MedicalStat

Decimals:

## Confidence and Prediction Interval of a Mean

With this tool you can can calculate both the prediction interval (PI) and the confidence interval (CI) of the mean value of a data set. Enter the mean value plus some additional info, depending on what you have, into the yellow input fields; either the standard deviation (SD) and the number of data in the data set (N) or the standard error (SE) and N. You can choose what precision level you want in the intervals; either 95 %, 96 %, ... etc. Furthermore, you can test whether a mean value could be lesser than, greater than or equal to a certain value using both a z-test and a t-test. A t-test is generally more precise, since it takes into consideration the size (N) of the data set. For large values of N the p-values of the two tests will differ only slightly and the approximated and exact intervals of the mean will be almost the same. A p-value less than 5 % (0.05) means that the null hypothesis is being rejected on a five percent significance level. The null hypothesis is that the mean value is either lesser than, larger than or equal to the value that that you compare it with in the input field.
For info about the formulas used in the calculations, please see the page medical statistics formulas.

What is known?
Mean SD N

Approx: SE % PI
% CI
Null Hypothesis (H0) Z Value P value
Mean

Exact: SE % PI
% CI
Null Hypothesis (H0) T Value P value
Mean

## Confidence Interval of a Proportion

Here you can calculate the confidence interval of a proportion (or "risk") by entering the info that you have into the yellow input fields. If you know the events (or "cases") out of the total sample of size N, then you should choose the option "events and N" in the drop-down selector menu. If, on the other hand, you already know the proportion and the sample size N, then you choose this option ... etc. You are being given both the approximated confidence interval (using the z-distribution) as well as the exact confidence interval (using the t-distribution) with the percentage of precision of your choice (the default is 95 %) . If N is large, the two intervals will differ only slightly. You can test whether the proportion could be lesser than, larger than or equal to a certain, given value by performing either a z-test or a t-test (or both). If the p-value in the test is below 0.05 then the null hypothesis can be rejected on a 5 % significance level, namely that the proportion could be either lesser than, greater than or equal to the value that you entered into the null hypothesis input field. The t-test is more precise, but if N is large the p-values in the two tests will differ only slightly.
For info about the formulas used in the calculations, please see the page medical statistics formulas.

What is known?
Events (cases) N

Approx: Proportion SE % CI
Null Hypothesis (H0) Z Value P value
Proportion

Exact: Proportion SE % CI
Null Hypothesis (H0) T Value P value
Proportion

## Confidence Interval of a Slope (Regression Coefficient)

The slope of a line is in this case the β value in the expression $$Y = \beta X + \alpha \: (+error)$$ from a linear regression.
N is the number of points (x, y) used in the linear regression.
The degrees of freedom is DF = N - 2.
The correlation coefficient R2 is defined by $$R^2 = \frac{SSR}{SST}$$ or $$R^2 = 1 - \frac{SSE}{SST}$$

SST = Sum of the Squares (Total) = SSE + SSR
SSR = Sum of the Squares (due to Regression)
SSE = Sum of Squares (due to Error)
For info about formulas and calculations, please see the page medical statistics formulas.

What is known?
β (slope) R2 N

SE % CI
Null Hypothesis (H0) T Value P value
β