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Grouped data are appropriately analyzed using univariate or multivariate analysis of variance (ANOVA and MANOVA, including pro le analysis of repeated measures), logistic regression, or discriminant analysis Ungrouped data are analyzed through bivariate or multiple regression, canonical correlation, cluster analysis, or factor analysis Some techniques apply to either grouped or ungrouped data For example, time-series analysis and survival analysis can be used to track behavior over time for a single group of cases or to compare behavior over time for different groups Chisquare and multiway frequency analysis can be used to compare contingencies in responses among categorical variables for a single group or to look for differences in responses among different groups Similarly, structural equations can be used to model responses of a single group or compare models among groups Tests of assumptions are performed differently depending on whether data are to be grouped or ungrouped during analysis.

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Basically, ungrouped data are examined as a single set, while grouped data are examined separately within each group or have entirely different criteria for assessing t to some assumptions, as discussed later Single Versus Multiple Responses Participants provide a single response in the classical betweensubjects ANOVA or chi-square designs In other designs participants may provide several responses, and those responses may be measured either on the same or on different scales Multivariate statistical techniques deal with multiple responses on different scales and are analyzed using such methods as MANOVA, canonical correlation, discriminant analysis, factor analysis, and structural equation modeling..

control subjects were selected from different populations of students As discussed earlier, random assignment into experimental and control conditions is usually performed to minimize the chance of any selection bias Finally, experimental mortality refers to attrition or subject drop out in an experiment For example, experimental mortality would be a problem if 50% of the subjects in the control condition dropped out of the experiment on test-taking anxiety while only 10% of the subjects in the experimental condition did so Experimenters must evaluate their research designs in order to minimize the influence of these seven threats to internal validity prior to conducting an experiment If any threat is operating in a research study, results are likely to be uninterpretable and the experimenters will be unable to reach meaningful conclusions based on their data External validity refers to the generalizability of the research results.

The word vbModeless is a built-in constant that has a value of 0. Therefore, the following statement works identically:

is the within-cell error effect associated with Yi jk and is equal to Yi jk j k ( ) jk . It re ects all effects not attributable to treatment level aj, treatment level bk, and the interaction of aj and bk.

The more similar the research experiment is to a real world situation, the more generalizable the findings However, the more careful an experimenter is about maximizing internal validity, the more likely he or she will minimize external validity A high degree of control and precision is necessary to minimize experimental and random error and thus maximize internal validity Therefore, carefully constructed laboratorybased research maximizing internal validity may jeopardize the generalizability (external validity) of the results For example, in the experiment on test-taking anxiety, all subjects completed the same stressful IQ test administered in a laboratory rather than a real test such as a final examination in one of their college courses Allowing subjects in this study to take a real examination would increase the generalizability of the results but compromise the internal validity of the study because course exams cannot be uniform.