# Review for Lessons 2 to 5 (Exam 1)

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### 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

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.    (Tell Me More...)

Sampling types:   (Tell Me More...)

• simple random sampling;
• stratified sampling;
• cluster sampling;
• systematic sampling;
• non-probability sampling schemes (e.g. voluntary/convenience/self-selected/ haphazard)

Comparative Study types:

• observational versus experimental;
• retrospective versus prospective;
• matched pair & block designs;
• subject-blinded/researcher-blinded/double-blinded

Variable types:

• explanatory / response / confounding;   (Tell Me More...)
• categorical / ordinal / discrete measurement/continuous measurement   (Tell Me More...)

Measurement issues:   (Tell Me More...)

• bias;
• reliability;
• validity

Sampling issues:

• low response rate;
• nonresponse bias;
• question wording issues;

sampling frame ≠ population; small sample size (low reliability); non-probability sampling schemes

Experiment issues:

• confounding variables;
• interacting variables;
• placebo, Hawthorne, and experimenter effects;
• lack of ecological validity and
• 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)    (Tell Me More...)

Measures of location:    (Tell Me More...)

• mean;
• median

Measures of variability:    (Tell Me More...)

• standard deviation;
• $$IQR (= Q_U – Q_L)$$

Measures of relative standing:

• percentiles;
• standard scores (also known as z-scores)

Pictures of distributions:

• boxplots or histograms for measurement variables    (Tell Me More...)
• piecharts or bar-graphs for categorical variables (bar graphs for ordinal variables)    (Tell Me More...)
• time series plots for tracking summaries over time (issues: trend; seasonality; random fluctuations)    (Tell Me More...)

Distribution shapes:   (Tell Me More...)

• skewed left/skewed right/symmetric/bimodal;
• normal (bell-shaped)

Standardized score = z =(value – average)/st. dev     (Tell Me More...)

or

Observed value = mean + (standardized score)(st. dev.)

Empirical 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)