As a statistical expert, I can tell you that the concept of a "negative mean difference" is a fundamental aspect of statistical analysis, particularly in the context of comparing two groups or sets of data. When we talk about mean differences, we are often referring to the difference between the means of two groups, such as the difference in average scores between two different treatments in an experiment, or the difference in average income between two different regions. In statistics, a negative mean difference indicates that the mean of one group is less than the mean of another group. This can occur in various scenarios, such as when evaluating the effectiveness of a new drug compared to a placebo, where a negative difference would suggest that the new drug is less effective. It's also possible in economic studies where a negative difference might indicate a decline in some economic indicator. Now, let's delve into the concept of a confidence interval (CI). A confidence interval is a range that we can say, with a certain level of confidence (e.g., 95%), contains the true mean difference between two groups. This range is derived from a sample and is used to make inferences about the population from which the sample was drawn. The 95% confidence interval mentioned in the reference material is a statistical tool that provides a range for the true mean difference. This interval is constructed using a sample mean difference and the standard error of the mean difference. The interval is calculated in such a way that if we were to take many samples and calculate the confidence interval for each, approximately 95% of those intervals would contain the true mean difference. It's important to note that the confidence interval can indeed include negative numbers. This is because the difference in means can be negative, and the confidence interval is meant to reflect the range of plausible values for the true mean difference. If the confidence interval includes zero, it suggests that there may not be a statistically significant difference between the two groups. However, if the entire confidence interval is below zero, it indicates that the mean of the first group is likely less than the mean of the second group, and vice versa. In summary, a negative mean difference is a common occurrence in statistical analysis and can be a significant finding depending on the context of the study. The confidence interval is a valuable tool for understanding the range within which the true mean difference is likely to fall, and it can certainly encompass negative values, reflecting the possibility of a negative mean difference. read more >>

The 95% confidence interval is providing a range that you are 95% confident the true difference in means falls in. Thus, the CI can include negative numbers, because the difference in means may be negative.read more >>