Examples using artificial data Example 1: One way, independent groups design 16 buyers saw one of four web pages and then purchased either product a, b, c, d, e, or nothing (after Fasolo, McClelland, & Lange, 2005). This is a oneway, independent groups design with four replicates. The null hypothesis is that what was purchased does not depend upon which page the buyer saw; the alternative hypothesis is that the page does influence the purchase. Of course, with nominal data, hypotheses are never directional. The hypothesis is tested by asking whether the proportion of nonmatches between columns is equal to the proportion of nonmatches within columns. Product purchased (artificial data)
Results Potential Matches: 120 Obtained Matches: 23
According to standard null hypothesis testing logic, these results are consistent with the null hypothesis at the .05 level of significance; the page does not affect the purchase. Example 2: Repeated measures design Data are diagnoses made by medical students, The responses are unconstrained, in that no set of possible diseases from which to choose was provided. The students named the disease (here, signified by the letters a, b, c, or d) they attributed to a patient who had the designated set of symptoms.
Results Potential Matches: 190 Obtained Matches: 41
Symptom effect is significant at .05 level. The medical students generally agreed on the diseases suggested by the symptom sets. Example 3: Repeated measures design Data are diagnoses made by medical students, The responses are unconstrained, in that no set of possible diseases from which to choose was provided. The students named the disease (here, signified by the letters a, b, c, or d) they attributed to a patient who had the designated set of symptoms.
Results Potential Matches: 190 Obtained Matches: 41
Symptom effect is not significant. Students tend to give idiosyncratic diagnoses without much regard for the symptoms. Example 4: Two way, independent groups design Career choices among 6^{th} graders (artificial data)
Results Potential Matches: 276 Obtained Matches: 87
Neither programs not grades significantly affect career choice. Example 5: Repeated measures design, subjects nested under their ethnicity ("mixed design") Subjects are nested under their ethnicity. Each subject read four political statements and guessed the ethnicity of its author. This is a three factor design (Political statements, Ethnicity, Participants). The usual pooling rules for sums of squares in nested designs (see Weiss, 2006, Chapter 11) are applied to the potential and observed matches to obtain the two error terms. Ethnicity ascribed to authors of political statements (artificial data)
Results Potential Matches: 276 Obtained matches: 47
Both ethnicity of the subject and the content of the political statement affect the response. The two factors contribute independently. 
