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Last revised: Feb 6, 9:00am

Midterm Review Guide

Format of Takehome Midterm Questions

• Short answer, 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 has center = μ and spread = σ.
• It 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. The true value of the measurement is μ.

Persons

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

Symbols

• μ     Population mean
  σ     Population standard deviation
  σ²   Population variance = square of σ
  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
• a    Slope of regression equation y = a x + b
• b    Intercept of regression equation y = a x + b
• a^  Slope of estimated regression equation y_i = a^ x_i + b^
• b^  Intercept of estimated regression equation y_i = a^ x_i + b^

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+
• Ideal measurement model: x_i = μ + e_i
• Linear regression model: y_i = ax_i + b + e_i
• Estimated Linear regression model: y_i - y = (r SD_y / SD_y) (x_i - x) or
                                                            y_i = a^x_i + b^

Definitions

• Controlled experiment, double blind, randomization, observational study, lurking variables (also called confounding factors), univariate dataset, histogram, density histogram, bin, Q0, Q1, Q2, Q3, Q4, IQR, mean, SD, SD+, trimmed mean, MAD, variance (=SD squared), z-scores, parsimonious, stem-plot, boxplot, normal plot, mild outliers, extreme outliers, normal density,  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, regression equation.
• 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 sample mean, SD, SD+, Q0, Q1, Q2, Q3, Q4, IQR, by hand.
• Compute the trimmed mean.
• 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.
• 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 of 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.
• Compute a regression equation given using the formula
        y - y = (r SD_y / SD_x) (x - x)
• Given a regression equation and x value find the predicted y value.
• Assess whether a regression model is adequate by looking at the residual plot and normal plot of the residuals.
• Interpret a residual plot (unbiased, biased, homoscedastic, heteroscedastic).
• Interpret R output used in and in projects 2a, 2abc and 3.

Explain

• Be able to explain in terms that someone not familiar with statistics will understand:
  
  1. What are the elements of a controlled experiment in medical research?
  2. 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.
  3. What does a histogram tell you and what does the height of a histogram rectangle represent if the bin widths are not all equal?
  4. What is the ideal measurement model?
  5. What is correlation and how does it relate to causation? Why is correlation not always the same as causation?
  6. What is a regression equation? What is required to have a good linear regression model?