WALDEN UNIVERSITY YOLANDA N. GEORGE-DAVID WEEK 4. ASSIGNMENT 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) 22 18 27 20 23 26 27 22 24 22 Treatment (X2) 19 17 24 21 27 21 23 18 19 22 Assignment: Explain whether you chose to use an independent-samples t-test or a matched-samples t test. Provide a rationale for your choice. The two variables (No Treatment X1 and Treatment X2) are independent of each other. I chose to use an independent-samples t-test because our resource defines Independent-samples t-test as the parametric procedure used to test sample means from two independent samples (Heiman 2015). Identify the independent and dependent variables. The dependent variable is the variable that measures a behavior or attribute of participants that we expect will be influenced by the independent variable. (Heiman 2015). The Dependent variable is the time it takes participants to fall asleep. Therefore, the independent variable is the treatment. Knowing you believe the treatment will reduce the amount of time to fall asleep, state the null and alternate hypotheses in words (not formulas). The null hypothesis is always the hypothesis of no difference (2015). With the two variables, there's no difference with the time to fall asleep whether treatment was given or not given. However, the Alternative Hypothesis is when the time to fall asleep is lower when treatment is given as compared to when no treatment is given. Explain whether you would use a one-tailed or two-tailed test and why. To be able to see if the treatments reduce the sleeping time, I would use a one-tailed test because a one-tailed test allows you to determine if one mean is greater or less than another mean, but not both. 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. Null Hypothesis, H0: There is no difference between the variances of Treatment X1 and No treatment X2. Compared to the alternative Hypothesis, H1: there is a difference between the variances of Treatment X1 and No treatment X2 I fail to reject Ho at 5% level of significance because p-value is 1.00 which is greater than alpha (0.05). Therefore, there is no difference between the variances of two groups (Treatment and No treatment). Hence decide to proceed with independent sample t-test with equal variances. Identify the obtained t value for this data set using SPSS. T value = 1.492 Identify the degrees of freedom and explain how you determined it. Degree of freedom = n1+n2-2 = 10+10-2 = 18 Identify the p value. p-value = 0.153 Explain whether you should retain or reject the null hypothesis and why. I reject H at 5% level of significance because P-Value = 1.00 and conclude that the time to fall asleep when treatment is less as compared to when no treatment is given. Explain what you can conclude about the effectiveness of visualization therapy. It is my conclusion that visualization therapy is effective. References: Heiman, Gary. Behavioral Sciences STAT 2, 2e, 2nd Edition. Cengage Learning, 2015. VitalBook file. L. Lehmann, E., & P. Romano, J. (N.D.). Testing Statistical Hypotheses (Third ed.). SPSS Output Group Statistics group Observation N Mean Std. Deviation Std. Error Mean no_treatment 10 23.10 2.961 .936 treatment 3.035 .960 10 21.10 Independent Samples Test Levene's Test t-test for Equality of Means for Equality of Variances F Sig. t df Sig. (2- Mean Std. Error 95% Confidence tailed) Difference Difference Interval of the Difference Lower Observation Equal variances assumed .000 1.000 1.492 18 .153 2.000 1.341 -.817 Upper 4.817 Equal variances not assumed 1.492 17.989 .153 2.000 1.341 -.817 4.817