Chi square test for independence of two attributes. Suppose N observations are considered and classified according two characteristics say A and B. We may be interested to test whether the two characteristics are independent. In such a case, we can use Chi square test for independence of two attributes. The example considered above testing for independence of success in the English test vis a vis immigrant status is a case fit for analysis using this test.

This lesson explains how to conduct a chi-square test for independence. The test is applied when you have two categorical variables from a single population. It is used to determine whether there is a significant association between the two variables. For example, in an election survey, voters might be classified by gender (male or female) and voting preference (Democrat, Republican, or Independent). We could use a chi-square test for independence to determine whether gender is related to voting preference. The sample problem at the end of the lesson considers this example. When to Use Chi-Square Test for Independence

The test procedure described in this lesson is appropriate when the following conditions are met: * The sampling method is simple random sampling.
* Each population is at least 10 times as large as its respective sample. * The variables under study are each categorical.
* If sample data are displayed in a contingency table, the expected frequency count for each cell of the table is at least 5. This approach consists of four steps: (1) state the hypotheses, (2) formulate an analysis plan, (3) analyze sample data, and (4) interpret results. State the Hypotheses

Suppose that Variable A has r levels, and Variable B has c levels. 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. H0: Variable A and Variable B are independent. Ha: Variable A and Variable B are not...

...CHI-SQUARE TEST (χ²):
Chi-square is a statistical test commonly used to compare observed data with data we would expect to obtain according to a specific hypothesis. For example, if, according to Mendel's laws, you expected 10 of 20 offspring from a cross to be male and the actual observed number was 8 males, then you might want to know about the "goodness to fit" between the observed and expected. Were the deviations (differences...

...Chi-square requires that you use numerical values, not percentages or ratios.
Then calculate 2 using this formula, as shown in Table B.1. Note that we get a value of 2.668 for 2. But what does this number mean? Here's how to interpret the 2 value:
1. Determine degrees of freedom (df). Degrees of freedom can be calculated as the number of categories in the problem minus 1. In our example, there are two categories (green and yellow); therefore, there is I degree...

...you conduct a chi-square test of independence, what is the expected frequency count of male Independents?
b) If you conduct a chi-square test of independence, what is the expected frequency count of female Democrats?
c) If you conduct a chi-square test of independence, what is the observed count of female Independents?
d) If you conduct a chi-square test of...

...Chi-Square Test
Chi-square is a statistical test commonly used to compare observed data with data we would expect to obtain according to a specific hypothesis. For example, if, according to Mendel's laws, you expected 10 of 20 offspring from a cross to be male and the actual observed number was 8 males, then you might want to know about the "goodness to fit" between the observed and expected. Were the deviations (differences between...

...CHI-SQUARE AND TESTS OF CONTINGENCY TABLES
Hypothesis tests may be performed on contingency tables in order to decide whether or not effects are present. Effects in a contingency table are defined as relationships between the row and column variables; that is, are the levels of the row variable diferentially distributed over levels of the column variables. Significance in this hypothesis test means that interpretation of the cell frequencies is warranted....

...2.3. The Chi-Square Distribution
One of the most important special cases of the gamma distribution is the chi-square distribution because the sum of the squares of independent normal random variables with mean zero and standard deviation one has a chi-square distribution. This section collects some basic properties of chi-square random variables, all of which...

...Chi-square tests
1. INTRODUCTION
1.1 χ2 distribution and its properties
A chi-square (χ2) distribution is a set of density curves with each curve described by its degree of freedom (df). The distribution have the following properties:
- Area under the curve = 1
- All χ2 values are positive i.e. the curve begins from 0 (except for df=1) increases to a peak and decreases towards 0 as its asymptote
- The curve is...

...THE CHI-SQUARE GOODNESS-OF-FIT TEST
The chi-square goodness-of-fit test is used to analyze probabilities of multinomial distribution trials along a single dimension. For example, if the variable being studied is economic class with three possible outcomes of lower income class, middle income class, and upper income class, the single dimension is economic class and the three possible outcomes are the three classes. On each trial, one...