Chi-square test for goodness of fit: Method
The Method dialog provides options for specifying exact tests.
Exact tests provides two additional methods for calculating significance levels for the statistics available through the Crosstabs and Nonparametric tests procedures. These methods, the exact and Monte Carlo methods, provide a means for obtaining accurate results when your data fail to meet any of the underlying assumptions necessary for reliable results using the standard asymptotic method. Available only if you have purchased Sampling and Testing.
Asymptotic results obtained from small datasets or sparse or unbalanced tables can be misleading. Exact tests enable you to obtain an accurate significance level without relying on assumptions that might not be met by your data. For example, results of an entrance exam for 20 fire fighters in a small township show that all five white applicants received a pass result, whereas the results for Black, Asian and Hispanic applicants are mixed. A Pearson chi-square testing the null hypothesis that results are independent of race produces an asymptotic significance level of 0.07. This result leads to the conclusion that exam results are independent of the race of the examinee. However, because the data contain only 20 cases and the cells have expected frequencies of less than 5, this result is not trustworthy. The exact significance of the Pearson chi-square is 0.04, which leads to the opposite conclusion. Based on the exact significance, you would conclude that exam results and race of the examinee are related. This demonstrates the importance of obtaining exact results when the assumptions of the asymptotic method cannot be met. The exact significance is always reliable, regardless of the size, distribution, sparseness, or balance of the data.
- Asymptotic only
- The significance level based on the asymptotic distribution of a test statistic. Typically, a value of less than 0.05 is considered significant. The asymptotic significance is based on the assumption that the data set is large. If the data set is small or poorly distributed, this may not be a good indication of significance.
- Monte Carlo
- An unbiased estimate of the exact significance level, calculated by repeatedly sampling
from a reference set of tables with the same dimensions and row and column margins as the observed
table. The Monte Carlo method allows you to estimate exact significance without relying on the
assumptions required for the asymptotic method. This method is most useful when the data set is too
large to compute exact significance, but the data do not meet the assumptions of the asymptotic
method.
- Confidence Level (%)
-
The confidence level of the estimates, expressed as a percentage. The value must a be a positive number less than 100
- Number of samples
- Specify the number of points that are sampled for the Monte Carlo approximation. The value must be a positive integer. The default value is 10000.
- Exact
- The probability of the observed outcome or an outcome more extreme is calculated
exactly. Typically, a significance level less than 0.05 is considered significant, indicating that
there is some relationship between the row and column variables.
- Time limit per test
- Sets the maximum time limit for calculating each test. If a test exceeds 30 minutes, it is recommended that you use the Monte Carlo method.
Specifying exact tests for the Chi-square test for goodness of fit
This feature requires Statistics Base Edition.
- From the menus choose:
- In the Chi-square test for goodness of fit dialog, expand the Additional settings menu and click Method.