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Type III Error
Type III error has been defined in two primary ways. First, researchers have described a Type III error as occurring when a research study provides the right answer but for the wrong question or research hypothesis. For example, in public health research, when a research hypothesis predicts risk differences between groups or across time periods, the study design requires adequate characterization of all relevant groups and time periods. If discrepancies are found among the research hypothesis, time periods, and the methods used to test the hypothesis, these discrepancies can lead to what seems to be answers to a specific question, when in fact the results support a different question. Second, other researchers have stated that in statistical tests involving directional decisions, a Type III error can occur when one accepts a specific directional alternative when in fact another alternative is true. In this case, the Type III error has a conditional probability, gamma, which is simply the probability of getting the direction of the effect wrong. The entry provides some examples of Type III errors and recommendations for avoiding Type III errors.
Examples
Stroke
As noted in the first definition, Type III errors can occur when one examines the causes of variation in risk for a disease between individuals, but it does not consider that the causes of interindividual risk might differ from the causes of disease rates over time, and from causes of rate differences between populations. For example, when determining the etiology of stroke, the sources of variation of risk might include differences between individuals in genetic vulnerability, current medical conditions, temporal changes in poverty, and access to health care, as well as population and societal differences in what type of health care system is available. Furthermore, each of these factors is distinct from the proximal cause of stroke, namely the deprivation of oxygen to the brain. Certainly, each of the factors discussed previously contributes to the risk for stroke. A Type III error can occur when a study is designed to ascertain the inter-individual differences in risk for stroke within a given population, but it neglects to look for causes of stroke that are constant within the population being studied. A Type III error can also occur when neglecting risk factors for stroke related to variation between populations and across time. Furthermore, a Type III error might occur when one determines the risk for stroke in more than one population and finds interindividual differences in risk of stroke that produce variation of stroke outcomes within one population, but it fails to realize that the causes that produce interindividual differences in risk for stroke in one population might be different from the factors that produced differences in average risk for stroke between two or more populations.
Interactive Effects from Rehabilitation after Stroke
In a large, multisite, randomized controlled trial using leisure therapy and conventional occupational therapy administered to patients who have had a stroke, Chris Parker and colleagues failed to demonstrate a benefit for patients in terms of improved mood, leisure activity, or independence in activities of daily living measured at 6 and 12 months. Based on the second definition of Type III error, one possible explanation of the failure to demonstrate an effect in this study might be the failure to consider interactive effects of the interventions, which might have produced a Type III error in interpretation of the results.
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