Can lower limit confidence interval negative?

As a statistical expert with extensive experience in data analysis and interpretation, I can provide an in-depth explanation of confidence intervals and address your question regarding the possibility of a lower limit being negative. Confidence intervals are a fundamental concept in statistical inference. They provide a range of values that are likely to contain the true population parameter with a certain level of confidence, often 95%. This means that if you were to take many samples from the same population and calculate a 95% confidence interval for each sample, about 95% of those intervals would contain the true population parameter. The lower limit of a confidence interval is not inherently restricted to being positive or negative. It is determined by the sample data and the statistical method used to calculate the interval. The lower limit can be negative if the sample data and the method of calculation result in a negative value for that limit. The 95% confidence interval specifically refers to the range that encompasses the true mean difference with 95% certainty. This interval can indeed include negative numbers. The reason for this is straightforward: if the difference in means (between two groups or over time) is negative based on the sample data, then the confidence interval reflects that possibility. It's important to note that a negative difference in means implies that the first group or earlier time period has a lower mean than the second group or later time period. Let's consider an example to illustrate this. Suppose you are comparing the average test scores of two groups of students, Group A and Group B. If the average score of Group A is lower than that of Group B, the difference in means will be negative. When you calculate a 95% confidence interval for this difference, it will start with a negative number (the lower limit) and extend to a positive number (the upper limit), assuming that the interval does not cross zero. The interpretation of a confidence interval is crucial. A 95% confidence interval does not mean there is a 95% chance that the interval contains the true parameter. Instead, it means that if the data collection process were repeated many times, 95% of the calculated confidence intervals would contain the true parameter. It's a statement about the method's reliability, not the probability of a particular interval containing the parameter. In summary, the lower limit of a confidence interval can be negative, reflecting the possibility that the true mean difference is negative. The confidence interval provides a range that encapsulates the uncertainty in the estimate of the true mean difference, and it is calculated based on the sample data and the chosen confidence level.

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.