Examples of unit-treatment additivity in the following topics:
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- Kempthorne and his students make an assumption of unit-treatment additivity.
- In its simplest form, the assumption of unit-treatment additivity states that the observed response from the experimental unit when receiving treatment can be written as the sum of the unit's response $y_i$ and the treatment-effect $t_j$, or
- The assumption of unit-treatment additivity implies that for every treatment $j$, the $j$th treatment has exactly the same effect $t_j$ on every experiment unit.
- The assumption of unit-treatment additivity usually cannot be directly falsified; however, many consequences of unit-treatment additivity can be falsified.
- For a randomized experiment, the assumption of unit-treatment additivity implies that the variance is constant for all treatments.
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- Paired-samples $t$-tests typically consist of a sample of matched pairs of similar units, or one group of units that has been tested twice.
- A paired difference test uses additional information about the sample that is not present in an ordinary unpaired testing situation, either to increase the statistical power or to reduce the effects of confounders.
- Paired samples $t$-tests typically consist of a sample of matched pairs of similar units, or one group of units that has been tested twice (a "repeated measures" $t$-test).
- A typical example of the repeated measures t-test would be where subjects are tested prior to a treatment, say for high blood pressure, and the same subjects are tested again after treatment with a blood-pressure lowering medication .
- Pairs become individual test units, and the sample has to be doubled to achieve the same number of degrees of freedom.
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- In this example, there is no interaction between the two treatments — their effects are additive.
- In contrast, if the average responses as in are observed, then there is an interaction between the treatments — their effects are not additive.
- A table showing no interaction between the two treatments — their effects are additive.
- A table showing an interaction between the treatments — their effects are not additive.
- Outline the problems that can arise when the simultaneous influence of two variables on a third is not additive.
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- In the design of experiments, the experimenter is often interested in the effect of some process or intervention (the "treatment") on some objects (the "experimental units"), which may be people, parts of people, groups of people, plants, animals, etc.
- Comparisons between treatments are much more valuable and are usually preferable.
- Often one compares against a scientific control or traditional treatment that acts as baseline.
- Blocking: Blocking is the arrangement of experimental units into groups (blocks) consisting of units that are similar to one another.
- To control for nuisance variables, researchers institute control checks as additional measures.
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- For example, a study conducted by Holbrook, Crowther, Lotter, Cheng and King in 2000 investigated the effectiveness of benzodiazepine for the treatment of insomnia.
- When the dependent variable is measured on a ratio scale, it is often informative to consider the proportional difference between means in addition to the absolute difference.
- That is, since the dependent variable is standardized, the original units are replaced by standardized units and are interpretable even if the original scale units do not have clear meaning.
- It is more meaningful to say that the means were 0.87 standard deviations apart than 1.47 scale units apart since the scale units are not well defined.
- This standardized difference in effect size occurs even though the effectiveness of the treatment is exactly the same in the two experiments.
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- Placebo-controlled studies are a way of testing a medical therapy in which, in addition to a group of subjects that receives the treatment to be evaluated, a separate control group receives a sham "placebo" treatment which is specifically designed to have no real effect.
- The purpose of the placebo group is to account for the placebo effect -- that is, effects from treatment that do not depend on the treatment itself.
- Such factors include knowing one is receiving a treatment, attention from health care professionals, and the expectations of a treatment's effectiveness by those running the research study.
- Thus, the relevant question when assessing a treatment is not "does the treatment work?
- " but "does the treatment work better than a placebo treatment, or no treatment at all?
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- The units of analysis are usually individuals (at a lower level) who are nested within contextual/aggregate units (at a higher level).
- Furthermore, multilevel models can be used as an alternative to analysis of covariance (ANCOVA), where scores on the dependent variable are adjusted for covariates (i.e., individual differences) before testing treatment differences.
- In addition, this model provides information about intraclass correlations, which are helpful in determining whether multilevel models are required in the first place.
- In organizational psychology research, data from individuals must often be nested within teams or other functional units.
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- For example, suppose we are evaluating the effects of a medical treatment.
- We enroll 100 subjects into our study, then randomize 50 subjects to the treatment group and 50 subjects to the control group.
- Paired sample t-tests typically consist of a sample of matched pairs of similar units or one group of units that has been tested twice (a "repeated measures" t-test).
- A typical example of the repeated measures t-test would be where subjects are tested prior to a treatment (say, for high blood pressure) and the same subjects are tested again after treatment with a blood-pressure lowering medication.
- By comparing the same patient's numbers before and after treatment, we are effectively using each patient as their own control.
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- Stents are devices put inside blood vessels that assist in patient recovery after cardiac events and reduce the risk of an additional heart attack or death.
- Treatment group.Patients in the treatment group received a stent and medical management.
- Proportion who had a stroke in the treatment (stent) group: 45=224 = 0:20 = 20%.
- These two summary statistics are useful in looking for differences in the groups, and we are in for a surprise: an additional 8% of patients in the treatment group had a stroke!
- In addition, there are many types of stents and this study only considered the self-expanding Wingspan stent (Boston Scientific).
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- A quarter of the patients were assigned a placebo, and the rest were evenly divided between 1g Vitamin C, 3g Vitamin C, or 3g Vitamin C plus additives to be taken at onset of a cold for the following two days.
- (b) What are the treatment and control groups in this study?
- (b) What are the experimental and control treatments in this study?
- Explanatory: Treatment, with 4 levels: placebo, 1g, 3g, 3g with additives.
- (b) Treatment is exercise twice a week.