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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 one-way, 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 non-matches between columns is equal to the proportion of non-matches 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
Sixth-grade children who had earned either “A” or “C” grades in science last year were assigned to write a synopsis of a specific television program they were asked to watch. The programs, all featuring scientists of a sort, were shown at 10 PM and not normally seen by these young viewers. One week later, all of the students were asked to list three careers they were considering. The children's first responses (signified here by a letter) were examined to see whether the program assignment differentially influenced career consideration, and whether this effect depended on the child’s previous success in science. In this case, the responses are careers.

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