Prediction Interval (New Observation)
Computes the prediction interval for a new individual observation, from a sample. Be careful not to confuse it with the confidence interval for the mean: that one estimates where the population mean lies; this one estimates where the next individual value you observe will fall — which is why it's always wider, carrying the uncertainty of the mean plus the natural variability of the data. The decisive factor is the √(1 + 1/n) under the t distribution. Enter the sample and the confidence level.
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Prediction Interval (New Observation)
Computes the prediction interval for a new individual observation, from a sample. Be careful not to confuse it with the confidence interval for the mean: that one estimates where the population mean lies; this one estimates where the next individual value you observe will fall — which is why it's always wider, carrying the uncertainty of the mean plus the natural variability of the data. The decisive factor is the √(1 + 1/n) under the t distribution. Enter the sample and the confidence level.
Where the next measurement will fall, not the mean
There's a common and costly confusion between two intervals that look like siblings but answer different questions. The confidence interval for the mean says where the population mean probably lies. The prediction interval says something far more ambitious: where the next individual observation you have yet to measure will fall.
The difference shows up in the formula. The interval for the mean carries only the uncertainty about where the center is, which shrinks as the sample grows. The prediction interval carries that plus the natural variability of a new data point, which doesn't vanish no matter how many points you collect. That's why it's always wider, and its characteristic factor is the √(1 + 1/n) under the t distribution, against the √(1/n) of the mean interval.
Enter the sample and the confidence level. The tool returns the mean and the bounds of the prediction interval. Use it when the question is about a future individual case — what the strength of the next part will be, the time of the next service call — and not about the average behavior of the process.
Related Tools
CI for the Ratio of Two Variances
Computes the confidence interval for the ratio between the variances of two normal populations, σ₁²/σ₂². Instead of just testing whether the variances differ, it gives a plausible range for how many times one is larger than the other. If the interval contains the number 1, there's no evidence the spreads are different. The calculation uses the F distribution, and because it's asymmetric, the bounds come from F quantiles with the degrees of freedom swapped. Enter the two samples and the confidence level.
CI for the Difference of Two Proportions
Computes the confidence interval for the difference between two proportions, using the Wald method. It's the companion to the two-proportion z-test and the basis of any A/B test reading: beyond saying whether the difference is significant, it shows the plausible range for its real size. If the interval doesn't contain zero, there's a significant difference. For example: variant A converted 45 of 100 and B, 30 of 100 — what's the interval for the difference? Enter the successes and the total of each group and the confidence level.
CI for Correlation (Fisher z Transform)
Computes the confidence interval for a correlation coefficient using the Fisher z transformation. The sampling distribution of r is skewed, especially near −1 or +1, which prevents applying the usual symmetric margin. Fisher solved this with a transformation that makes the distribution approximately normal; you build the interval on that scale and then map back to r. The result is an asymmetric interval, narrower on the side near the extremes. Enter the coefficient r and the sample size.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.