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Elementary Statistics

Elementary Statistics. Chapter 3. Definitions. In a designed experiment , the researcher actively imposes some treatment on the units or subjects in order to observe the responses.

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Elementary Statistics

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  1. Elementary Statistics Chapter 3

  2. Definitions • In a designed experiment, the researcher actively imposes some treatment on the units or subjects in order to observe the responses. In an Observational study, the researcher simply observes the subjects or units and records variables of interest.

  3. Definitions • A response variable (Y) measures an outcome of the study. It is a variable that is thought to depend in some way on the explanatory variable.

  4. Definitions • An explanatory variable or factor (X) is a variable that is thought to explain or cause the observed outcomes. It is a variable that is thought to explain the changes in the response variable.

  5. Definitions • The possible values of the explanatory variable are called the levels of that explanatory variable. A treatment is a specific combination of the levels of the explanatory variables.

  6. Confounding • A confounding variable is a variable whose effect on the response variable cannot be separated from the effect of the explanatory variable on the response variable.

  7. Observational Studies • A retrospective study is a study of past events. Researchers identify subjects that have experienced certain responses and look back to see if the subjects also had various factors or explanatory variables. Subjects may be asked to recall past events. A retrospective study works from the responses to the potential explanatory variables.

  8. Observational Studies • A prospective study is a study of ongoing or future events. Researchers identify subjects which have various explanatory variables or factors and follow them into the future and record the responses. A prospective study works from the potential explanatory variables to the responses.

  9. Let’s Do It! • P. 147, 3.5

  10. Definitions • A treatment group is a group of subjects or experimental units that receive an actual treatment. A control group is a group of subjects or experimental units that are treated identically in every way, except that they do not receive an actual treatment.

  11. Assigning the units • Random allocation is a planned use of chance for assigning the units to the treatments. An experiment is completely randomized if the experimental units are randomly assigned to the treatment combinations.

  12. Think About It • A researcher has a treatment group and a control group. The control group will receive a placebo. The subjects will be randomly assigned to one of the two groups. Those in the treatment groups receive a bottle of medication marked “DRUG,” while those in the control group receive a bottle of medication marked “PLACEBOS.” What is wrong with the researcher’s experimental design?

  13. The Placebo Effect • The placebo effect is a phenomenon in which receiving medical attention, even administration of an inert drug, improves the condition of the subjects.

  14. The Placebo Effect • Experimenter bias is the distortion that can arise on the part of the experimenter due to how the subjects are assigned to the groups, which variables are measured and how they are measured, and how the results are interpreted. The bias is generally in the direction of the researcher’s theory.

  15. The Placebo Effect • A single-blind experiment is one in which only the subjects are ignorant of which treatment they receive. A double-blind experiment is one in which neither the subjects nor those working with the subjects knows who is receiving which treatment.

  16. Think About It • Why not save money and assign just one subject to each of the two groups? Suppose that we only had two subjects and assigned one at random to the vitamin C treatment and the other to receive a placebo. The subject receiving the vitamin C was a male and had only one cold. The subject receiving the placebo was a female and had three colds. Would you trust these results and conclude that vitamin C leads to fewer colds?

  17. Replication • If at least two units are assigned to each treatment combination, we have replication in an experiment. If there is the same number of units assigned to each treatment combination, the experiment design is balanced.

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