Question

A - In comparing a treatment population with the control we found a difference in means of 35%,P<0.05. B - In comparing a treatment population with the control we found a difference in means of 35%,P<0.10. C - In comparing a treatment population with the control we found a difference in means of 0.3%,P<0.05. The results in A are substantial and significant. The results in B are substantial and not significant. The results in C are significant, but not substantial. The results in A are substantial and significant. The results in B are substantial and significant. The results in C are significant, but not substantial. The results in A are substantial and significant. The results in B are substantial and not significant. The results in C are significant and substantial. None of the above

Answer 1

We were asked to evaluate the correctness of three statements: A, B, and C:

A - substantial (difference in means = 35%) and significant (P<0.05)
B - substantial (difference in means = 35%) but not significant (P>0.05)
C - not substantial (difference in means = 0.3%) but significant (P<0.05)

Considering these, let's break down each statement to fully understand what they're saying.

In statement A, the difference in means is 35%, which is considered substantial or large. Also, the p-value is less than 0.05, which makes this difference statistically significant. Hence, statement A is correct.

In statement B, while the difference in means is still substantial at 35%, this time the p-value is greater than 0.05, meaning the difference is not statistically significant. This can occur when the sample size is small, or there's a great deal of variability in the data. Hence, statement B is not correct.

In statement C, the difference in means is very small, only 0.3% and therefore not substantial. However, the p-value is less than 0.05, which makes this difference statistically significant. That can happen if the sample size is huge, even very small differences can become statistically significant. Hence, statement C is not correct.

So, in light of this analysis, only the first statement is correct which states that the difference is both substantial (35%) and significant (P<0.05). Thus, the answer to the question is A.