Question

according to the simple linear regression result above.

Interpret the results in terms suitable for the clinician, describing the statistical strength of evidence and possible clinical importance [Note, as a guide, that a difference of 5 in Methicillin DDDs would be of clinical importance.].

Note: MRSA, in this case, is a binary variable and Methicillin is a continuous variable.

Where I am confused is that since p=0.711 there is no doubt that the null hypothesis is accepted, but since both 5 and -5 lies in the 95%CI, does it indicates that there is still a possibility that clinical importance exists.

Ho: there is no difference between MRSA and non-MRSA children in Methicillin.

Answer 1

According to the results of the simple linear regression:

Methicillin = 1.17*mrca + 74.93

As mrca is a binary variable, we need to look at the coefficient of mrca to see whether there is a difference in Methicillion DDDs between MRSA and non-MRSA children

As the p-value = 0.711 > 0.05, we fail to reject the null hypothesis. Hence, we can conclude that there is no statistical evidence to say that there is a difference.

But if we look at the confidence interval of the coefficient of mrsa, it is (-5.02, 7.35). The true coefficient can be more than 5 or less than -5. This is the interval which is likely to contain the true population coefficient. Hence, there is a possibility that the absolute difference is 5 or more OR a possibility that the absolute value of the coefficient is 5 or more. Hence, we can say that there is a possible clinical importance, however we cannot be sure.