Learn about Confidence Interval

Confidence Interval

What do you mean by Confidence Interval?

The Confidence Interval (short form- CI) is defined as the range of values that are likely to include a value of a population that lies between a specific degree of confidence. Confidence Interval is often written in terms of percentage% whereas, the mean of a population falls between the lower interval and higher interval.

In easy words, a confidence interval is defined as an interval in which the measurements of a try-out lie between the lower recorded value and highest recorded value (lowest or highest interval).

Easy Understanding of Confidence Intervals

1. A confidence interval displays the possibility that a parameter will lie between the highest or lowest value or somewhere close to the mean value.
2. In a sampling method, the degree of certainty or uncertainty is also measured by the Confidence Interval.
3. A confidence interval is often constructed by using levels of confidence of 99% or 95%.

Getting Familiar With the Concept of Confidence Intervals

Confidence intervals measure the degree of the certainty or uncertainty of a specimen method. This interval takes any number of possible limits with the common one being 99% or a 95% of confidence limit. 

Confidence Interval is measured using a method of statistics or a statistics based test called a T-Test. People who study Statistics as a profession use the concept of confidence intervals to measure the not certain nature of a sample.

For example- For example, if an individual constructs a confidence interval with a 95% or 99% confidence level, he/she is confident that 95 out of 100 times the estimate will fall between the upper and lower values which are given by the confidence interval.

A confidence interval is a parameter of values of various ranges which are bound to be present within the minimum and maximum capacity or the statistically-based mean value.  

Calculating the Confidence Interval

Let us consider that a team of researchers is analysing and recording the average height of football players in a school’s football team. To do so the researchers will take a sample at random from the football team and establish a mean height. Say for instance which is 5 Foot, 8 Inches (5’8).

Then the mean height of players in the football team is said to be 5 Foot, 8 Inches which is also considered to be a point in the estimated mean value finding. A point average value is only of limited use to the researchers as it does not completely reveal the estimated uncertainty which is associated with the sample.

One has no idea that this recorded value of the height is a sure shot certainty and if it will or will not be true for all the team members of the football team.

Point estimates provide less information than confidence intervals. The researchers arrive at an upper and lower bound that contains the true mean 95 per cent of the time by creating a 95 percent confidence interval using the sample’s mean and standard deviation and assuming a normal distribution as depicted by the bell curve.

Let us assume that now the interval lies between 5 Foot 7 inches and 5 foot 9 inches. If the researchers take 100 random recordings from the football team players as a whole, the mean should fall between  5 Feet 7 inches and 5 feet 9 inches in 95 of those recorded samples

In case the researchers wish to get an even greater confidence interval, then they can increase the recorded interval to a 99% confidence interval. By doing so a wider range is created, and it even makes room for a greater number of the recorded sample mean values or recordings. 

If in case the researchers reached the 99% confidence interval as being between 5 feet 7 inches and 5 feet 9 inches, they can expect a 99 out of 100 recorded samples to be completely evaluated to contain a desirable and estimated mean value between these numbers.

Formula

The formula used to find the confidence intervals are-

For mean:

CI (Confidence Interval) = x̄  ±  Zc sn

CI – Confidence Interval for a population.

X̄ – Sample Mean

Zc – Z value for a Confidence level

S – Sample Standard Deviation

n – Number of elements in a sample.

Conclusion

The Confidence Interval (short form- CI) is defined as the range of values that are likely to include a value of a population that lies between a specific degree of confidence.

With the help of big samples, one is allowed for more precise estimations of the population mean than smaller samples, the confidence interval estimated from a large sample is very thin.

Statistics play an important role in our daily lives when it comes to the analysis of data and information gathering. If one is able to gather, represent and note down data carefully with proper ups and downs and all the other values then the statistical report will be perfect. 

Without the proper knowledge, the statistical report of a given set of data will not be put down to analysis correctly.