A researcher is interested in determining whether acupuncture affects pain tolerance. An experiment is performed in which 15 students are randomly chosen from a large pool of university undergraduate volunteers. Each subject serves in two conditions. In both conditions, each subject receives a short-duration electric shock to the pulp of a tooth. The shock intensity is set to produce a moderate level of pain to the unanesthetized subject. After the shock is terminated, each subject rates the perceived level of pain on a scale of 0–10, with 10 being the highest level. In the experimental condition, each subject receives the appropriate acupuncture treatment prior to receiving the shock. The control condition is made as similar to the experimental condition as possible, except a placebo treatment is given instead of acupuncture. The two conditions are run on separate days at the same time of day. The pain ratings in the accompanying table are obtained.
a. What is the alternative hypothesis? Acupuncture treatment and placebo.
b. Once you have generated a hypothesis, the process of hypothesis testing becomes important, comparing your results against the null hypothesis. Assume a nondirectional hypothesis is appropriate.
c. What is the null hypothesis?
d. Using 0.052 tail, what is your conclusion?
One tail represents a positive effect or association; the other, a negative effect.) A one-tailed hypothesis has the statistical advantage of permitting a smaller sample size as compared to that permissible by a two-tailed hypothesis. Unfortunately, one-tailed hypotheses are not always appropriate; in fact, some investigators believe that they should never be used.
e. What error might you be making by your conclusion
f. in part c?
g. To what population does your conclusion apply?
h. Subject Acupuncture Placebo
i. 1 4 6
j. 2 2 5
k. 3 1 5
l. 4 5 3
m. 5 3 6
n. 6 2 4
o. 7 3 7
p. 8 2 6
q. 9 1 8
r. 10 4 3
s. 11 3 7
t. 12 4 8
u. 13 5 3
v. 14 2 5
w. 15 1 4
cognitive, health
a. The alternative hypothesis in this scenario would be that acupuncture affects pain tolerance, meaning that there is a difference in pain ratings between the acupuncture treatment and the placebo treatment.
b. Once you have generated the hypothesis, the next step is to compare the results against the null hypothesis through hypothesis testing. In this case, a nondirectional hypothesis is appropriate since we do not have any specific expectations about the direction of the effect.
c. The null hypothesis would state that there is no difference in pain ratings between the acupuncture treatment and the placebo treatment. In other words, acupuncture does not affect pain tolerance.
d. Using a 0.052 tail, we can draw a conclusion based on the p-value. If the p-value is less than 0.052, we would reject the null hypothesis and conclude that there is a significant difference in pain ratings between the acupuncture treatment and the placebo treatment.
e. The error you might be making by your conclusion in part c is a Type I error. This occurs when you reject the null hypothesis, even though it is true. In other words, you may mistakenly conclude that there is a significant difference in pain ratings when there is actually no difference.
f. To minimize the risk of making a Type I error, it is important to use appropriate statistical significance levels and consider using a two-tailed hypothesis test.
g. Your conclusion would apply to the population of university undergraduate volunteers from which the 15 students were randomly chosen. It should be noted that the generalizability of the conclusion may be limited to this specific population.
h-t-w: Subject | Acupuncture | Placebo
... i ............. 1 .................. 4 ............... 6
... j ............. 2 .................. 2 ............... 5
... k ............. 3 .................. 1 ............... 5
... l ............. 4 .................. 5 ............... 3
... m ............. 5 .................. 3 ............... 6
... n ............. 6 .................. 2 ............... 4
... o ............. 7 .................. 3 ............... 7
... p ............. 8 .................. 2 ............... 6
... q ............. 9 .................. 1 ............... 8
... r ............. 10 ............... 4 ............... 3
... s ............. 11 ............... 3 ............... 7
... t ............. 12 ............... 4 ............... 8
... u ............. 13 ............... 5 ............... 3
... v ............. 14 ............... 2 ............... 5
... w ............. 15 ............... 1 ............... 4
In this table, the pain ratings for each subject under the acupuncture and placebo conditions are provided.