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Midterm Review Guide

Read in Textbook

Chapters 1 and 2.

Format of Exam Questions

• Short answer, multiple choice, short essay, problems, SPSS analysis

Short Summary of Material before the Midterm Exam

• A univariate dataset can be summarized by a histogram or boxplot.

• A univariate normal dataset
  
  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.
  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 linear regression model is y_i = a x_i + e_i, where the random errors e_i are unbiased, homoscedastic, and normally distributed.

Persons

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

Definitions

• Controlled experiment, double blind, randomization, observational study, lurking variables (also called confounding factors), univariate dataset, histogram, density histogram, bin, mean, median, standard deviation (SD vs. SD+), variance, 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 (Van der Waerden's method), normal plot, bivariate dataset, bivariate normal, correlation, R-squared value, causation, regression line, residual plot (residuals vs. predicted values, unbiased, biased, homoscedastic, heteroscedastic), root mean square error.

• Where appropriate, 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 within 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, ∞).

• Given a number p between 1 and 100, find the percentile for that value, 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 SPSS to compute proportions under the normal curve with Cdf.Normal.

• Use SPSS to compute percentiles with Idf.Normal.

• Find normal scores using Van der Waerden's method.

• 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 using residual and normal plots.

• Interpret a residual plot (unbiased, biased, homoscedastic, heteroscedastic).

• Compute the root mean squared error using this formula:
  RMSE = SD_y √(1 - r²)

• Create a crosstabs table.

• Interpret the output of SPSS analyses similar to the ones in the examples and in projects 2 and 3.

Explain

• Be able to explain in terms that someone not very familiar with statistics will understand:
  1. What to the sample mean and SD tell you about a dataset?

  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.