A researcher is interested in whether herbal remedies are effective in relieving allergies, and
if so, which ones are most effective. The researcher takes a group of 20 allergy sufferers and randomly assigns each one to receive herbal tea, a homeopathic administration of
allergens, a traditional antihistamine, or a placebo pill. The dependent measure is the number of allergy complaints by patients during weeks 2-3 of the treatments. The research
analyzed the data using an ANOVA, which resulted in the following table:
Analysis of Variance for Herbal Remedies
DF SS MS F P
Group 3 43.75 14.583 6.01 0.000
Error 16 38.80 2.425
Total 19 82.55
Using the above table, we can conclude that:
a. the data provide strong evidence that allergy complaints are related to herbal remedies.
b. the data provide strong evidence that allergy complaints are related to herbal remedies
in the following way: The mean number of allergy complaints for people who take
placebo pills is higher than The mean number of allergy complaints for people who take
herbal tea, which in turn is higher than the mean number of allergy complaints for people
who take homeopathics or traditional antihistamines.
c. the data provide strong evidence that the four mean allergy complaint scores
(representing the four allergy remedies) are all equal.
d. the data do not provide sufficient evidence that allergy complaints are related to herbal remedies
Based on the information provided in the ANOVA table, we can conclude that:
a. the data provide strong evidence that allergy complaints are related to herbal remedies.
This is because the p-value (0.000) is less than the predetermined significance level (usually 0.05), indicating that the result is statistically significant. In other words, there is a strong likelihood that the observed differences in allergy complaints between the herbal remedies are not due to chance.
b. the data provide strong evidence that allergy complaints are related to herbal remedies in the following way: The mean number of allergy complaints for people who take placebo pills is higher than the mean number of allergy complaints for people who take herbal tea, which in turn is higher than the mean number of allergy complaints for people who take homeopathics or traditional antihistamines.
This conclusion goes beyond what can be directly inferred from the ANOVA table. The table provides information about the overall statistical significance of the herbal remedies, but it does not provide specific details about differences between each remedy. To make these comparisons, post-hoc tests like Tukey's Honestly Significant Difference (HSD) test or Bonferroni correction can be conducted.
c. the data provide strong evidence that the four mean allergy complaint scores (representing the four allergy remedies) are all equal.
This conclusion contradicts the information in the ANOVA table. The ANOVA F-value (6.01) suggests that there is variability in the mean allergy complaint scores between the herbal remedies.
d. the data do not provide sufficient evidence that allergy complaints are related to herbal remedies.
This conclusion is incorrect based on the ANOVA table. The low p-value (0.000) indicates that there is indeed strong evidence to suggest a relationship between allergy complaints and herbal remedies.