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Exploring Measurement Types and Experimental Design in Statistics

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This collection focuses on key concepts and definitions related to statistical measurement types and experimental design. It outlines various types of data including ordinal, nominal, and continuous measurements, and discusses the implications of sample selection, including random, systematic, and stratified sampling methods. The text emphasizes the importance of properly conducted observational and experimental studies, addressing potential confounding factors and the significance of replication and appropriate sample sizes in research. This guide serves as an essential resource for students and professionals in statistics and research methodologies.

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Exploring Measurement Types and Experimental Design in Statistics

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  1. Test your knowledge • A complete collection of elements to be studied is: • Type of measurement involving data that may be arranged in some order but differences between data values are meaningless: • Type of data resulting from finite number of values. • Numerical measurement describing some characteristic of a population. • Type of data resulting from infinitely many possible values. • Type of measurement where differences are meaningful and includes an inherent starting point. • Numbers representing counts or measurements. • Type of measurement where there is meaningful amounts of differences between data, but no natural starting point. 9. Sub collection of elements drawn from a population:

  2. Section 1-4 Design of Experiments

  3. Key Concept • If sample data are not collected in an appropriate way, the data may be so completely useless that no amount of statistical torturing can salvage them.

  4. Definition • Observational study: observing and measuring specific characteristics without attempting to modify the subjects being studied • Experiment: apply some treatment and then observe its effects on the subjects; (subjects in experiments are called experimental units)

  5. Does drinking at least five carbonated sodas a week improve a student’s GPA? • Observation: Compare the GPA’s of a sample of students who drink more than five sodas a week with those who drink less. • Experiment: From a random group of students, require some to drink more than five sodas per week, and require the rest to drink less. After a couple of years, compare their GPA’s.

  6. Definitions • Cross sectional study: data are observed, measured, and collected at one point in time • Retrospective (or case control) study • data are collected from the past by going back in time • Prospective (or longitudinal or cohort) study • data are collected in the future from groups (called cohorts) sharing common factors

  7. Definition • Confounding occurs in an experiment when the experimenter is not able to distinguish between the effects of different factors

  8. Controlling Effects of Variables • Blinding: subject does not know he or she is receiving a treatment or placebo • Blocks: groups of subjects with similar characteristics • Completely Randomized Experimental Design: subjects are put into blocks through a process of random selection • Rigorously Controlled Design:subjects are very carefully chosen

  9. Ex1: We want to see the effects a new treatment has on people with heart disease. What could confound the results of this study? Ex2: We want to see the outcome of a pill on cholesterol level. What can confound the results of this study?

  10. Replication and Sample Size • Replication: repetition of an experiment when there are enough subjects to recognize the differences from different treatments • Sample Size: use a sample size that is large enough to see the true nature of any effects and obtain that sample using an appropriate method, such as one based on randomness

  11. Definitions • Random Sample: members of the population are selected in such a way that each individual member has an equal chance of being selected • Simple Random Sample (of size n) subjects selected in such a way that every possible sample of the same size n has the same chance of being chosen

  12. Random Sampling selection so that each individual member has an equalchance of being selected

  13. Systematic SamplingSelect some starting point and then select every k th element in the population

  14. Convenience Samplinguse results that are easy to get

  15. Stratified Samplingsubdivide the population into at least two different subgroups that share the same characteristics, then draw a sample from each subgroup (or stratum)

  16. Cluster Samplingdivide the population into sections (or clusters); randomly select some of those clusters; choose all members from selected clusters

  17. Methods of Sampling - Summary • Random • Systematic • Convenience • Stratified • Cluster

  18. Definitions • Sampling error the difference between a sample result and the true population result; such an error results from chance sample fluctuations • Nonsampling error sample data incorrectly collected, recorded, or analyzed (such as by selecting a biased sample, using a defective instrument, or copying the data incorrectly)

  19. Statdisk • Technology Project, p. 37

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