In: Statistics and Probability
A researcher is interested in evaluating two different treatments developed to treat depression. Test her hypothesis that the treatments lead to different results. Her data are below (a higher value indicates higher depression). YOU NEED TO CALCULATE THE MEANS AND THE STANDARD DEVIATIONS FOR YOUR DATA.
Relaxation Meditation
24 32
22 32
31 27
27 23
23 38
34 34
28 23
Formulate the hypotheses.
Determine the critical value(s).
Calculate the test statistic.
Calculate and evaluate Cohen’s d and r2.
What decision can you make and what does it indicate?
What type of error could you be making and what would that mean?
Report your results with an APA-style phrase.
From the givend data
(1) Null and Alternative Hypothesis:
H0: The two methods give same result
H1: The two methdos give differnt result
(2) Critical t: ±2.17882
Reject H0 if t value is not in t critical values
(3) Test Statistic:
(4)
It is medium effect
(5) since t value is in t critical values so we accept H0
(6) Type I error: The sample results give there exist significant difference between the two methods but fact is no difference between two methods
Type II error: The sample results give there exist no significant difference between two methods but fact is significant difference between two methods
(7) We conclude that there is no significant difference between the means of two methods. i.e. The two methods give same result