Chi-square notes

What is a Chi-test used for? Pronounced like kite, not like cheese! This test is used to check if the difference between expected and observed results is significant. For example- whether any difference is caused by chance or if there are other factor’s affecting results, like error. Used to test a null hypothesis -results are due to random chance.

Equation

For example, if we tossed a balanced coin 100 times, we would expect it to come up heads about 50 times and tails about 50 times. How far from this prediction could the observations be and still fit our prediction? Assume the results of our 100 trials were as follows: »observed expected Heads Tails Could we get this variation by chance alone? If so, what is the probability of getting these results by chance? Is it likely or extremely unlikely?

Because it is impossible to prove the correctness of a good hypothesis, scientists choose instead to work their hypotheses so they can reject a poor hypothesis. We will follow this convention. And if we must reject a poor hypothesis, when we analyze the observations, we can then consider what might have caused our unexpected results, what else might be going on.

Coin example our “null hypothesis” is that there is no significant difference between our observed results and the ones we expected. First, let’s calculate the chi-square value.

Step 1: Chi-square value »observed expected Heads Tails CHI-SQUARE (X2) = (observed – expected )2 + (observed-expected)2 expected expected For the example above: X2 = (55-50)2 + (45-50)2 = =

Step 2: Degrees of freedom Find your degrees of freedom. # of variables that may vary: We had two variables, subtract one! Degree of freedom/df=1 If we had 4 variables, subtract one! Df would be 3

Step 3: Analyze data/look at chart The table shows the “critical values of Chi- Square” and the probability of getting each value as a function of the number of degrees of freedom. To use the table, use the line that corresponds to your degrees of freedom.

We will always use the.05 row in this class. Step 4: Accept or reject hypothesis: If your chi-square value is less than the critical value, you can accept the hypothesis, if the value is more, you need to reject your hypothesis. Our chi-value was 1, What does this tell us about our data? Not due to error, flipping of coins is due to chance!