# Chi square and value relationship

### Chi Square Statistics

Suppose that the ratio of male to female students in the Science Faculty is Now we must compare our X2 value with a c2 (chi squared) value in a table of c with. This lesson explains how to conduct a chi-square test for independence. but the relationship is not necessarily causal, in the sense that one variable "causes" The P-value is the probability of observing a sample statistic as extreme as the . And, a chi-square value can not tell you what the relationship is between two variables, only that a relationship exists between the two variables. There are no .

The variables under study are each categorical. If sample data are displayed in a contingency tablethe expected frequency count for each cell of the table is at least 5.

## 9.2 - Statistical Significance of Observed Relationship / Chi-Square Test

This approach consists of four steps: The null hypothesis states that knowing the level of Variable A does not help you predict the level of Variable B. That is, the variables are independent. Variable A and Variable B are independent. Variable A and Variable B are not independent.

The alternative hypothesis is that knowing the level of Variable A can help you predict the level of Variable B. Support for the alternative hypothesis suggests that the variables are related; but the relationship is not necessarily causal, in the sense that one variable "causes" the other.

Formulate an Analysis Plan The analysis plan describes how to use sample data to accept or reject the null hypothesis.

The plan should specify the following elements. Often, researchers choose significance levels equal to 0. Use the chi-square test for independence to determine whether there is a significant relationship between two categorical variables.

Analyze Sample Data Using sample data, find the degrees of freedom, expected frequencies, test statistic, and the P-value associated with the test statistic. The approach described in this section is illustrated in the sample problem at the end of this lesson.

The degrees of freedom DF is equal to: I mentioned some of this above, when contrasting types of data and so on.

### CHI SQUARED TEST

This section will consider other things that the Chi-square test is not meant to do. First of all, the Chi-square test is only meant to test the probability of independence of a distribution of data.

It will NOT tell you any details about the relationship between them. If you want to calculate how much more likely it is that a woman will be a Democrat than a man, the Chi-square test is not going to be very helpful.

## Chi-Square Test for Independence

However, once you have determined the probability that the two variables are related using the Chi-square testyou can use other methods to explore their interaction in more detail. For a fairly simple way of discussing the relationship between variables, I recommend the odds ratio. Some further considerations are necessary when selecting or organizing your data to run a Chi-square test.

The variables you consider must be mutually exclusive; participation in one category should not entail or allow participation in another.

In other words, the data from all of your cells should add up to the total count, and no item should be counted twice. You should also never exclude some part of your data set. If your study examined males and females registered as Republican, Democrat, and Independent, then excluding one category from the grid might conceal critical data about the distribution of your data.

It is also important that you have enough data to perform a viable Chi-square test. If the estimated data in any given cell is below 5, then there is not enough data to perform a Chi-square test.

In a case like this, you should research some other techniques for smaller data sets: There are also tests written specifically for smaller data sets, like the Fisher Exact Test. Degrees of Freedom A broader description of this topic can be found here. The degrees of freedom often abbreviated as df or d tell you how many numbers in your grid are actually independent.