Learning Objectives from Chapters 1, 2, and 3, EST 505
Compute probabilities for events given an experiment
Use the complement rule to find a specified probability
Apply probability rules to answer specific questions: additive rule for disjoint events, multiplication rule for independent events
Describe the steps of the Scientific Method
Distinguish between observational studies (surveys) and experiments
State 3 principles of experimental design: randomization, replication and use of comparison or control
Distinguish between populations and samples, parameters and statistics.
Explain why we sample populations
Select a simple random sample and describe its 2 key properties
Explain why stratified sampling is beneficial (compared to SRS)
Recognize examples of nonrandom samples
Distinguish between the concepts of bias, precision and accuracy.
Distinguish between the sample standard deviation and a standard error of a stastistic.
Solve problems using the probability distribution of a variable
Classify a measurement into one of 3 (or 4) levels of data measurement: nominal, ordinal, & continuous (discrete vs. continuous)
Create a random variable from observed outcomes,
Distinguish between discrete and continuous random variables,
Solve problems using the probability distribution of a random variable
Be able to identify a binomial random variable.
Compute the mean and variance of a binomial probability distribution as well as its associated probabilities.
Distinguish statistical hypotheses from scientific hypotheses, but explain how they are connected
Using the binomial probability distribution, state Ho and Ha, set an a level (perhaps), compute and interpret a P-value, and make a correct conclusion regarding Ho, i.e., conduct a statistical hypothesis test
Differentiate between Type I and Type II error
Explain what the power of a test is and what factors affect it.
Distinguish between practical and statistical significance
Learning Objectives from Chapters 5, 6, 7, 8 for EST 505
Recognize the general form of a chi square statistic
Use a Chi square table properly in execution of a statistical hypothesis test
Explain what degrees of freedom represent
and correctly determine their value for a specific
Distinguish between Goodness of Fit tests, tests for homogeneity, and tests of independence.
Recognize the appropriate probability distribution for a set of data (multinomial, poisson, etc.) to be used in a goodness of fit test.
Apply pooling procedures when appropriate for a chi square test.
Properly estimate the parameter in a Poisson or binomial distribution given a set of sample data.
Properly compute expectations under an assumed model for comparison to observed data.
Chapter 6 section 3
Determine the mean and variance of the sampling distribution of sample means.
Explain why the sampling variance of a sample mean is small than that of a single observation from a population.
Chapter 7 (sections 1 and 3)
Describe the main features of a normal distribution
Compute a standardized value for any observation from a normal distribution and interpret its value.
Use a Z table (standard normal) properly to determine probabilities for a range of Z values.
Explain and use the central limit theorem to describe the type of sampling distributions for sample means of various sizes.
Recognize the connections and the main difference between a t-statistic and a Z-statistic.
Use a t table (with appropriate df) properly to determine probabilities for a range of t values.
Use t-test to infer about a single mean via statistical hypothesis testing (set up the appropriate Ho and Ha, write the probability statement to be solved, compute the test statistic and determine the p-value.)
Construct and interpret confidence intervals for a population mean when s is unknown.
Recognize the equivalency of a matched pairs t-test and a single mean t-test.
Properly execute a hypothesis test for 2 means recognizing three scenarios: s1 = s2, s1 ` s2, s1`s2 but n1 and n2 are large.
Compute a pooled estimate of variance when appropriate
Conduct an F-test for equal population variances (set up the appropriate Ho and Ha, write the probability statement to be solved, compute the test statistic and determine the p-value.)
Recall concepts of type I and II error, power, etc.
Learning Objectives from Chapters 9 and 10, EST 505
Understand how Analysis of Variance works, i.e., how is it that we test if population means are equal by comparing 2 variance terms?
Understand that the total sums of squares of y-values is partitioned into two sources, that due to treatments and that due to error.
Be able to determine the appropriate degrees of freedom if given the number of treatments and number of replications per treatment.
Compute an appropriate F statistic, determine the p-value and test Ho: m1 = m2 = mk vs. Ha: not all equal with equal and unequal sample sizes.
Understand the assumptions underlying ANOVA.
Conduct multiple comparison procedures (Fishers lsd, Duncans and Bonferronis). Understand how they control for type I error rate. Know which are more or less powerful, more or less conservative regarding type I error rates.
Be able to construct single df contrasts for preplanned comparisons. Understand that orthogonal contrasts represent a partitioning of the treatment sums of squares.
Understand the differences and connections between regression and correlation (p. 261)
Recognize the predictive ability of a regression model, with a dependent (response) and independent (explanatory) variable
Know the equation for the model (unknown) and the regression line.
Understand the principle of least squares
Be able to compute and interpret estimates of the slope and y-intercept.
Understand the assumptions underlying the linear regression model and the ways of assessing those assumptions through residual plots
Be able to predict using the regression line and compute a residual. Understand the difference between an observation and a prediction.
Understand what the sample variance around the trend line represents
Be able to test if the slope is equal to zero (and why one would want to do this test)
Understand the effects of outliers and influential points on the location of a regression line.
Construct an interval estimator for the slope, the predicted value of the mean of Y for a given value of X, and the predicted value of a single Y, given an X value.
Compute the correlation coefficient and understand what it represents, what level of data measurement is necessary, its possible range of values, etc.
Interpret the coefficient of determination.
Be able to conduct a hypothesis test of the population correlation coefficient and recognize the connection to this and the variability that of ys that is explained by the variability of the xs.
Understand that correlation does not equal causation and what is necessary to establish causation.
Compute Spearmans rank correlation and distinguish between when you use it versus (Pearsons) correlation coefficient, r.