Wading Through the Data Swamp:
Program Evaluation 201

Module 3: Variable - Are They Related? - Page 13 of 18

Chi-Square Applet

Now that you have learned about contingency tables and chi-square, take a look at the applet below. As you will see, the numbers and labels used in this contingency table applet are the same as the numbers we used in our alcohol contingency table.

This applet will give you a visual representation of the numbers we have used to calculate our chi-square value. The columns of cells represent the numbers of participants and non-participants. Rows represent the numbers of kids using and not using alcohol. Blue represents numbers greater than the expected frequency. Red represents numbers lower than the expected frequency. The more intense the colors, the greater the statistical difference between the participant group and nonparticipant group. As you can see, the participants and non-participants differed in their alcohol use (depicted by strong colors). This difference cannot be attributable to chance alone. The chi-square score of 02 = 13.3 is greater than our critical value of 3.84 that we calculated earlier. The probability (depicted here as "p=3OF-4" or "p<0003") means that there is less than a 3 in 1,000 chance that the differences between the groups is attributable to chance. This is good news for Jack.

Exercise: Now, lets play with the numbers so they are not statistically significantly different. Plug in 30 participants using alcohol and 20 participants not using alcohol. We get a chi-square value of 02 = 2.94, which is less than the critical value of 3.84. Therefore, the groups' alcohol use is not statistically significantly different. The p value tells us that there is a more than a 8% chance (p = .0863) that the differences we see might be due to chance. Remember that in the social sciences, we don't want more than a 5% chance (p = 0.05) that the differences are due to chance.

Point: Just because two numbers "look" different does not mean that they are statistically different.

This applet from Seeing Statistics™ is used under license. Any reproduction or other use is strictly prohibited.

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