treatment method and variables such as age, gender, cholesterol levels, heights, weights, etc. this would therefore extend our test to a more complex statistical model such as multiple linear regression. This is statistically efficient in determining the deference and measuring the important variables regarding the topic of interest.
Scholars and research can also extend the research study between VR and CPT treatment methods whereby they employ a larger sample for study, used additional explanatory variables, and use different statistical techniques and models. By doing so, accurate research can be documented on the association between PSTD treatment and the fitted explanatory variables. Additionally, the most significant variables affecting PST treatment would, therefore, be investigated and identified.
References.
Adams, K. A., & Lawrence, E. K. (2018). Research methods, statistics, and applications. Sage Publications.
Kim, T. K. (2015). T-test as a parametric statistic. Korean Journal of anesthesiology, 68(6), 540.
McHugh, M. L. (2013). The chi-square test of independence. Biochemia Medica: Biochemia Medica, 23(2), 143-149.
Pagano, R. R. (2012). Understanding statistics in the behavioral sciences (Vol. 1). Cengage Learning.
SzéKely, G. J., & Rizzo, M. L. (2013). The distance correlation t-test of independence in high dimension. Journal of Multivariate Analysis, 117, 193-213.