Contents
What does it mean if the confidence interval contains 0?
Zero is the null value of the parameter (in this case the difference in means). If a 95% confidence interval includes the null value, then there is no statistically meaningful or statistically significant difference between the groups.
Why is a confidence interval not a probability?
The main reason that any particular 95% confidence interval does not imply a 95% chance of containing the mean is because the confidence interval is an answer to a different question, so it is only the right answer when the answer to the two questions happens to have the same numerical solution.
What is the 95% confidence interval for the population?
A sample that had two data points, each with values of 6 has a sample mean of 6. A 95% confidence interval for the population mean would be 4.6 to 7.4. This clearly does not overlap with 95% of the normal distribution, so it will not contain 95% of the population.
Can a null be rejected in a 95% confidence interval?
Conversely, if the null is contained within the 95% confidence interval, then the null is one of the values that is consistent with the observed data, so the null hypothesis cannot be rejected.
Can a confidence interval tell the true value of an estimate?
Confidence intervals are sometimes interpreted as saying that the ‘true value’ of your estimate lies within the bounds of the confidence interval. This is not the case. The confidence interval cannot tell you how likely it is that you found the true value of your statistical estimate because it is based on a sample, not on the whole population.
Are there margin of error in confidence intervals?
While there is a margin of error associated with a confidence interval, there are other places that errors can creep into a statistical analysis. A couple of examples of these kinds of errors could be from an incorrect design of the experiment, bias in the sampling or an inability to obtain data from a certain subset of the population.