## Chi-Squared Independent Test

The extension of contingency table is to test the null hypothesis that the two variables in the table are actually related (dependent) or not. The interactive program below will automatically compute the Chi-Square values from your raw data including the chi-square probability and interpret the result of the analysis. (Yes, this program is free to use. Just donate for further development if you feel delighted).

To use the program, you need to copy and paste or type two lists of data. Each list indicates data of one variable data. The data item can be a number or a string. The two lists must have the same number of data. The lists of data are separated by comma (if you type a space, the program will automatically insert a comma for you). Then, click "Do Independent Test" button.

The example given here is taken from the sample questionnaire of this tutorial variable Activity Time in Parks and variable Mode to go to park. Feel free to change the sample data with your own data.

The outputs of the program are:

1. Count table: count the number of common occurrence between the two lists
2. Independent table: count the ideal number of common occurrence if the two variables are assumed to be independent
3. Chi-square value: the manual & spreadsheet computation can be seen in the previous section of this tutorial
4. Degree of freedom = (total rows-1)*(total columns-1)
5. Chi-square probability (computed numerically, this is similar to look up at Chi-Square statistical table but more automatic task)
6. Interpretation: decision whether the two variables are related or not related at 5% level of significance.

In the next section , you will learn different method to analyze your data using conditional probability , and Bayes Theorem .