# Are confidence intervals difficult in statistics

## Ways to increase the accuracy of the confidence interval

### Increase the sample

Often the easiest way to reduce the margin of error is to increase the sample size. As a rule, the larger the number of observations, the smaller the interval around the sample statistics. Therefore, by collecting more data, you can often get a more accurate estimate of the population parameter.

You should weigh the benefits of greater accuracy against the more time and resources required to collect a larger sample. For example, to get a confidence interval that is so small that it contains only the population parameter, you need to measure each audit unit in the population. It is obvious that such a strategy i. d. R. is unfit.

The smaller the variation in the data, the more accurately you can estimate a population parameter.

The reason for this is that a reduced spread of the data reduces the standard deviation and thus also the margin of error for the estimated value. Although it can be difficult to reduce the dispersion in your data, sometimes you can by adjusting the way you collect the data. For example, you can use a connected sample design to compare two groups. You could also potentially reduce variability by improving the process with greater consistency or more accurate measurements.

### Use a one-sided confidence interval

With a one-sided confidence interval, the margin of error is lower than with a two-sided confidence interval. However, a one-sided interval only indicates whether a parameter is smaller or larger than a cutoff value. A one-sided interval does not provide any information about the parameter in the opposite direction. Therefore, to improve the accuracy of an estimate, use a one-tailed confidence interval only when the estimate is likely to be either greater or less than a cutoff value, but not both.

For example, a beverage company wants to determine the amount of dissolved solids in its table water. The less dissolved solids, the better. When calculating a two-sided confidence interval, the upper limit of the interval is 18.4. Since the company is only interested in the upper limit, a one-sided confidence interval can be calculated instead. With a one-sided confidence interval, it is found that the upper limit for the amount of dissolved solids is even lower at 17.8 mg / L.

### Decreasing the confidence level

The advantage of a lower confidence level is that you get a narrower, more accurate confidence interval. The downside is less certainty that the confidence interval contains the population parameter that is relevant to you.

Therefore, lower the confidence level only if the advantage of higher accuracy outweighs the disadvantage of lower security in your situation. For example, if increasing the sample size in your study is too costly, the lower the confidence level, the narrower the interval, but at the expense of confidence.