Behavioral Objectives for PSYC 6430

The student should be prepared to:

  1. Define "internal validity" and "external validity." Identify or give examples of eight kinds of threats to internal validity and four kinds of threats to external validity. Discuss each.
  2. Identify or give examples of the first six designs presented in Campbell & Stanley. For each design, identify strengths and weaknesses.
  3. Identify the critical element that distinguishes experimental from nonexperimental research. Using examples, explain how this allows one to be more confident in making causal attributions.
  4. Explain how extraneous variable control, achieved by either statistical means (blocking, analysis of covariance, etc.) or by procedures for data collection (constancy, balancing, randomization), can influence power and threats to valid inference. Describe the interpretative problems created by using blocking or ANCOV with nonexperimental data or when the covariate (blocking variable) is measured after the experimental treatments are administered.
  5. Given a hypothetical research example, critique the research. Identify any confounds or other limitations and redesign the research to overcome these. Choose an appropriate method of statistical analysis.
  6. Give(n) an example of psychological research, identify independent, dependent, and extraneous variables.
  7. Discriminate between random vs nonrandom sampling procedures and between random sampling vs random assignment to treatment groups.
  8. Summarize the differences among nominal, ordinal, interval, and ratio scales of measurement, especially with respect to the relationships between true scores and measurements. Include discussion of (and definition of) "monotonic relationship" and "linear relationship" in your answer.
  9. Discuss the relationship between scale of measurement and choice of inferential statistic. [Gaito, 1980, Psychological Bulletin. 87: 564-567].
  10. Discriminate between discrete and continuous variables, populations and samples, parameters and statistics, and descriptive and inferential statistics.
  11. Describe the skewness and kurtosis of a distribution of scores. Explain what it is that kurtosis measures.
  12. Define and discuss measures of central tendency (location) [mode, median, mean] and variability (dispersion) [range, probable error or semi-interquartile range, interquartile range, mean absolute deviation, variance, standard deviation]. Given a data set, calculate these statistics.
  13. Construct stem-and-leaf plots and boxplots. Define leading digits, trailing digits, depth, median location, hinge location, H-spread, hinges, fences, adjacent values, and outliers (as defined by Tukey).
  14. Given the probability distribution of a discrete variable, compute its expected value.
  15. Discuss the origins of the .05 level of statistical significance (Cowles & Davis, 1982, Amer. Psychol. 37: 553-558).
  16. Define and discuss unbiasedness, sufficiency, consistency, resistance, and relative efficiency as properties of estimators.
  17. Define "linear transformation" and summarize the effects of linear transformations upon a variable's mean, variance, and standard deviation. Given the mean and variance of distribution A and specification of some linear transformation thereof, find the mean, variance, and standard deviation of the transformed scores.
  18. Demonstrate that even though sample variance is an unbiased estimator of population variance, sample deviation is not an unbiased estimator of population standard deviation.
  19. Describe how one would empirically construct the sampling distribution of a specified statistic (sum, mean, median, mode, variance, difference between means, ratio of variances, number of successes, etc.).
  20. Explain the logic used in hypothesis testing, referring to sampling distributions, critical values, test statistics, rejection and nonrejection regions, alpha, and significance levels.
  21. Distinguish between point estimation and interval estimation, including discussion of the meaning of a confidence coefficient.
  22. Define Type I and Type II errors, alpha, beta, and power. Explain the conditional nature of the probability referred to as "alpha" and discuss how this complicates answering the questions, "What are my chances of making a Type I error?" and "What are the chances that this published rejection of the null hypothesis is a Type I error?"
  23. Give examples of or identify directional vs. nondirectional hypotheses, discuss the relative merits of each, and describe the connection with one- vs. two-tailed tests.
  24. Succinctly define p, the exact significance level.
  25. State the decision rule that compares p to some criterion and decides whether or not to reject the null hypothesis.
  26. Explain what "robustness" of an inferential statistic is.
  27. Tell what proportion of the area under a normal curve is beyond 0.00, 0.67, 1.00, 1.645, 1.96, 2.33, 2.58, and 3.00 standard deviations above the mean.
  28. Convert odds to probabilities and vice versa.
  29. Distinguish among and give examples of the three different basic approaches to (definitions of) probability (analytic or rational; empirical or relative frequency; subjective). Explain what a random variable is in terms of its domain and range. Describe how a probability distribution may be associated with a random variable. Discuss the differences between discrete and continuous random variables.
  30. Give an example to explain the difference between permutations and combinations.
  31. Define or explain or apply basic concepts of probability, including: independence, mutual exclusion, exhaustion, joint-, conditional-, and marginal-probabilities, and additive- and multiplicative-rules.
  32. Give examples of how Chi-square can be used to do a goodness of fit test or a contingency table analysis, or, given one of these research situations, choose and conduct the appropriate analysis.
  33. Describe how the Pearson Chi-square analysis of contingency tables follows directly from its null hypothesis, the definition of independence, and the multiplication rule of probability.
  34. Identify three common misuses of the Pearson Chi-square statistic and relate these misuses to the assumptions of Chi-square in the context of contingency table analysis.
  35. Identify two inferential statistics that use one-tailed tests of nondirectional hypotheses and explain why they do so.
  36. Discuss the use of the "correction for continuity" in c 2 analysis.
  37. Explain how to do a one-way Chi-square goodness of fit test (or a one-way ANOVA, parametric or nonparametric) with directional rather than nondirectional hypotheses.
  38. Describe the consequences (in terms of alpha and beta) of small sample sizes in Chi-square contingency table analyses.
  39. State the central limit theorem and explain its importance in testing hypotheses about sums or means.
  40. Describe the sampling distribution used to test hypotheses about means when the population variance is unknown. Referring to the distribution of sample variances, explain why the sampling distribution used to test hypotheses about means when population variance is unknown is different from a normal curve. Describe what happens to this sampling distribution when sample size increases. Given data, conduct the hypothesis test.
  41. Detail the circumstances under which the independent groups t-test is vs. is not robust to violation of its assumptions, and detail what those assumptions are. Describe how data transformations and/or trimming or Winsorizing samples might be used to condition data so that assumptions are met. Discuss James Bradley's work on the robustness of Z, t, and F tests and the difficulty he has had in getting it published (Bulletin of the Psychonomic Society, 1982, 19: 271-274; 1982, 20: 85-88; 1984, 22: 463-466).
  42. Describe how the analysis of data testing a null hypothesis of equality of means would differ from the standard analysis if the population variances were heterogeneous and could not be equalized with nonlinear data transformations. Explain how would one come to conclude that the population variances were heterogeneous enough to warrant using special analytic techniques for testing the hypotheses about means.
  43. Describe how one would use F to test the null hypothesis that two populations have identical variances and how this analysis would differ from that which tests the null hypothesis that one variance is greater than or equal to another variance. Given data, conduct such a test. Discuss Levene's test, O'Brien's test, and a t-test for heterogeneity of nonindependent variances.
  44. Describe how a matched-pairs t-test can be reduced to a one mean t-test. Given data, conduct such a test.
  45. Explain how a matched-pairs design (t-test) may be either more or less powerful than an independent group design.
  46. Explain how to construct a 95% confidence interval for some parameter. Explain what 95% confidence means. List several factors that determine the width of a confidence interval and explain how they do so. Given data, construct confidence intervals about a mean.
  47. Describe how meta-analysis is used and of what value it is.
  48. Discuss common misconceptions about the relationships among sample size, significance level (p), and confidence in the results of research (Nelson, Rosenthal, & Rosnow, 1986, Amer. Psychol., 41: 1299-1301).
  49. Draw hypothetical distributions of a sample mean representing an exact null hypothesis and an exact alternative hypothesis and : a.) identify alpha, beta, power, critical value, and rejection region; b.) referring to these curves, describe how power is affected by changes in alpha or in sample size; c.) explain how other factors affect power (assume that the population variance is known and the underlying distribution is normal); d.) given formulas and tables, conduct any of the power analyses covered in Howell.
  50. Describe the circumstances under which it is reasonable to "accept" a null hypothesis rather than simply "failing to reject" it. Include an explanation of the difference between a "sharp (point) null hypothesis" and a "loose (range) null hypothesis."
  51. Discuss common misinterpretations of failures to replicate previously significant research (Tachibana, 1980, Percept. Motor Skills, 51: 37-38).
  52. Define d (effect size) as it is used to measure the effect of a dichotomous independent variable upon a continuous dependent variable. Give Cohen's (1969) definitions of small, medium, and large values of d.
  53. Describe the effect of unequal sample sizes upon the power of an independent samples t-test.
  54. Frank Schmidt believes that testing null hypotheses is not a very useful method for psychological researchers to employ (Psychological Methods, 1996, 1, 115-129). Summarize his argument.
  55. Define "covariance". Given a bivariate data set, compute covariance and convert the covariance into a Pearson r. Explain how covariance, like variance, is a special sort of mean.
  56. Given data, compute univariate sums-of-squares and bivariate cross-products sums-of-squares using (as specified) deviation or nondeviation formulas. Show your work, including formulas used. Convert these into regression coefficients.
  57. Explain how the scatterplot quadrants in which most of the values fall determine the direction of the Pearson r. Include the Z-score formula for r in your explanation. Referring to that formula, present r as a mean.
  58. Distinguish between correlation analysis and regression analysis on: a) statistical grounds and b) pragmatic grounds. Do not discuss assumptions of inferential statistics in making this distinction.
  59. Present the General Linear Model in its bivariate form and explain the meaning of each component of the model.
  60. List three distinctly different sources of error variance in bivariate linear regression.
  61. With a bivariate data set one can construct two linear regression lines: one for predicting Y from X, another for predicting X from Y. Describe how the relationship between these two lines changes with changing values of r. Define the point where these two lines always intersect regardless of the value of r.
  62. Given a value of r, interpret that value in terms of how many standard deviations predicted Y increases for each standard deviation increase in known X.
  63. Explain what is meant by "regression toward the mean" when predicting Y from X. Specify the relationship between the value of r and the amount of such regression toward the mean. Find one value of X for which there would be no regression towards the mean on predicted Y regardless of the value of r.
  64. Explain how a bivariate linear regression line is very much like a mean (Hint: the mean is the value of a single variable that minimizes the sum of squared deviations about it).
  65. Explain the significance of slopes and intercepts in regression analyses and describe how one can obtain an r from a regression analysis' slope and two standard deviations.
  66. Describe the partitioning of sums of squares in bivariate linear regression analysis and explain how r is related to these partitioned sums of squares. Give a deviation formula for each SS.
  67. Show how to set up a Bivariate Linear Regression Analysis of Variance Source Table and how to obtain the values that go into that table. Explain how one can use an F or a t-statistic to test the null hypothesis that the slope and the r equal zero in the population. Given data, conduct such an analysis.
  68. Explain the least squares criterion as it is applied to bivariate regression analysis.
  69. Explain the utility of the coefficient of determination. Relate it to a ratio of sums of squares and to r. Define the coefficient of alienation and relate it to a ratio of sums of squares and to r.
  70. Explain regression/correlation in terms of the relationship between variance in Y (X is unknown or r = 0) and the variance in predicted Y.
  71. Show how to compute the standard error of estimate given actual Y and Y predicted from a linear regression. Relate this quantity to the residual (error) variance or Mean Square Error. Explain how the residual variance is a special sort of mean, just like any other variance is a special sort of mean. Find one circumstance under which the standard error of estimate for predicted Y would equal the standard deviation in Y.
  72. Draw a linear regression line in Cartesian space. Sketch in: a) Confidence limits for E (Y|X), the expected average value of Y given X, and b) Confidence limits for a predicted individual value of Y|X. Explain the difference between these two types of confidence intervals.
  73. Give an example illustrating how two different bivariate populations can: a) have identical slopes for the relationship between X and Y but different values of Pearson r, or b) have identical r's but different slopes, or c) have identical r's and slopes but different intercepts. Draw scatter plots to illustrate this.
  74. Describe the assumptions necessary to use the sample estimated residual variance (mean square error, the square of sample standard error of estimate) as an unbiased estimate of population residual variance (the amount of variance in Y not attributable to X's linear relationship with X).
  75. Describe the assumptions of a test of the null hypothesis that a population product moment correlation coefficient is zero (with the interpretation that such a value of r means that X and Y are independent random variables).
  76. Describe the assumptions involved in testing null hypotheses about bivariate regression coefficients. Sketch out a scatterplot showing no violations of assumptions. For each assumption, sketch out a scatterplot illustrating violation of that assumption.
  77. Describe the assumptions necessary to use linear correlation/regression coefficients as descriptive statistics.
  78. Explain how very small sample sizes can produce spuriously large values of r2 (values much larger than that present in the parent population from which the data were randomly sampled). Explain why r2 will equal 1.00 when n = 2 regardless of the correlation between X and Y in the parent population. Name and describe a statistic that provides a relatively unbiased estimate of population r2 given sample r2 and n.
  79. Describe the possible effects of a) range restriction and b) heterogeneous subsamples upon the value of r.
  80. Some researchers mistakenly believe that there are some inferential statistics (two mean t-tests and ANOVA) that permit causal inference and others (correlation and regression analyses) that do not. The truth is that correlation (covariance, association) is necessary but not sufficient to establish causation. Use the relationship between the independent groups t-test and a significance test for r to illustrate the folly of these researchers. Explain what design characteristic(s) must be present to interpret the correlation between X and Y as a cause-effect relationship. Use research examples to illustrate your argument.
  81. Describe the circumstances under which one would employ: a) a biserial correlation and b) a tetrachoric correlation.
  82. Contrast the Pearson r with the Spearman rho with respect to the measurement of the linearity/monotonicity of the association between X and Y. Present bivariate data sets to illustrate the contrast. Define monotonicity of a line, referring to its slope. Given data, compute a Spearman rho.
  83. Discuss the relationships among the independent groups t-test, the product moment correlation coefficient, and point-biserial correlation coefficient.
  84. Discuss the relationships among the phi coefficient, the product moment correlation coefficient, and the Chi-square analysis of 2 x 2 contingency tables.
  85. Describe the most simple way of computing a Spearman rank order correlation coefficient for a sample of 100 pairs of scores containing several tied ranks.
  86. Give an example of data that could be analyzed with Kendall's tau and start the analysis.
  87. Write the general equation for a bivariate linear regression, identify each of its terms, and describe how the regression line and the data from which it was generated can be represented in a two-dimensional space (using a Cartesian coordinate system). Do the same for a trivariate regression (two predictors) in three dimensional space, describing the regression plane. Now, off into hyperspace. Do the same for a regression with p (p > 2) predictors.
  88. Define R, the multiple correlation coefficient, as a bivariate correlation.
  89. Discuss why multiple linear regression coefficients are sometimes referred to as partial regression coefficients.
  90. State null and alternative hypotheses used in analyses of variance (ANOVA).
  91. Starting with the structural model that Yij = Grand Mean + t j + eij derive the deviation formulae for the sums of squares for a one-way independent samples ANOVA. (Hint: start by substituting the relevant statistics for Grand Mean, t j, & eij.
  92. Given a set of not more than 20 scores, integers ranging from 0 to 10, divided equally or unequally into 2 to 4 one-way groups with integer means, compute by hand an independent samples ANOVA on these scores, presenting the results in a standard source table. Use deviation formulas or nondeviation (totals) formulas (as specified) to compute the sums of squares.
  93. Summarize the logic of a one-way independent samples ANOVA, including the partitioning of the sums-of-squares, the expected values for the two relevant mean squares, the expected value of the F-ratio when the null hypothesis is true, the conversion of F into a significance level, and the use of this significance level as a measure of the apparent veracity of the null hypothesis. Explain why a one-tailed probability is appropriately used to evaluate the nondirectional null hypothesis in ANOVA. Explain how this one-tailed p would be adjusted if one correctly predicted (with directional hypotheses) the order of the K (sample) treatment means.
  94. Given sample variance, sample mean, and sample size for each of K groups, with sample size constant or not constant across groups, compute treatment and error mean squares for a one-way independent samples ANOVA.
  95. Explain the differences between fixed-effects, random-effects, & mixed-effects ANOVAs and give examples of each.
  96. Describe the assumptions of a one-way independent samples ANOVA, comment on the robustness of the ANOVA to violations of one or more of these assumptions, and discuss methods of correcting for violation of assumptions (data transformations, trimmed or Winsorized samples, Box's method, and the Welch test).
  97. Use eta, the curvilinear correlation coefficient, to explain the link between one-way independent samples ANOVA analysis and curvilinear regression.
  98. Define and comment upon eta-squared and omega-squared as measures of an independent variable's magnitude of effect. Explain how holding extraneous variables constant can artificially inflate such "variability accounted for" statistics and make interpretation difficult [Eagly, 1987, American Psychologist, 42: 756-757].
  99. Given formulas and tables, determine how many subjects are needed in each treatment group in order for a one way independent samples ANOVA to have a specified probability of detecting a treatment effect of a specified magnitude.
  100. Distinguish among per comparison, per experiment, and familywise error rates and tell how to compute each.
  101. Distinguish between a priori and a posteriori multiple comparison tests of treatment means and compare and contrast several techniques available for making such comparisons. Identify the procedure which requires that an omnibus ANOVA be significant. (See Ryan, Psychological. Bulletin, 56: 394-396.)
  102. Explain what orthogonal contrasts are, why they are mathematically beautiful, and what their practical value is. Find a complete set of orthogonal coefficients for a K group design, or, given a set of orthogonal coefficients, be able to identify whether or not they are orthogonal.
  103. State the Bonferroni inequality and show how it can be used to control alpha familywise.
  104. Describe Sidak's (J. Amer. Stat. Assoc., 62: 626-633) modification of the Bonferroni inequality and explain how it can be used to increase power (relative to that of the Bonferroni procedure) when making multiple comparisons.
  105. Identify the circumstance in which Fisher's LSD would be the procedure of choice (hold familywise error rate at the stated level while maintaining power) for pairwise comparisons following a significant one-way ANOVA. Should you ever need to justify using LSD in this circumstance, refer your critic to page 370 of Howell (4th edition) or to Levin et al., Psychological Bulletin, 1994, 115, 153-159.
  106. Describe a situation in which one would be justified in making a particular comparison between two group means even though the ANOVA done on data from these two (and several other) groups was not significant (see Howell, 4th ed., p. 372).
  107. Describe the relationships among t, F, and q (the studentized range statistic).
  108. Howell used to recommend the Student-Newman-Keuls test for making pairwise comparisons with four or five groups, but he now (4th edition) recommends the Ryan/Einot/Gabriel/Welsch (REGWQ) procedure. Compare this procedure to the Tukey and Student-Newman-Keuls procedures. Explain why you would probably need a computer to conduct this test.
  109. Explain what an ANOVA interaction is in terms of: a) additivity of the main effects of independent variables A and B in determining the combined effect of A and B, and b) differences among simple main effects. Distinguish between monotonic and nonmonotonic interactions. Distinguish between nested and crossed factors. Explain and give an example of a triple interaction among independent variables in ANOVA. Explain what a main effect is. Explain how an independent variable may involve comparisons either "between subjects" or "within subjects," including discussion of "independent samples," "randomized blocks," and "split plot" designs.
  110. Use the computer to analyze data with any of the statistical procedures covered in class. Be especially familiar with the SAS statistical package.
  111. Pick the correct statistical analysis given the following information:  a. whether X is dichotomous, categorical (K > 2), or continuous;  b. whether Y is dichotomous, categorical (K > 2), or continuous;   c. whether Y (or X) is normally distributed at each level of X (or Y); d. whether Y has the same distributional shape at each level of X;  e. whether the variance in Y (or X) is constant across levels of X (or Y);  f. whether the Y scores at one level of X are correlated with the Y scores at another level of X.  On the basis of this information, describe one (or more) complete and appropriate statistical analyses. You want to know whether X and Y are associated in the population from which you have randomly sampled N experimental units (subjects). You have measured or manipulated X and then measured Y on each unit. Your primary interest is in the effect of X on the location of Y. If you are given incomplete information, you must specify what additional information you need to choose an analytic technique. There may be more than one X, factorially combined.

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