Review for Lessons 1 to 4 (Exam 1)
Review for Lessons 1 to 4 (Exam 1)Introduction
This page is essentially the page of formulas and notes that you can use to study for Exam 1. You will find a printable version of this in Canvas that you can print out and bring to your proctored exams. The printable version also includes the normal table which you may need for the exam as well.
However, this web page contains much more information than the printable version. Click on the 'Tell Me More...' links to access the basic idea behind, examples and further references for the topics listed on this page.
Outline of Material Covered on Exam 1
 Margin of Error
 The Margin of Error for a sample proportion from a random sample is around \(1 / \sqrt{n}\) where n is the sample size. It does not depend on the population size.

 Sampling Types

 simple random sampling
 stratified sampling
 cluster sampling
 systematic sampling
 nonprobability sampling schemes (e.g. voluntary / convenience / selfselected / haphazard)
 Comparative Study types:

 observational versus experimental
 retrospective versus prospective
 matched pair & block designs
 subjectblinded /researcherblinded / doubleblinded
 Variable types

 explanatory / response / confounding
 categorical / ordinal / discrete measurement / continuous measurement
 explanatory / response / confounding
 Measurement Issues:

 bias
 reliability
 validity
 Sampling Issues

 low response rate
 nonresponse bias
 question wording issues
sampling frame ≠ population; small sample size (low reliability); nonprobability sampling schemes
 Experiment Issues:

 confounding variables
 interacting variables
 placebo, Hawthorne, and experimenter effects
 lack of ecological validity
 generalizability
 Observational Study Issues:

 confounding
 claiming causation when only association is shown
 extending the results inappropriately
 using the past as a source of data
 The Five Number Summary

 minimum, lower quartile, median, upper quartile, maximum
 Measure of Location

 mean
 median
 Measures of Variability:

 standard deviation
 \(IQR (= Q_U – Q_L)\)
 Measures of Relative Standing

 percentiles
 standard scores (also known as zscores)
 Pictures of Distributions

 Boxplots or Histograms for Measurement Variables
 piecharts or bargraphs for categorical variables (bar graphs for ordinal variables)
 time series plots for tracking summaries over time (issues: trend / seasonality / random fluctuations)
 Boxplots or Histograms for Measurement Variables
 Distribution Shapes:

 skewed left / skewed right / symmetric / bimodal
 normal (bellshaped)
 Standardized Score
 The zscore is equal to the value minus the average all divided by the standard deviation
 Observed Value
 The observational value is equal to the mean plus the product of the standardized score times the standard deviation
 Emperical Rule
 if a distribution is close to the normal curve then about 68% of the values are within one standard deviation of the mean and 95% are within two standard deviations of the mean
 Percentiles of the normal distribution depend only on standard scores (z)