Question

-Formulate both null and alternative hypotheses for the client, and explain why the hypotheses need to be directional or non-directional.

-Determine what statistical test should be used to analyze the data.

-Summarize all information used to determine the correct statistical test (e.g., number of groups, type of data collected, independent or repeated measures)

-Provide a sample size and critical values in relation to the hypothesis.

-State what statistical test should be used (be specific since you have all of the information you need to determine the critical value(s)).

-Discuss what the statistical analysis will do in answering the hypotheses and question(s) for the client. Also discuss any potential problems to watch out for, including an appropriate sample size to meet the assumptions of the statistical test.

Client Scenario: Jackson Hole Mind and Body Works

My name is Jane, and I am a licensed counselor who owns a business in Jackson Hole, Wyoming. This past year, I started a couple laughing yoga classes that combine the anxiety removing benefits of yoga with the emotional release of laughter. It has been a lot of fun and many clients love it, but a competitor has been criticizing my new approach as a sham and quackery. I am confident that my laughing yoga classes are beneficial, but I would like you to perform a study that examines the impact of my approaches from a scientific perspective. I know that science needs to be objective, so I would like you to setup a study for me as a nonbiased researcher. My thoughts are that I could give you the email addresses of clients who are willing to be in the study, and you would ask each of them questions, and then analyze the results.

            I would like you to examine two types of therapy I conduct, my laughing yoga therapy and my more traditional cognitive behavioral therapy.   I expect that 40 participants will be available from my laughing yoga classes, and that 50 participants will be available from my traditional cognitive behavioral therapy sessions. It would be nice if you asked questions related to clients’ current healthy living practices and use of positive emotions. You can determine the exact questions to ask clients. I was thinking that I would offer each participant in the study a couple free smoothie drinks at a local juice bar for participating in the research.

Answer 1

For the given scenario Jane wants to check the hypothesis or claim whether the laughing yoga therapy is more effective than the traditional cognitive behavioural therapy. For checking this claim, the null and alternative hypothesis is given below:

Null hypothesis: H₀: There is no any statistically significant difference in the laughing yoga therapy and traditional cognitive behavioural therapy.

Alternative hypothesis: H_a: The laughing yoga therapy is more effective than the traditional cognitive behavioural therapy.

For checking above hypotheses we will use the two sample t-test for checking the significant difference in the two population means. We will use the one-tailed test or upper tailed / right-tailed test for this scenario. The symbolic hypotheses are given as below:

H₀: µ₁ = µ₂ vs. H_a: µ₁ > µ₂, one-tailed/upper tailed test

Where, µ₁ = mean score for laughing yoga therapy and µ₂ is mean score for traditional cognitive behavioural therapy.

From the given information we are given n₁ = 40 for laughing yoga therapy and n₂ = 50 for traditional cognitive behavioural therapy. We will assume 5% level of significance and separate population variances for this test.

After finding out the average scores and standard deviations for the samples for both methodologies, we will find out the test statistic value by using the following formula:

t = (X1bar – X2bar) / sqrt[(S₁² / n₁)+(S₂² / n₂)]

Also, we will find the critical value and P-value by using the t-table or excel or any other calculator or software. Based on the comparison between the p-value and alpha value or test statistic and critical value, we will take the proper decision regarding the null hypothesis.