A randomized comparative experiment compared the effects of two types of deep-brain stimulation (pallidal stimulation and subthalamic stimulation) on change in motor function, as blindly assessed on the Unified Parkinson's Disease Rating Scale, part III (UPDRS-III). The abstract of the study said: "Mean changes in the primary outcome did not differ significantly between the two study group (P = 0.50)." The P-value refers to a null hypothesis of "no change" in measurements between pallidal stimulation. Explain clearly why this value provides no evidence of change.
If P = 0.50, it is indicating that the difference would be found 50% of the time solely by chance.
THE NULL ALWAYS STATED THAT THERE IS NO RELATION BETWEEN THE TWO VARIABLES.
To understand why the given P-value of 0.50 provides no evidence of change, it is important to first understand what a P-value represents in the context of hypothesis testing.
In statistical hypothesis testing, the P-value is a measure of the strength of evidence against a null hypothesis. The null hypothesis, in this case, states that there is "no change" in the measurements between pallidal stimulation. The alternative hypothesis would then suggest that there is a difference between the two types of deep-brain stimulation.
The P-value provides the probability of observing a test statistic (or more extreme) under the assumption that the null hypothesis is true. If the P-value is small (typically below a predetermined significance level, such as 0.05), it suggests that the observed data is unlikely to have occurred if the null hypothesis were true. In other words, a small P-value indicates strong evidence against the null hypothesis.
However, in this case, the given P-value is 0.50, which is larger than the typical significance level of 0.05. This means that if the null hypothesis of "no change" were true, there is a 50% chance of obtaining a test statistic as extreme as the one observed (or even more extreme) simply due to random chance.
Based on this interpretation, the high P-value of 0.50 provides no significant evidence against the null hypothesis. It suggests that the observed data is fairly consistent with the assumption of "no change" between the two types of deep-brain stimulation. Hence, there is no reason to conclude that there is a difference in motor function change between pallidal stimulation and subthalamic stimulation based on the given study's findings.