# What does a chi-square value mean

## Chi square

In exercise 1 it was found that chi-square can have a value between zero and a multiple of N (number of cases in the investigation) - depending on N, the distribution of the data in the crosstab and the size of the crosstab. In our previous example (steps 2 and 4) we found a value of 3.4979 for chi-square. Is this a large or a small value? What does he say?

Catholicnot catholic
CVP voters166
other1315
Chi square: 3.4979
• If the cases in the crosstab were completely evenly distributed, the chi-square would be 0.
• However, the determined value of chi-square in our example is 3.4979 and indicates a deviation from a completely even distribution of the cases (apparently the majority of Catholics actually vote for the CVP - non-Catholic respondents tend to vote other parties than the CVP).
• However, the question arises as to how significant the determined deviation of the calculated chi-square value from zero is. Can we reject the null hypothesis "no connection"? We now formulate this question in a way that statistics can give us an answer:
• How likely is it to get a value of 3.4979 for chi-square (in a 2x2 crosstab) by sheer coincidence in the sample selection when in fact there is no relationship between the variables of interest?

Fortunately, like other statistical measures, chi-square also has a typical sampling distribution. This means that we know the probability with which corresponding values ​​of chi-squared come about purely by chance without there being a connection between the variables of interest.

In the case of a 2x2 crosstab, this distribution looks like this (vertical the probability, horizontal the corresponding values ​​of chi-square): This standard distribution for 2x2 tables shows:

• Increasing values ​​of chi-square become increasingly unlikely.
• A value of chi-square = 3.84 occurs with a probability of 5% (p = 0.05), even if no context exists between the variables. 3.84 is the critical value of chi-square on the Level of significance of 5%.
• A value of chi-square = 6.63 occurs with a probability of 1% (p = 0.01), even if no context exists between the variables. 6.63 is the critical value of chi-square on the Level of significance from 1%.
• A value of chi-square = 7.88 occurs with a probability of 0.5% (p = 0.005), even if no context exists between the variables. 7.88 is the critical value of chi-square on the Level of significance of 0.5%.