What is the difference between 95% confidence level and 99% confidence level?

A 95% confidence interval is a range of values that you can be 95% certain contains the true mean of the population. This is not the same as a range that contains 95% of the values. The graph below emphasizes this distinction.

The graph shows three samples (of different size) all sampled from the same population.

With the small sample on the left, the 95% confidence interval is similar to the range of the data. But only a tiny fraction of the values in the large sample on the right lie within the confidence interval. This makes sense. The 95% confidence interval defines a range of values that you can be 95% certain contains the population mean. With large samples, you know that mean with much more precision than you do with a small sample, so the confidence interval is quite narrow when computed from a large sample.

Don't view a confidence interval and misinterpret it as the range that contains 95% of the values.

A 95% chance of what?

It is correct to say that there is a 95% chance that the confidence interval you calculated contains the true population mean. It is not quite correct to say that there is a 95% chance that the population mean lies within the interval.

What's the difference?

The population mean has one value. You don't know what it is (unless you are doing simulations) but it has one value. If you repeated the experiment, that value wouldn't change (and you still wouldn't know what it is). Therefore it isn't strictly correct to ask about the probability that the population mean lies within a certain range.

In contrast, the confidence interval you compute depends on the data you happened to collect. If you repeated the experiment, your confidence interval would almost certainly be different. So it is OK to ask about the probability that the interval contains the population mean.

It is not quite correct to ask about the probability that the population mean is within the interval. It either is in the interval or it isn't. There is no chance about it. What you can say is that if you perform this kind of experiment many times, the confidence intervals would not all be the same, you would expect 95% of them to contain the population mean, you would expect 5% of the confidence intervals to not include the population mean, and you would never know whether the interval from a particular experiment contained the population mean or not.

Nothing special about 95%

While confidence intervals are usually expressed with 95% confidence, this is just a tradition. Confidence intervals can be computed for any desired degree of confidence.

People are often surprised to learn that 99% confidence intervals are wider than 95% intervals, and 90% intervals are narrower. But this makes perfect sense. If you want more confidence that an interval contains the true parameter, then the intervals will be wider. If you want to be 100.000% sure that an interval contains the true population, it has to contain every possible value so be very wide. If you are willing to be only 50% sure that an interval contains the true value, then it can be much narrower.

We’ve seen what the mean police confidence scores are for men and women in our survey sample. What are the potential police confidence mean scores for men and women in the entire population?

Another way to look at our measure of police confidence is to calculate confidence intervals. Our dataset, while quite comprehensive, only includes information about our sample,the 42,604 people who answered questions regarding their confidence in the police. We can calculate the means of variable values in our dataset, but we cannot be one hundred percent certain that the CSEW sample is representative of the true means across the entire population of England and Wales. We can, however, calculate a range of values within which the mean across the entire population is likely to fall. This range of values is called a confidence interval. It is possible to calculate a 95% confidence interval and a 99% confidence interval. These intervals are simply a way of giving a range of values that we are fairly (either 95% or 99%) confident includes the true population mean.

A 99% confidence interval will allow you to be more confident that the true value in the population is represented in the interval. However, it gives a wider interval than a 95% confidence interval. For most analyses, it is acceptable to use a 95% confidence interval to extend your results to the general population.

So, let’s begin by calculating a 95% confidence interval for the mean level of confidence in the police.

Select Analyze, Descriptive Statistics, and then Explore.

Move policeconf1 to the Dependent List box and then click OK.

Your output table should look like the one on the right.

You can see in the table above that the Lower Bound of our 95% Confidence Interval is 13.4856 and the Upper Bound is 13.5675. We can interpret these results by saying that we are 95% confident the mean score for confidence in the police for all people in England and Wales will fall between 13.4856 and 13.5675. This is a simple interpretation of the interval – there are more nuances to the actual interpretation – but this will be adequate for now.

Now we can calculate a 99% confidence interval for mean confidence in the police.

Select Analyze, Descriptive Statistics, and then Explore.

Our variable policeconf1 should still be in the Dependent List box. Click on the Statistics tab on the upper right. In the dialogue box that opens, make sure Descriptives is marked and change the Confidence Interval for Mean from 95% to 99%.

Your output should look like the table on the right.

What is the 99% confidence interval for mean confidence in the police?

How would you interpret this confidence interval?

Summary

You’ve just calculated 95% and 99% confidence intervals using the data in our continuous variable, policeconf1. Confidence intervals allow us to generalize our findings from the samples from which our data was taken to the population from which our survey sample was drawn. This ability to generalize one’s findings is often very helpful in social science research.

What is the difference between the 95% and 99% confidence level?

Should I use 95 or 99 confidence interval?

Why is the 99% confidence interval larger than the 95% interval?

What is the 99% confidence level?