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AP Statistics Section 10.2 B

AP Statistics Section 10.2 B. Comparative studies are more convincing than single-sample investigations. For that reason, one-sample inference is less common than comparative inference. Paired t procedures are called for in the following situations.

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AP Statistics Section 10.2 B

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  1. AP Statistics Section 10.2 B

  2. Comparative studies are more convincing than single-sample investigations. For that reason, one-sample inference is less common than comparative inference. Paired t procedures are called for in the following situations

  3. A matched pairs designexperiment. 1. Subjects are matched in pairs andeach treatment is given to onesubject in each pair. 2. Each subject receives bothtreatments in some order. Before-and-after observations on the same subjects.

  4. To compare the responses to the two treatments in a matched pairs design or before-and-after measurements on the same subjects, apply one-sample t procedures to the observed difference.

  5. The parameter in a paired t procedure is: 1. the mean difference in the responses to the twotreatments within matched pairs of subjects in theentire population (when subjects are matched inpairs) 2. the mean difference in response to the twotreatments for individuals in the population (whenthe same subject receives both treatments 3. the mean difference between before-and-aftermeasurements for all individuals in the population(for before-and-after observations on the sameindividuals).

  6. Example: Our subjects are 11 people diagnosed as being dependent on caffeine. Each subject was barred from coffee, colas and other substances containing caffeine. Instead, they took capsules containing caffeine. During a different time period, they took placebo capsules. The order in which subjects took caffeine and the placebos was randomized. The table contains data on two of several tests given to the subjects.

  7. “Depression” is the score on the Beck Depression Inventory. Higher scores show more symptoms of depression. “Beats” is the number of beats per minute the subject achieved when asked to press a button 200 times as quickly as possible. We are interested in whether being deprived of caffeine affects these outcomes. Let’s construct a 90% confidence interval for the mean change in depression score. As always, we will follow the Inference Toolbox format.

  8. Step 1: Parameter The population of interest is We want to estimate _____________________ (the mean difference in depression score that would be reported if all individuals in the population took both the caffeine capsule and the placebo)

  9. Step 2: Conditions Since the population standard deviation of the differences in depression scores is not known we will use ___________________________to construct a confidence interval for since.SRS:

  10. Normality: if not normal: boxplot?Normal probability plot?

  11. Independence:

  12. Step 3: Calculations

  13. Step 4: Interpretation

  14. Random selection of individuals for a statistical study allows us to generalize the results of that study to a larger population.Random assignment of treatments to subjects in an experiment lets us investigate whether there is evidence of a treatment effect, which might suggest that the treatment caused the observed difference

  15. Robustness of t ProceduresAn inference procedure is called robust if the probability calculations involved in that procedure remain fairly accurate when a condition for use of the procedure is violated. For confidence intervals, this means that the stated confidence is still fairly accurate.

  16. As long as there are no significant departures from Normality (especially outliers), the t procedures will work quite well. Because both s and are not resistant to outliers the t procedures are not robust against outliers.

  17. Using the t ProceduresExcept in the case of small samples, the assumption that the data are an SRS from the population of interest is moreimportant than the assumption that the population distribution is Normal.

  18. Sample size less than 15. Use t procedures if the data are close to Normal. If the data are clearly non-Normal or if outliers are present, do NOT use t procedures.Sample size at least 15. The t procedures can be used except in the presence of outliers or strong skewness.Large samples. The t procedures can be used even for clearly skewed distributions when the sample size is large, say _______. Note: Outliers are still a problem!!!

  19. If the data you have is the entire population of interest, then there is no need to perform inference of any kind.

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