Confidence Intervals
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 ztest and a ttest. A ttest is generally more precise, since it takes into
consideration the size (N) of the data set. For large values of N the pvalues of the two tests will differ only slightly and the approximated and exact intervals of
the mean will be almost the same. A pvalue 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.


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 dropdown 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
zdistribution) as well as the exact confidence interval (using the tdistribution) 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 ztest or a ttest (or both). If the pvalue 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 ttest is more
precise, but if N is large the pvalues in the two tests will differ only slightly.


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.
