If your estimated chi-square value is larger than the chi-square critical value, **your null hypothesis** is rejected. If your estimated chi-square value is smaller than the crucial chi-square value, you "fail to reject" your null hypothesis.

- How do you interpret a chi-square statistic?
- Should I use a t-test or a chi-square?
- How do you know if chi square is significant?
- What happens to the critical value for a chi-square test when the size of the sample is increased?
- What is the null hypothesis for Chi Square?
- What is the chi-square critical value at a 0.05 level of significance?
- How do you find the degrees of freedom for a chi-square test?
- What does it mean if the chi-square is zero?

A chi-square test allows you to state "we can reject the null hypothesis of no association at the 0.05 level" or "we have...".

You can compare your estimated chi-square value to a critical value from a chi-square table. There is a considerable difference if the chi-square value is bigger than the critical threshold. This means that the data are unlikely to have come from the population under study.

There are two ways of determining whether or not the chi-square test is significant. The first method is called the asymptotic approach. It works by calculating an estimate for the probability of obtaining a chi-square value this large or larger by chance. If this probability is small, then we can say with confidence that the observed value of the chi-square statistic is unlikely to have been generated by chance alone.

The second method is called the exact approach. Instead of estimating the probability, it calculates **the actual probability**: the ratio of the number of samples that produce a value at least as great as **the observed value** to the total number of samples in the population. If this probability is small, then we can say with certainty that the sample came from a population with **more coincidences** than would be expected by chance alone.

These probabilities are usually small even when there is evidence of significance using the asymptotic approach. This means that we can be certain that the observed value of the chi-square statistic is unusual in some way.

The critical value falls as the sample size grows. C. The chi-square critical value is unrelated to sample size.

The Chi-Square test's null hypothesis states that there is no association between the categorical variables in the population; they are independent. If this assumption holds, then the value of **the Chi-Square statistic** follows a chi-square distribution with the degree of freedom equal to the number of categories - 1.

With a level of significance of **05 and 7 degrees** of freedom, the critical chi-square value is 14.067. This suggests that there is precisely 0.05 of the area under the chi square distribution to the right of kh2 = 14. 067 for 7 degrees of freedom.

This number can be used in place of the standard 95% confidence interval for the percentage of cases in which an event will occur. For example, if we were to repeat this experiment 100 times, we would expect 5 or fewer occurrences of the event. Therefore, with 95% confidence, we can say that the percentage of events is between 0 and 5%.

The degrees of freedom for the chi-square are computed as df = (r-1) where r is the number of rows and c is the number of columns. The null hypothesis can be rejected if the observed chi-square test statistic is larger than the crucial value. For example, to reject the null hypothesis that results of coin flips are equal with 95% confidence, we need a test statistic smaller than 3.84. The critical value is determined by the degree of freedom for the chi-square test.

A low chi-square score indicates a good correlation between your two sets of data. In principle, chi-squared would be 0 if your observed and predicted values were identical ("no difference"); however, this is unlikely to occur in practice. A chi-square value of 0.05 or less is usually considered evidence of a good fit.

The chi-square test is used to see if there is any relationship between **two variables**. It provides a way of testing whether one set of observations is like **another set** of observations that we know about. For example, we might want to know if children's names are likely to be repeated within families. We could do this by comparing the frequencies of different names among siblings vs. strangers on the street. The chi-square test is useful for these sorts of comparisons because it gives us a way of checking whether there is any pattern to how names are chosen by parents.

There are two main assumptions behind using **the chi-square test**: first, that the samples are representative of the populations from which they were drawn; second, that other factors are not influencing the association being studied. If these assumptions are not valid, then we cannot assume anything about the population from which the samples were drawn. For example, if we were to find that children's names were more likely to be repeated among siblings than strangers, this would not necessarily mean that children's names are important to their families.