Today we continue the »Streuspanne Lexicon« with the entry »K wie kritische Werte« (English: C for Critical Values). Our lexicon is not a regular episode, but a section to refer to short explanations without having to go into detail again and again in a separate episode. The podcast team explains a term briefly and concisely in just a few minutes.
The new entry in our Streuspanne-Lexicon is all about »C for critical values« – and, as always in our lexicon, it's short and sweet in just a few minutes.
Critical values are used to determine the significance of results in statistical analyses. In other words, they help to determine whether an observed effect is due to chance or is actually significant.
To determine critical values, one pretends that only chance is acting and then determines extreme marginal events that are very rare. The significance – a kind of rarity measure – determines what »rare« actually means. The exact calculation requires a little knowledge of probability theory, although there are formulae available for the common test procedures.
To illustrate the importance of critical values, in this entry we briefly consider a common example involving the toss of a coin: Suppose we want to find out whether a coin is fair or not. To do this, we toss the coin ten times and observe that it lands nine times on heads and only once on tails. This may seem unusual, but it could also happen by chance. To check this, we look at the probabilities for different outcomes. The ranges in which the number of heads and tails tosses are considered typical of a fair coin are defined as critical values – as outcomes outside these ranges are considered rare enough not to be due to pure chance. Thus, we can use these critical values to determine whether the observed result is significant or not.
In the lexicon entry, we also compare the critical values with the p-values and mention our last regular episode, which deals with the p-values in detail. Here you can find this episode »p-values – Not the Last Word in Wisdom«
Jochen also mentions the binomial distribution, a brief explanation of which can be found in the »Scattering Margin Lexicon« for »B for Binomial Distribution«.
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