Lecture 01/02

Students will be able to:

• distinguish between categorical and quantitative variables or data and, within each type, respectively, to distinguish between ordinal and non-ordinal categorical variables and between discrete and continuous quantitative variables.
• define distributions and frequency tables.
• distinguish between bimodal, unimodal, normal, leptokurtic, platykurtic, skewed, and symmetric distributions
• construct histograms from raw data, including setting category boundaries for continuous data (or discrete data with low frequencies within data classes).
• calculate the value of a summation notation expression.
• calculate summary statistics (mean, mode, median, range, interquartile range, standard deviation, and variance) from raw data.
• select the appropriate transformation to add or subtract a constant or to alter the scale of a data set.
• select the appropriate transformation and transform raw data to normalize skewed data.
• predict the effect of the transformation on the mean and standard deviation of the data.

Lecture 03

Students will be able to:

• determine whether or not a situation represents random sampling or not.
• distinguish between a parameter and a statistic
• define sampling error and be able to identify both bias and homogeneity in samples.
• use both theoretical means and empirical means to estimate probability.
• calculate combined probabilities when each probability is independent of other probabilities (including both the union and intersection of independent probabilities) using both algebraic formulas and probability tree diagrams.
• define the axes for probability distributions.
• calculate binomial probabilities and binomial distributions.
• apply the binomial distribution to make predictions of the outcomes from situations that conform to the assumptions of the binomial distribution.
• calculate the mean and standard deviation of the binomial distribution.

Lecture 04

Students will be able to:

• define the normal curve and explain each axis.
• explain the difference between a symmetric and a skewed distribution and apply these concepts to the normal curve.
• calculate the inflection points of a normal curve, given its mean and standard deviation.
• define leptokurtosis and platykurtosis.
• describe the relationship between probability and the area under the normal curve.
• calculate z-scores.
• calculate the appropriate probabilities and z-scores from actual data as an answer to a question about the data, assuming the data is normally distributed.
• calculate actual and expected (based on normality) cumulative percentages, plot one versus the other, and correctly conclude whether or not the data is distributed normally based on the plot.
• calculate the continuity correction and apply it to situations that require it.

Lecture 05

Students will be able to:

• define sampling variation.
• define, in their own words,  a sampling distribution.
• draw a sampling distribution from given data and label the axes.
• evaluate a variable and correctly decide if it is a dichotomous or if it can be transformed so that it becomes dichotomous.
• calculate and graph the binomial distribution.
• evaluate the area under the curve of a binomial distribution in terms of probability.
• apply the binomial distribution to problem scenarios.
• distinguish between quantitative versus  qualitative variables.
• define and calculate the expected mean and standard deviation of sample means drawn from a quantitative variable.
• calculate the standard deviation of sample means.
• predict the effect of the central limit theorem on the mean of sample means and the standard deviation of sample means.
• predict and calculate the effect of sample size on the mean of sample means and the standard deviation of sample means.
• apply the continuity correction when calculating the probability of a defined set of outcomes.

Lecture 06

Students will be able to:

• distinguish between estimation in general and statistical estimation using the concept of p-values.
• define a confidence limit.
• distinguish between the standard deviation of a sample and the standard error of the mean.
• calculate the standard error of the mean from a sample.
• use the tables in the book to look up t values for given sample sizes and tail probabilities.
• calculate a confidence interval for the true mean of a population given the true mean and standard deviation.
• calculate a confidence interval for the true mean of a population given a sample randomly drawn from that population.
• use a confidence interval calculation to correctly evaluate questions about a research scenario.
• give the conditions of validity for the use of the confidence interval.
• determine if it is appropriate to use the confidence interval for a given scenario.
• calculate the appropriate sample size to use when given an estimate of the true standard deviation, a level of confidence, and a estimation of the experimental effect.
• list the assumptions pertinent to confidence intervals and correctly detect what about a scenario conforms or fails to conform to each assumption.
• calculate a confidence interval for the mean expressed as a proportion (or an expected value expressed as a proportion).

Lecture 07

Students will be able to:

• determine if a two populations are independent of one another.
• compute the standard error of the difference between sample means using the unpooled method.
• calculate the confidence interval for the difference between two sample means given either sample data or means, standard deviations, and sizes of two samples.
• calculate the degrees of freedom appropriate for use in comparing means.
• give the conditions of validity for the use of the confidence interval for the difference between two sample means.
• determine if it is appropriate to use the confidence interval for the difference between two sample means for a given scenario.
• state the null hypothesis appropriate to a given scenario.
• state the alternative hypotheses (both one- and two-way) appropriate to a given scenario.
• calculate the t statistic given the means, standard deviations, and sizes of two samples.
• use the t statistic and degrees of freedom to determine a p-value (both one- and two-way).
• correctly reject or accept the null and alternative hypotheses from a comparison of the p value with a given critical (alpha) value (both one- and two-way).
• give the conditions of validity for the use of the t-test for testing the significance of a difference between two sample means.
• determine if it is appropriate to use the t-test for testing the significance of a difference between two sample means for a given scenario.
• describe both type I and II errors for a given scenario.
• define significant effect size and calculate it for a given scenario.
• define the power of a statistical test and determine, using the tables in the textbook, the minimum sample size that will provide for a specified level of power given an expected standard deviation and an alpha level.
• explain why the t-test is parametric and the Wilcoxson-Mann-Whitney test is not.
• choose the correct test to use (t or Wilcoxson-Mann-Whitney) given a scenario calling for a test for a difference between two populations.
• explain the choice made in the previous objective.
• calculate the Wilcoxson-Mann-Whitney statistic.
• use the Wilcoxson-Mann-Whitney test to test directional and non-directional hypotheses about the difference between two populations (given a scenario as background).
• give the conditions of validity for the use of the Wilcoxson-Mann-Whitney test for testing the significance of a difference between two samples.
• determine if it is appropriate to use the Wilcoxson-Mann-Whitney test for testing the significance of a difference between two samples for a given scenario.

Lecture 08

Students will be able to:

• determine if a given scenario describes an observational study and identify the observational unit, response variable, explanatory variable, and any relevant extraneous variables.
• correctly assess the effect of observational studies' weaknesses on a given observational study.
• define spurious association and describe a scenario that illustrates the concept.
• define confounding and describe a scenario that illustrates the concept.
• describe case studies and explain why they are a type of observational study.
• distinguish an experiment from an observational study.
• identify the experimental unit, treatment, treatment levels, control, and controlled variables in a given experiment.
• define blinding and double blindiing and describe scenarios that illustrate the concepts.
• distinguish positive from negative controls and and describe scenarios that illustrate the concepts.
• define placebo and explain the placebo effect.
• define historical control and describe a scenario that illustrates the concept.
• define bias and describe a scenario that illustrates the concept.
• distinguish error from bias.
• distinguish mistakes from error.
• distinguish measurement error from sampling error.
• correctly block a given experimental scenario.
• plan a randomized blocks design experiment given an experimental scenario.
• explain the necessity for replication in experiments.
• define pseudoreplication association and correctly assess if pseudoreplication occurs in a given scenario.
• determine if nesting is part of a given experimental design and, if so, which variables are nested.
• explain the reason for nesting in a given experimental variable.
• identify the combinations of allocation of experimental units and sampling method.
• identify and explain which combinations can be used to draw cause-effect inferences.

Lecture 09

Students will be able to:

• identify correctly paired observations.
• state the null and alternative hypotheses (directional and non-directional) that apply to a given experimental scenario involving the comparison of paired samples.
• calculate the paired sample t and determine the corresponding p value (both directional and non-directional) .
• correctly reject or accept the null and alternative hypotheses from a comparison of the p value with a given critical (alpha) value (both one- and two-way).
• give the conditions of validity for the use of the t-test for testing the significance of a difference between two sample means.
• determine if it is appropriate to use the t-test for testing the significance of a difference between two sample means for a given scenario.
• calculate the confidence interval for the difference between the means of paired samples given a p value.
• give the conditions of validity for the use of the confidence interval for the difference between paired sample means
• determine if it is appropriate to use the confidence interval for the difference between paired sample means for a given scenario.
• explain why the paired t-test may be more precise than the unpaired t-test.
• choose the correct test to use (paired t-test, signs test, or Wilcoxson Signed-Ranks test) given a scenario calling for a test for a difference between paired populations and correctly explain the choice.
• state the null and alternative (both directional and non-directional) hypotheses for the Signs test given an experimental scenario.
• calculate the Signs test statistic and determine the corresponding p value (both directional and non-directional) .
• use the p value from the Signs test to evaluate the null and alternative (both directional and non-directional) hypotheses about the difference between paired samples (given a scenario as background).
• give the conditions of validity for the use of the Signs test for testing the significance of a difference between paired samples.
• determine if it is appropriate to use the Signs Test for testing the significance of a difference between paired samples for a given scenario.
• state the null and alternative (both directional and non-directional) hypotheses for the Wilcoxson Signed-Ranks test given an experimental scenario.
• calculate the Wilcoxson Signed-Ranks test statistic and determine the corresponding p value (both directional and non-directional) .
• use the p value from the Wilcoxson Signed-Ranks test to evaluate the null and alternative (both directional and non-directional) hypotheses about the difference between paired samples (given a scenario as background).
• give the conditions of validity for the use of the Wilcoxson Signed-Ranks test for testing the significance of a difference between paired samples.
• determine if it is appropriate to use the Wilcoxson Signed-Ranks Test for testing the significance of a difference between paired samples for a given scenario.

Lecture 10

Students will be able to:

• distinguish between categorical and quantitative variables.
• distinguish between goodness-of-fit models and contingency models of data prediction.
• graphically compare the normal and Chi-square distributions and the changes in the shape of the Chi-square distribution as the degrees of freedom increase.
• state the null and alternative hypotheses (directional and non-directional) that apply to a given experimental scenario involving categorical data and a goodness-of-fit situation.
• calculate the Chi-square statistic and determine the corresponding p value (both directional and non-directional) for the above scenario.
• correctly reject or accept the null and alternative hypotheses from a comparison of the p value with a given critical (alpha) value (both one- and two-way) for the above scenario.
• give the conditions of validity for the use of the Chi-square test for testing the significance of fit between data and predicted data from a goodness-of-fit model.
• determine if it is appropriate to use the Chi-square test for testing the significance of fit between data and predicted data from a goodness-of-fit model for a given scenario.
• state the null and alternative hypotheses (directional and non-directional) that apply to a given experimental scenario involving categorical data and a contingency probability situation (for both  2 x 2 and r x k tables).
• calculate the Chi-square statistic and determine the corresponding p value (both directional and non-directional) for the above scenario.
• correctly reject or accept the null and alternative hypotheses from a comparison of the p value with a given critical (alpha) value (both one- and two-way) for the above scenario.
• give the conditions of validity for the use of the Chi-square test for testing the significance of fit between data and predicted data from a contingency model (for both  2 x 2 and r x k tables).
• determine if it is appropriate to use the Chi-square test for testing the significance of fit between data and predicted data from a contingency model for a given scenario (for both  2 x 2 and r x k tables).
• state the null and alternative hypotheses (directional and non-directional) that apply to a given experimental scenario involving categorical data and the use of Fisher's Exact Test.
• calculate the p value (both directional and non-directional) for the above scenario based on Fisher's Exact Test.
• correctly reject or accept the null and alternative hypotheses from a comparison of the p value with a given critical (alpha) value (both one- and two-way) for the above scenario.
• give the conditions of validity for the use of Fisher's Exact Test for testing the significance of fit between data and predicted data from a goodness-of-fit model.
• determine if it is appropriate to use Fisher's Exact Test for testing the significance of fit between data and predicted data from a goodness-of-fit model for a given scenario.
• calculate the confidence interval for the difference between probabilities for a 2 X 2 contingency table.
• give the conditions of validity for the use of the confidence interval for the difference between probabilities for a 2 X 2 contingency table.
• determine if it is appropriate to use the confidence interval for the difference between probabilities for a 2 X 2 contingency table for a given scenario.
• given an appropriate scenario based on paired data points, construct a 2 x 2 contingency table to test for concordance.
• calculate the p value from the above table and evaluate the null hypothesis of equal probabilities.
• using McNemar's Test, calculate the p-value and evaluate the null hypothesis of equal probabilities.
• calculate the relative risk and odds ratio from appropriate scenarios.

Lecture 11a

Students will be able to:

• predict the effect of multiple statistical tests on the experiment-wide error rate.
• state the null and alternative hypotheses for one-way analysis of variance.
• calculate the total, between group, and within group sum of squares.
• calculate mean squares for within and between groups.
• calculate the pooled standard deviation for the total data from the within-group mean square.
• state  and explain the experimental model for one-way ANOVA.
• explain what is meant by partitioning the variation.
• state  and explain the partitions of variation for a one-way ANOVA.
• construct a one-way ANOVA table.
• use global F tests to accept or reject the null hypothesis for one-way ANOVA.
• relate the F statistic with the t statistic.
• identify the blocking scheme from a given experimental scenario.
• calculate the sum of squares for blocks, treatment sum of squares, and error sum of squares from a blocked experiment.
• state  and explain the experimental model for one-way ANOVA for a blocked experiment.
• state the equation that predicts the data as a sum of effects for a blocked experiment.
• construct a one-way ANOVA table for a blocked experiment.
• use global F tests to accept or reject the null hypothesis for one-way ANOVA of a blocked experiment.

Lecture 11b

Students will be able to:

• distinguish between fixed-effects and random-effects models.
• set up a two-way factorial experimental design from a given research scenario and correctly identify the factors, levels and replications involved.
• detect and interpret graphical representations of interactions among independent factors.
• state the null and alternative hypotheses tested by a factorial design.
• calculate sum of squares for the main effects, interaction, error, and total for a two-way ANOVA.
• state  and explain the experimental model for a two-way ANOVA.
• state  and explain the partitions of variation for a two-way ANOVA.
• construct a two-way ANOVA table.
• use global F tests to accept or reject the null hypothesis for one-way ANOVA.
• use linear contrasts to compare levels of a factor, stating the null hypothesis and evaluating the results of the contrast calculation using a t-test.
• adjust post-hoc comparisons of levels using the Student-Neuman-Keuls test and the Bonferroni Adjustment

Lecture 12

Students will be able to:

• contrast regression and correlation.
• relate regression to causation and association.
• calculate least-squares regression lines (both slope and intercept)
• define and diagram a residual value.
• calculate sum of squares for the residuals and the residual standard deviation.
• interpret the meaning of the residual standard deviation in an experimental context.
• state the assumptions of linear regression.
• diagram outliers, influential datapoints, and curvilinearity and explain how each affects the estimated regression line.
• use residual plots to detect bias and violations of assumptions.
• use transformations to reduce curvilinearity.
• calculate the standard error of beta-1 (estimate of the slope).
• calculate a confidence interval for beta-1.
• test the  hypothesis that beta-1 is equal to zero.
• interpret the results of testing beta-1 in an experimental context.
• calculate the coefficient of determination.
• calculate the correlation coefficient.
• distinguish between the coefficient of determination and the correlation coefficient.
• use the correlation coefficient to interpret a regression in an experimental context.

Lecture 13

Students will be able to:

• calculate the confidence interval for a sample variance or standard deviation.
• test the hypothesis that a sample variance is equal to a known or expected variance.
• test the hypothesis that two sample variances are equal.
• calculate power when a sample size and effect size are given.
• use the Sheffé, tests to compare group means when there are more than two means to compare
• define Monte Carlo Simulation, Markov Chain Simulation, and MCMC Simulation