In this article, we are going to talk in depth about confidence interval including its meaning, importance, statistical significance, and so on.
Confidence intervals(CI) are basic statistical concepts. A confidence interval represents the possibility that a parameter will fall between two values around the mean. It expresses the degree of uncertainty surrounding a certain result. We normally use them with a margin of error. Confidence intervals are calculated and expressed as a percentage, mainly using confidence levels of 95 percent or 99 percent. We’ll have a better idea of those percentages in a few moments.
The confidence interval estimate (CI) for both continuous and categorical variables is a range of likely values for the population proportion based on:
The following is the formula for calculating Confidence Interval for the mean:
If you’re still uncertain about what a confidence interval is or what it does, let me explain it to you in a different way.
The first thing that you must note is how statistics is all about estimation/prediction/forecasting. We devise various methods only to be able to predict things and draw conclusions. We also happen to find various ways to make sure that our prediction is accurate(Prediction accuracy plays a role there.) It all begins with estimation and then analyzing that estimation based on past events and examining its accuracy. Now that we’ve clarified this notion, let’s look at whether the confidence interval is a tool for estimating or not.
You know how, normally, when we want to draw conclusions about a population, we take a sample from that population. We ask them to fill out certain survey forms or polls. And then the results that we get from those are what we assume are the results for the entire group of population for which we want to draw conclusions. But, if you asked the entire population to fill out the survey forms and polls, would you get the same conclusion as you did from examining the sample? This is when the confidence interval comes into play. It shows how certain you are that the findings of a poll or survey are representative of what you would expect to discover if you had asked the entire population to fill out the same survey forms or polls.
When attempting to calculate a confidence interval, the following assumptions must be made:
A confidence level of 95% indicates that if the survey or experiment were repeated, the data would match the results from the full population 95% of the time. As I demonstrated with the confidence interval example previously, we don’t always have the time to poll/survey everyone. But what would happen if we did? With a 95% confidence level, you can almost be confident that your results are the same as if you surveyed everyone.
A confidence interval for the mean is a method of determining the real population mean. Instead of providing you with a single value for the mean, a confidence interval provides both, a lower and upper estimate.
The following is the formula for calculating CI for the Mean:
In Excel, we will compute the 95 percent confidence range for the mean. The following is the sample data that we will be using:
The first step will be to enter this information into a single column in Excel. I entered the information into cells A1 through A20.
This is what the data looks like currently:
The second thing we’ll do is go to the “Data” tab and then to the “Data Analysis” option in the upper right corner.
After that, we’ll click “Descriptive Statistics” and then “OK.”
We must now fill in the blanks to convey to Excel what we need to generate.
This is what your tab will look like:
Once you have clicked “OK“, the following are the results you will encounter:
The confidence level we get for this data is 45.82902071. A confidence level of 95% or higher is generally considered ideal.
The term “asymmetric confidence interval” simply refers to the fact that the point estimate does not fall directly in the middle of the CI. If you don’t follow the assumptions, this can happen. However, this frequently arises when the interval contains a random error or unsystematic error or systematic bias. Systematic bias is a type of measuring inaccuracy that is directional. Positive systematic bias increases the upper bound of a confidence interval, whereas negative systematic bias decreases the lower bound of a confidence interval.