Statistical Reasoning in Psychology

Statistical Project Part 1
The Problem
The research question is to compare the effectiveness of two drugs, A and B, in lowering anxiety. This research question requires the research to design an equivalence randomized controlled trial where patients diagnosed with anxiety are randomized to treatment A, and B. Measures to enhance validity and reliability include using a computer-generated randomization sequence and double blinding of participants and researchers.
Review of Relevant Research
D’Elia et al. (1974) compared the anxiolytic effect of doxepin with diazepam. The authors recruited 47 patients with anxiety who were randomized into the doxepin and diazepam arms. Similar formulations of the two drugs in color, shape, size, and taste were administered for eight weeks at fixed doses in the first week and varied according to the protocol after the fourth week. Anxiety was rated using a validated rating scale at the start of the trial and after two, four, and eight weeks of treatment. Data analysis included descriptive statistics for demographic characteristics, severity of anxiety, adverse drug reactions, social functioning, etiology, and prognosis. The student t-test was used to compare pre-and post-test group characteristics. The authors found no significant differences in the efficacies of doxepin and diazepam in the treatment of anxiety.
Kleber (1980) compared the efficacy of ketazolam, diazepam, and placebo in a 28-day, double-blind randomized controlled trial. Fifty-six patients with moderate to severe anxiety for more than a month and without psychosis or depression were randomized into the ketazolam, diazepam, or two placebo arms. Responses were measured using the HAS, Physician’s Global Impressions, Target Symptoms, Self-Rating Symptom Scale, and Patient’s Global Impressions at the beginning of the trial and after one, two, and four weeks. One-way analysis of variance (ANOVA) was used to analyze primary and secondary efficacy outcomes and compare baseline and endpoint scores. The HAS mean total scores for ketazolam were significantly better than placebo in Weeks 2 and 4; HAS mean total scores did not differ from those of place in all the assessments. Ketazolam was also superior to diazepam in the Physicians Global Impressions measurements.
He et al. (2019) performed a network meta-analysis of fluoxetine, paroxetine, sertraline, fluvoxamine, citalopram, escitalopram, duloxetine, venlafaxine, vilazodone, levomilnacipran, and vortioxetine in the treatment of generalized anxiety disorder. The authors sought to determine the best drug for GAD in terms of efficacy and safety using combined evidence from direct and indirect comparisons in randomized controlled trials. He et al. (2019) concluded that duloxetine, venlafaxine, and escitalopram were more effective than vortioxetine, and vortioxetine and escitalopram were more acceptable than vilazodone. The authors defined efficacy in anxiolytic treatment as the Hamilton Anxiety Score (HAS) weighted mean difference. Therefore, the sample data provided will be treated as absolute reductions in HAS after treatment with the two drugs.
Research Hypothesis
The research hypothesis captures the researcher’s actual belief about the relationships between the comparative treatments. It can be stated as a lack of equality (negating the null hypothesis) or a prediction in the direction of the difference, starting that drug A is more or less effective than B. In this study, a prediction of the direction of the difference was not made. Therefore, the research hypothesis is stated as follows: H1: Drug A and drug B have different efficacies in anxiety treatment, and null hypothesis as H0: There is no difference in the effectiveness of drugs A and B in treating anxiety.
Choice of Test Method
In this scenario, a two-tailed test is appropriate as the research hypothesis does not predict the direction of the effect. Consequently, point estimates of the impact falling into either the lower or upper tails of the confidence interval of the population mean will be interpreted as significant and provide enough basis for rejecting the null hypothesis. Since an alpha-value of 0.05 has been chosen for the scenario, the critical regions will be ± α/2, equal to ± 0.025.
Sample and Sampling Method
Sixty participants were selected from among patients attending a mental health clinic for treatment of anxiety. The selection criteria and informed consent forms were prepared before recruitment. The study used purposive sampling to select 60 participants who will be randomized to either arm. Purposive sampling is appropriate since the study will apply predetermined inclusion criteria, such as accepting participants with HAS scores within a predetermined range informed by treatment guidelines and relevant to the study objectives.
Limitation of Sampling Method
The purposive sampling method may introduce selection bias in the study; however, randomization of participants fulfilling selection criteria reduces the risk of bias by reducing allocation bias. Biased samples are not representative of the population of patients diagnosed with anxiety. Consequently, findings from studies using unrepresentative (non-random) samples are not generalizable to the population.
Collection of Demographic Data
Descriptive data, such as age, gender, race, and income levels, is typically collected in studies recruiting participants from the general population. Descriptive characteristics provide additional metrics to ascertain the effectiveness of the sampling method to yield a representative sample. At the same time, the data supports granular analyses, for example, differences in effectiveness across genders, and may help identify confounding variables that enhance the quality of the inferences and generalizability of research findings.
Findings
The provided data set was assumed to contain reductions in HAS after both drugs had been administered for four weeks. All the participants completed the treatment, thus eligible for per protocol analysis. A two-sided student t-test was used to compare the means and test the significance of the difference. Group1, equivalent to drug A, had an average reduction of 5.6, and Group2, equivalent to drug B, had an average decrease of 7.3. The calculated p-value for obtaining such means from a sample of 30 is 0.000651, which is lower than 0.025. Therefore, we conclude that drug B is more effective than drug A in treating anxiety.

References
D’Elia, G., Von Knorring, L., Marcusson, J., Mattsson, B., Perris, C., & Persson, G. (1974). A double blind comparison between doxepin and diazepam in the treatment of states of anxiety. Acta Psychiatrica Scandinavica, 50(s255), 35–46. https://doi.org/10.1111/j.1600-0447.1974.tb08892.x
He, H., Xiang, Y., Gao, F., Bai, L., Gao, F., Fan, Y., Lyu, J., & Ma, X. (2019). Comparative efficacy and acceptability of first-line drugs for the acute treatment of generalized anxiety disorder in adults: A network meta-analysis. Journal of Psychiatric Research, 118, 21–30. https://doi.org/10.1016/j.jpsychires.2019.08.009
Kleber, R. J. (1980). Ketazolam compared to diazepam and placebo in the treatment of anxiety. Journal of International Medical Research, 8(6), 439–445. https://doi.org/10.1177/030006058000800615