What makes confidence interval wider

The size of the standard error is due to two elements:. One thing we can do is to increase the sample size. As a general guide, to halve the standard error the sample size must be quadrupled.

However, in cases where such precision is not required there is a point where the gain in precision is not worth the cost of increasing the size of the sample. The figures in Table 1 below were obtained for the average income of males and females in a fictitious survey for unemployment. How much better do males do than females in the income stakes? That, of course, is the difference in the sample. What is the difference between males and females likely to be in the population? Confidence intervals are focused on precision of estimates — confidently use them for that purpose!

What is a relative confidence limit? If for a given arithmetic mean value, 0. Your email address will not be published. Remember that there is variability in your outcomes and statistics. The more individual variation you see in your outcome, the less confidence you have in your statistics.

In addition, the smaller your sample size, the less comfortable you can be asserting that the statistics you calculate are representative of your population. A confidence interval provides a range of values that will capture the true population value a certain percentage of the time.

Confidence intervals use the variability of your data to assess the precision or accuracy of your estimated statistics. You can use confidence intervals to describe a single group or to compare two groups. We will not cover the statistical equations for a confidence interval here, but we will discuss several examples. Here the number 7 is your margin of error. For example, the odds ratio of 0.

As the confidence level increases, the confidence interval widens. There is logical correspondence between the confidence interval and the P value see Section If the P value is exactly 0. Together, the point estimate and confidence interval provide information to assess the clinical usefulness of the intervention.

Confidence intervals with different levels of confidence can demonstrate that there is differential evidence for different degrees of benefit or harm.

Confidence intervals are often seen on the news when the results of polls are released. This is an example from the Associate Press in October Emphasis added. Although it is not stated, the margin of error presented here was probably the 95 percent confidence interval.

In the simplest terms, this means that there is a 95 percent chance that between Conversely, there is a 5 percent chance that fewer than The precise statistical definition of the 95 percent confidence interval is that if the telephone poll were conducted times, 95 times the percent of respondents favoring Bob Dole would be within the calculated confidence intervals and five times the percent favoring Dole would be either higher or lower than the range of the confidence intervals.

Instead of 95 percent confidence intervals, you can also have confidence intervals based on different levels of significance, such as 90 percent or 99 percent.