What does the chi-square goodness of fit test determine?

Answer 1

The chi-square goodness of fit test determines whether a set of categorical data have an expected value that is similar to the observed value. For example, if you hypothesized that each Zodiac animal sign has the same proportion of people, then you would look at a sample. You would organize that sample into a chart showing how many people fit into which Zodiac animal. This is your observed value. Then you would have another table to express what your expected value is, which is 1/12 of the total sample population (because there are 12 Zodiac animal signs). Your null hypothesis is that each Zodiac animal sign will have 1/12 of the population.

Next, you verify that you can use the chi-square test. To use the chi-square test you must verify that all your expected counts are over 5.

Afterwards, you need to calculate a special variable notated as x^2. For each animal, you take the ((observed-expected)^2) / expected. Then you add it up. This is your x^2.

Afterwards, you find the P-Value by using a chart or a calculator.

If your P-Value is small, this means that the sample could not have occurred by chance and as a result, you can reject your null hypothesis. You would have significant evidence to prove that each Zodiac animal contains a different proportion. If your p-value is large, you fail to reject your null hypothesis.