Null model

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A null model is a statistical model that is built on the null hypothesis .

Explanations

The null model assumes that the observed data arose purely by chance, without causal dependence on influencing factors. The null model is used to test on the observed data whether an assumption about one or more influencing variables is significant. If the test confirms the null model, however, this is not proof of the correctness of the null model, but only leads to the rejection of the hypothesis of the previously assumed dependency. The null model cannot be proven, but only refuted.

The detailed mathematical-formal treatment of the topic can be found in the article Statistical Test .

example

  • Real Situation: A certain fortune teller claims that she can predict the future.
  • The model constructed for this purpose: This fortune teller can predict the future.
  • The influencing factor: the foreknowledge of the future.
  • The hypothesis: the "foreknowledge of the future" influencing factor can influence the test result in such a way that a future event can be correctly predicted.

To test this hypothesis, a suitable null model is built:

  • The null model: this fortune teller cannot predict the future.
  • The influencing factor "the foreknowledge of the future" is not effective.
  • The null hypothesis: the prediction and the event arise purely by chance.

For the test you take an urn with two identical balls, except that one of the balls is colored white and the other black. Now let the fortune teller predict whether she will draw a white or a black ball and write down her answer. Then let the fortune teller blindly draw a ball and note whether the prediction has come true or not. Then the ball is put back in the urn and the balls are shuffled. This process is repeated 100 times.

Two possible outcomes of the test are now discussed:

1. The prediction came true in 100 cases.

In this case, there is a high probability that the hypothesis is correct and that the model "This fortune-teller can predict the future" correctly reflects reality in terms of foreknowledge of the future.

2. The forecast came true in 50 cases.

This result corresponds to the probability of the null hypothesis, namely the pure chance of drawing a white or black ball and predicting it correctly. In this case, one can assume with high probability that the hypothesis was wrong and that the model "This fortune teller can predict the future" does not correspond to reality.

If you hadn't made a null model, set up a null hypothesis and calculated its probability, then the fortune teller could have said: "Well, my predictions are not always correct, but in 50 cases they have come true! That's a lot!"

However, this result is also no proof of the validity of the null model, because it could be that many other influencing factors that were not taken into account, such as weather, moon phase, star constellation, atmosphere, etc., have had an effect and hindered a more precise foresight of the future .

Of course, in specific cases the null hypothesis can look much more complicated and it can be much more difficult to calculate the probability of the null model. An example of the detailed calculation of the probability of a null model is provided by George Pólya in his article A Probability Problem in Plant Sociology .

Individual evidence

  1. ↑ Null model at www.mbaskool.com. Retrieved November 25, 2018.
  2. ^ Pólya, G .: A probability problem in plant sociology . Quarterly publication of the Natural Research Society in Zurich. 75 (1930): pp. 211-219. Retrieved online on November 17, 2018.

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