# Confidence Interval vs. Tolerance Interval vs. Prediction Interval

In statistics, Intervals are an estimation methodology that utilizes sample data to generate value ranges likely to contain the population value of interest. It's a means to characterize the results. Businesses can benefit from applying Interval statistics in estimations, or in predicting future events.

The most popular of which is Confidence Intervals which is helpful in validating the range of estimation. However, this method isn’t always applicable to all business needs. Tolerance Intervals (useful in manufacturing industry) and Prediction Intervals (useful in retail, supply-chain industry) can also be an advantageous technique for companies that want to support their business objectives with appropriate statistical methods.

## Confidence Intervals

Businesses use Confidence Intervals to evaluate the reliability of a specific estimate. Given that estimates are not entirely reliable, this method can aid companies in understanding how confident they can be in their estimates, and if it’s in their best interests to act on them.

Confidence Intervals encompass the following:

• A span of values obtained from sample statistics that contain the value of an unknown population parameter
• Random in character, meaning two samples from a given population won’t produce identical Confidence Intervals.
• Only evaluate sampling errors in correlation to parameters of interest.

Determining the success level of future sales is a critical concern for many businesses, and Confidence Intervals can be particularly useful in this instance. For example, a business may want to estimate how many products they will sell during a certain financial period but won’t know the true number with real certainty until the end of that period. However, the value of future sales and the range sales are likely to fall within, can be evaluated via a collection of customer data, historical sales figures, and other sources.

## Prediction Intervals

Prediction Intervals are a type of Confidence Interval that can be used with predictions from linear and nonlinear models. Businesses can utilize this method as an estimate of an interval whereby future observations will reside, with certain expectations, given what’s already been observed.

Prediction Intervals include the following:

• Prediction of the value of the dependent variable, given particular settings of the independent variables.
• There’s increased uncertainty when predicting an individual value instead of the mean value. Therefore they’re always wider than the corresponding confidence interval of the prediction.
• A range of values for a product’s features that represents where the value of a single new observation is likely to fall with a specified level of confidence.

For example, a manufacturing business developing mobile phones might have 95% confidence that phone charges will last between 100 and 110 hours. Assuming this experiment was repeated several times, 95% of the time the phone charge will last within this range.

• Prediction Interval indicates where the value will likely fall in the future.
• If there’s a 95% Prediction Interval of 90 to 120 hours for phone charges, the business would know that future mobile phones in production will fall into that range 95% of the time.

## Tolerance Intervals

Tolerance Intervals are used to predict a range of outcomes for specified events. Changes are found by making comparisons to client conditions to tolerance limits that envelop a portion of the population. Businesses utilize this method to help identify cases where surplus variation can cause problems.

Tolerance Intervals include the following:

• A specified proportion of the population.
• Both the proportion of the population and confidence levels have to be stipulated.
• The tolerance factors set by you and the value is close to 100%.

Using the same example from Prediction Intervals, the manufacturing business developing mobile phones would utilize Tolerance Intervals to cover a specific proportion of the population for a certain confidence level.

• Thus 75% of the time, the phone charge will fall into the interval of 90-120 hours, with 95% confidence.

## Utilizing Intervals for Business Applications

Businesses need to benefit from analytics solutions that are adaptive to their specific scenarios, utilizing the appropriate methods to support their business needs and overall goals.

Professional research analysts from Research Optimus (ROP) have been providing analytical solutions for businesses for over a decade. ROP can help companies enhance their ability to make intelligent decisions with accurate statistical analysis that employs a range of Interval statistics customized for unique business requirements. For more information on ROP’s offerings and how your business can be benefitted with our statistical analysis, contact us.

Mutual Fund Managers