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Midterm Review Guide

Format of Exam Questions

• Short answer, multiple choice, short essay, problems, interpret R output

Items to Know for Midterm

• A univariate dataset can be summarized by a histogram or boxplot.
• A normal histogram
  
  • can be described by a normal histogram with center = μ and spread = σ.
  • can be parsimoneously described by its sample mean (x), which approximates μ and its sample standard deviation (SD+), which approximates σ.
• A bivariate normal dataset
  
  • forms an ellipse shaped cloud. It can be parsimoniously described by x, y, SD_x+, SD_y+, and r.
• The ideal measurement model is x_i = μ + e_i, where the random errors e_i are unbiased, homoscedastic, and normally distributed.

Persons

• Pascal, Graunt, de Moivre, Cotes, Gauss, Fisher, Tukey

Symbols

• μ     Population mean
  σ     Population standard deviation
  σ²   Population variance
  x     Sample mean
  SD  Sample standard deviation, divide by n.
  s_x = SD+  Sample standard deviation, divide by n - 1.
  Q0  Minimum value in sample
  Q1  1st Quartile = 25th Percentile
  Q2  2nd Quartile = 50th Percentile
  Q3  3rd Quartile = 75th Percentile
  Q4  Maximum value in sample

Formulas

• Interquartile Range: IQR = Q3 - Q1
• Inner fences for boxplot: Q1 - 1.5 × IQR; Q3 + 1.5 × IQR
• Outer fences for boxplot: Q1 - 3.0 × IQR; Q3 + 3.0 × IQR
• z-score for individual observations: z = (x - x) / SD+
• Standard error of the average: SE_ave = SD+ / √n
• z-score for sample average: z = (x - μ) / SE_ave
• Ideal measurement model: x_i = μ + e_i
• Linear regression model: y_i = ax_i + b + e_i

Definitions

• Controlled experiment, double blind, randomization, observational study, lurking variables (also called confounding factors), univariate dataset, histogram, density histogram, bin, variance (=SD squared), parsimonious, Q0, Q1, Q2, Q3, Q4, IQR, stem-plot, boxplot, normal plot, mild outliers, extreme outliers, normal histogram, ideal measurement model, bias, center, spread, plot of x_i vs. i (unbiased, biased, homoscedastic, heteroscedastic, standard normal curve), critical point, inflection point, standard units, standard error of the mean, normal score, normal plot, bivariate dataset, bivariate normal, correlation, causation.
• Know both the defining formula and the intuitive idea behind the concept.

Know How To

• Construct a stem-plot, also called a stem-and-leaf display.
• Determine the number or percentage of observations in an interval of a histogram (assuming the data in each bin is distributed uniformily.
• Compute the mean, SD, SD+, Q0, Q1, Q2, Q3, Q4, IQR, by hand.
• Draw a histogram with possibly unequal class widths.
• Compute the median, Q1, Q3, IQR, and mean of a histogram.
• Estimate the proportion of observations in an interval for a histogram.
• Find the proportion of observations in a given interval of a normal histogram using the standard normal table.
• Write down or discuss the ideal measurement model.
• Compute the standard error of the average and a 95 confidence interval for the true measurement in the ideal measurement model
• Draw the boxplot and use it to detect outliers.
• Given an x-value, x, and SD_x, compute the z-score.
• Use the normal table to determine the proportion of observations in a bin of the form [a, b], (-∞, a], or [a, ∞), or (-∞, ∞)
• Obtain percentiles using a normal table: work backwards by looking up the proportion in the body of the table to find the corresponding z-score, then use x = z * mu + sigma, if necessary.
• Use the R function pnorm to compute proportions under the normal curve.
• Use the R function qnorm to compute percentiles under the normal curve.
• Obtain normal scores using the standard normal table.
• Interpret a normal plot (normal, skewed to the left or right, thin tails, thick tails).
• Discuss a plot of x_i vs. i.

Explain

• Be able to explain in terms that someone not familiar with statistics will understand:
  
  1. What to the sample mean and SD tell you about a dataset? What are other ways to estimate the center and spread of a histogram.
  2. What does a histogram tell you and what must you watch out for of the bin widths are not all equal?
  3. What is the ideal measurement model?
  4. The original and current definitions of the meter, second, and kilogram.
  5. What is correlation and how does it relate to causation?
  6. Why is correlation not always the same as causation?
  7. What is a regression equation? What is required to have a good linear regression model.