East Carolina University
Department of Psychology
During the course of the semester each student should acquire the ability to:
Discriminate between: descriptive statistics and inferential statistics; populations and samples, and parameters and statistics.
Use standard summation notation.
Construct and utilize grouped and ungrouped frequency distribution tables, histograms, stem-and-leaf displays, and box-and-whisker plots.
Identify distributions' shapes (skewness, modality).
Discriminate between random and nonrandom sampling procedures.
Summarize the differences among nominal, ordinal, interval, and ratio scales of measurement.
Discuss the relationship between scale of measurement and choice of inferential statistic.
Discriminate between discrete and continuous variables.
Discriminate between experimental and nonexperimental research.
Give(n) an example of experimental psychological research, identify independent, dependent, and extraneous variables.
Compute mean, median, mode, range, interquartile range, mean absolute deviation, variance, and standard deviation.
Use SPSS to do statistical computations.
Compare and contrast three different measures of central tendency and five different measures of dispersion.
Define and discuss unbiasedness, consistency, sufficiency, resistance, and relative efficiency as properties of estimators.
Compute and utilize z-scores and other standard scores.
Know the values of z marking off the middle 50%, 68%, 90%, 95%, 98% and 99% of a normal distribution.
Use the normal curve table and SPSS to obtain areas under the curve given values of z and vice versa.
Distinguish among and give examples of the three different basic approaches to (definitions of) probability (analytic or theoretical or classical or rational ; empirical or relative frequency; subjective).
Convert from odds to probabilities and vice versa.
Construct and interpret odds ratios.
Define or explain and utilize basic concepts of probability, including: independence, mutual exclusion, exhaustion, joint-, conditional-, and marginal-probabilities, and additive- and multiplicative-rules.
Describe how one would empirically construct the sampling distribution of a specified statistic (sum, mean, median, mode, variance, difference between means, ratio of variances, etc.).
Explain the logic used in hypothesis testing, referring to null and alternative hypotheses, sampling distributions, critical values, rejection and nonrejection regions, alpha, exact significance level (p), and test statistics.
Define Type I and Type II errors, alpha, beta, and power. Succinctly define p, the exact significance level, and state the decision rule that compares p to alpha and decides whether or not to reject a null hypothesis.
Produce, utilize, and discriminate between directional and nondirectional hypotheses, and one- and two-tailed probabilities.
State the central limit theorem and explain its importance in testing hypotheses about means.
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 and how it is different from a normal curve.
Give a simple example explaining the concept of degrees of freedom.
Distinguish between point estimation and interval estimation, including discussion of the meaning of a confidence coefficient.
Explain how to construct a 95% confidence interval for some parameter. Explain what "95% confidence" means. List three factors that determine the width of a confidence interval and explain how they do so.
Compute estimates of and confidence intervals for standardized effect size.
Define and give (or recognize) examples of independent samples designs vs correlated samples designs (within subjects or repeated measures and matched pairs or randomized blocks). Be able to choose and compute the inferential statistic appropriate for a particular design.
Discuss advantages and disadvantages of within subjects designs.
List and explain the assumptions of the independent groups t-test.
Explain the use of pooled variance estimates in the independent groups t-test. Identify circumstances under which one should not pool variances and explain how such an unpooled analysis should be conducted.
Recognize and explain problems associated with the confounding of variables.
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) refering to these curves, describe how power is affected by changes in alpha or in sample size, and; c) explain how other factors affect power. Assume that the population variance is known and the underlying distribution is normal.
Explain how a matched-pairs design (t-test) may be either more or less powerful than an independent groups design.
Estimate the number of subjects needed to have a specified probability of detecting an effect as large or larger than some specified minimum nontrivial effect size.
Calculate power given effect size, alpha, and other relevant statistics.
Describe the circumstances under which it is reasonable to "accept" a null hypothesis rather than simply "failing to reject" it.
Construct and interpret scatter plots and residuals plots.
Present the General Linear Model in its bivariate form and explain the meaning of each component of the model.
Explain the least squares criterion as it is applied to regression analysis.
Explain the utility of the coefficient of determination. Relate it to a ratio of sums of squares.
For variables X and Y, explain the relationships among sum of deviation cross products, covariance, r, and the degree and direction of linear relationship.
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).
Explain the significance of slopes and intercepts in regression analyses and describe how one can obtain an r from a regression analysis' slope.
Describe the partitioning of sums of squares in bivariate linear regression analysis and explain how r2 is related to these partitioned sums of squares.
Explain regression/correlation in terms of the relationship between variance in Y(X is unknown or r2 = 0), the variance in predicted Y, and the error variance in Y.
Show how to compute the standard error of estimate given actual Y and Y predicted from a linear regression.
Describe the assumptions necessary to use MSE as an unbiased estimate of population error variance.
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).
Describe the assumptions involved in testing null hypotheses about bivariate regression coefficients.
Describe the possible effects of a) range restriction and b) extraneous variance upon the value of r.
Discuss the relationships among the independent groups t-test, the product moment correlation coefficient, and the point-biserial correlation coefficient.
Discuss the relationships among the phi coefficient, the product moment correlation coefficient, and the chi-square analysis of 2 X 2 contingency tables.
Describe the most simple way of computing a Spearman rank order correlation coefficient for a sample of 100 pairs of scores containing 25 tied pairs at 15 different ranks.
Place confidence limits on average or individual values of predicted Y given X.
Construct a confidence interval for rho.
Expand the bivariate linear model to a multiple regression. Give an example of a multiple regression.
State null and alternative hypotheses used in analyses of variance.
Given sample variance, sample mean, and sample size for each of k groups, with sample size constant across groups, compute treatment and error mean squares for a one-way independent samples ANOVA.
Given a set of not more than 20 scores, integers ranging from 1 to 10, divided equally 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.
Summarize the logic of a one-way independent samples ANOVA, including the partitioning of the sums-of-squares, what it is that the two relevant mean squares estimate, 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 fit between the data and the null hypothesis.
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.
Define and comment upon two different measures of magnitude of effect used with ANOVA.
Place a confidence interval on eta-squared.
Explain the use of Fisher's LSD as a multiple comparison technique.
Explain how one could use the Bonferroni inequality or Sidak's modification thereof to control alpha familywise in a set of c multiple comparisons.
Explain why the REGWQ is the recommended test when one wishes to make pairwise comparisons among the means from four or more groups.
Give an example of a two-way factorial design. Define main effects, interaction, and simple main effects. Discuss the advantages of the factorial design over the one-way design.
Explain and give an example of a triple interaction.
Conduct one-way within-subjects ANOVA. Explain the difference between crossed and nested factors. Discuss the use of counterbalancing to control order effects.
Give examples of how chi-square can be used to: a) test null hypotheses about variance, b) do a goodness of fit test, and c) do contingency table analyses OR, given one of these research situations, prescribe the appropriate analysis.
Identify two inferential statistics that use one-tailed tests of nondirectional hypotheses and explain why they do so.
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.
Discuss the differences between parametric and nonparametric inferential procedures. Contrast the hypotheses they test and the assumptions they make. Include Wilcoxon's rank tests and Friedman's test in your discussion.
Given a hypothetical research example with data, choose and conduct an appropriate statistical analysis. Interpret the results. Be able to compute any of the statistics mentioned in this document or in the textbook. Be able to interpret and critique published research reports using these statistics.
Discuss two undesirable effects of uncontrolled extraneous variables: a) added noise, and b) confounding. Identify ways to control each, comment upon the seriousness of each, and identify situations in which control is likely to be difficult to achieve (give examples).
Write an APA-style summary statement for any statistical procedure covered in this class.
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This page most recently revised on the 12th of April, 2012.