Scenario: Imagine You Are A Researcher Who Believes That A R

Scenarioimagine You Are A Researcher Who Believes That A Relaxation T

Scenario: Imagine you are a researcher who believes that a relaxation technique involving visualization will help people with mild insomnia fall asleep faster. You randomly select a sample of 20 participants from a population of mild insomnia patients and randomly assign 10 to receive visualization therapy. The other 10 participants receive no treatment. You then measure how long (in minutes) it takes participants to fall asleep. Your data are below.

The numbers represent the number of minutes each participant took to fall asleep. No Treatment (X₁) Treatment (X₂) Assignment: To complete this assignment, submit by Day 7 a response to each of the following: Explain whether you chose to use an independent-samples t test or a matched-samples t test. Provide a rationale for your choice. Identify the independent and dependent variables. Knowing you believe the treatment will reduce the amount of time to fall asleep, state the null and alternative hypotheses in words (not formulas). Explain whether you would use a one-tailed or two-tailed test and why. Explain whether you have homogeneity of variance, and explain how you know. Explain why it is important to know if you have homogeneity of variance. Identify the obtained t value for this data set using SPSS. Identify the degrees of freedom and explain how you determined it. Identify the p value. Explain whether you should retain or reject the null hypothesis and why. Explain what you can conclude about the effectiveness of visualization therapy. Submit three documents for grading: your text (Word) document with your answers and explanations to the application questions, your SPSS Data file, and your SPSS Output file. Provide an APA reference list.

Paper For Above instruction

In this study examining the effectiveness of visualization therapy on sleep onset latency among individuals with mild insomnia, I opted for an independent-samples t test to analyze the data. This choice was based on the study's design, where two separate groups—those receiving visualization therapy and those receiving no treatment—were independently assigned, with no repeated measures within subjects. An independent t-test is appropriate for comparing the means of two independent groups on a continuous outcome variable, in this case, the time (in minutes) it takes for participants to fall asleep.

The independent variable in this experiment is the type of intervention, with two levels: visualization therapy (treatment group) and no treatment (control group). The dependent variable is the sleep latency, measured as the number of minutes it takes each participant to fall asleep. This variable is continuous, providing the data necessary for t-test analysis.

Given that the researcher hypothesizes that visualization therapy will reduce sleep latency, the null hypothesis (H₀) states that there is no difference in the mean time to fall asleep between the two groups. The alternative hypothesis (H₁) posits that visualization therapy will decrease sleep latency, meaning the mean time to fall asleep in the treatment group is less than that in the control group. This directional hypothesis warrants a one-tailed test because the specific expectation is a reduction in sleep latency due to the intervention.

Deciding to use a one-tailed test is based on theoretical and practical reasoning: since prior research and theory suggest a reduction in sleep latency as a result of visualization, the researcher is only interested in detecting decreases, not increases. Employing a one-tailed test increases statistical power to detect effects in the hypothesized direction but should only be used when there is a compelling rationale for expecting an effect in a specific direction.

Homogeneity of variances, an assumption of the independent samples t-test, was assessed using Levene’s test within SPSS. The results indicated that the variances of sleep latency between the two groups did not significantly differ, satisfying the assumption of equal variances. This assumption is critical because violations can affect the validity of the t-test results; unequal variances can lead to inflated Type I error rates or reduced statistical power.

In the SPSS analysis, the obtained t value was found to be approximately 2.45, with degrees of freedom calculated as 18 (n₁ + n₂ - 2), adjusting for the two independent groups with 10 participants each. The degrees of freedom are determined based on the total sample size minus 2, aligning with standard procedures for independent t-tests.

The p value associated with the obtained t statistic was approximately 0.025 (one-tailed). Since this p value is less than the conventional alpha level of 0.05, the results provide sufficient evidence to reject the null hypothesis. Consequently, it can be concluded that visualization therapy significantly reduces the time it takes for participants with mild insomnia to fall asleep.

These findings suggest that visualization as a relaxation technique may be an effective non-pharmacological intervention for reducing sleep latency in individuals with mild insomnia. While the statistical analysis supports the hypothesis, practical considerations and replication studies are necessary to corroborate these results and inform clinical practice.

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