Estimation

Estimation is the method to predict the range of statistical values by decided probability. 0.05 (5 percent) is often used as the probability.

The graph is the case of the estimation of average. But for example, estimation is also used for Regression Analysis .

Confidence Interval

The average calculated from data directly is the average of samples. So we have questions that, "The value of average is able to be trusted?" or "If I take sampling again, how much the value of the average?".

Confidence interval is the answer of the question. It is the interval where the value of the average is included. The graph of this page is the case of the probability is 0.95 (95 percent).

Average(Ave), standard deviation(Std), sample number(n)

SQRT() means the square root.
If using EXCEL, for example,
Upper of the confidence interval =AVERAGE(A3:A7)+TINV(1-0.95,COUNT(A3:A7)-1)*STDEV(A3:A7)*SQRT(1/COUNT(A3:A7))

Prediction Interval

"Data" in the graph of this page is the value of individual samples. So we have a question that "If I take sampling once more, how much of the value of next data?". This value is important to use the output of the analysis to the prediction of the future.

Prediction interval is the answer of the question. It is the interval where the value of individual sample data is includes. The graph of this page is the case of the probability is 0.95 (95 percent).

Average(Ave), standard deviation(Std), sample number(n)

Feature of Confidence Interval and Prediction Interval

Confidence interval and prediction interval have common feature.

• If standard deviation is small, the interval is narrow.
• If the probability is low, the interval is narrow.
• If the number of samples is many, the interval is narrow. (This feature appears on confidence interval strongly.)

If we use these intervals for real work, there are cases that, "The interval is too wide to use for controls." We need to consider these features to improve the interval.