Question

Consider an experiment taste-testing six types of chocolate chip cookies: 1 (brand A, chewy, expensive), 2 (brand A, crispy, expensive), 3 (brand B, chewy, inexpensive), 4 (brand B, crispy, inexpensive), 5 (brand C, chewy, expensive), 6 (brand D, crispy, inexpensive). We will use twenty different raters randomly assigned to each type (120 total raters). I have constructed five preplanned contrasts for these treatments, and I obtain p-values of .03, .04, .23, .47, and .68 for these contrasts. Discuss how you would assess the statistical significance of these contrasts, including what issues need to be resolved.

Answer 1

Statistical significance of chocolate cookie taste-test contrasts must consider multiple comparison adjustments. P-values below 0.05 suggest significance but require reassessment with methods like the Bonferroni correction or Tukey's method.

Step-by-step explanation:

The student's question relates to an experiment taste-testing six types of chocolate chip cookies and the statistical significance of preplanned contrasts obtained from that experiment. In assessing the statistical significance of these contrasts, several issues must be resolved. When multiple tests are performed, as with multiple contrasts, there is an increased chance of a Type I error—rejecting a true null hypothesis. Therefore, we must adjust for multiple comparisons to maintain the overall error rate—common methods include Bonferroni correction or Tukey's method. A p-value less than 0.05 often indicates statistical significance. However, after adjustment for multiple comparisons, some of these contrasts' p-values may not indicate significance. In the present instance, with original p-values of .03, .04, .23, .47, and .68, the contrasts corresponding to the first two p-values may indicate a significant difference, but this would need to be re-evaluated after the adjustment.