What Statistical Test would you run to determine if the different therapies have different effects on mental health?

A team of psychiatric nurses designed a study in which 12 psychiatric patients diagnosed as having Generalized Anxiety Disorder were randomly assigned to one of three new types of therapy, here labeled X, Y, and Z. One year after therapy, the patients’ overall mental health scores were as follows:

 

Mental Health Assessment

Therapy X   Therapy Y         Therapy Z

85                 78                     79

79                 81                     83

84                 68                     75

67                 75                     74

 

What Statistical Test would you run to determine if the different therapies have different effects on mental health? (Don’t forget to tell me what the p level should be). State the Null and Alternative Hypotheses. Please run the test and paste any relevant information below, then interpret your findings.

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