How do you interpret a confidence interval


Confidence interval


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With a "random sample" one can make statements about an unknown "population". The range of values ​​in which one expects the relevant parameter of the population with a certain probability is called Confidence interval (English: confidence interval).

The width of the confidence interval is called precision the estimate. It depends on the one you want security the estimate (in the example 99%), the "sample size" and the "standard error" of the sample statistics. The complementary probability of the certainty, the uncertainty of the estimate, is called Probability of error designated. The probability given with a confidence interval, the certainty , can be interpreted as follows: If one were to draw an infinite number of samples of the same size and use the same interval width for each estimate, then the actual parameter of the population would be % of the estimates within the respective confidence interval. Since in empirical social research one usually only has a Sample, this interpretation is not particularly helpful.

To calculate the confidence interval, the "sample distribution" of the respective statistic must be known. For the estimation of an arithmetic mean one usually uses the -Distribution «, since the spread of the examined characteristic in the population is also unknown in most cases and has to be estimated with the sample data. Otherwise the "normal distribution" could be used. The »normal distribution« is used approximately to estimate a share value. Since, in empirical social research, samples are selected without replacing, the standard error must be multiplied by a correction factor for finite totalities in the case of selection sentences over 5% (see "Selection technique").



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