Course ID: | ERSH 8310. 3 hours. |
Course Title: | Applied Analysis of Variance Methods in Education |
Course Description: | Experimental design and the analysis of data from experiments, including orthogonal analysis of variance for single and multifactor designs, randomized blocks, repeated measures, and mixed models. |
Oasis Title: | App Analysis of Vari Mthds Edu |
Duplicate Credit: | Not open to students with credit in ERSH 8310E |
Prerequisite: | ERSH 4300/6300 or ERSH 4300E/6300E |
Semester Course Offered: | Offered every year. |
Grading System: | A-F (Traditional) |
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Course Objectives: | Objectives:
UNIT I
1. Given a small data set and summary calculations determine the standard error of
the statistic of interest (sample mean, difference between means).
2. Define and interpret the meaning of a Type I error, Type II error, and
statistical power.
3. Describe the interrelationship between Type I, Type II errors, and statistical
power.
4. Given a research context and summary data identify the appropriate critical
value for the test statistic for a specific hypothesis and confidence interval.
5. Given a computed t-statistic estimate the p-value
UNIT II
1. Given summary calculations (i.e., SS, MS F ) complete an ANOVA summary table
and interpret the results in terms of the hypothesis tested.
2. Given descriptive statistics (i.e., sample means, standard deviations,
variances), compute the ANOVA summary table and F-ratio
3. Given the results reported in an ANOVA summary table or descriptive statistics,
identify specific differences using the Bonferroni procedure.
4. Develop confidence intervals for specific contrasts of interest.
5. Describe the effect on the Type I error rate when data assumptions are violated.
6. Given a research problem identify appropriate procedures for increasing
statistical power and reducing Type II errors.
7. Calculate statistical power for a specific research study.
8. Determine the necessary sample size needed to answer a specific research
question with reasonable statistical power.
9. Given a description of a research study and a computer printout or facsimile
interpret the results of the analysis and draw appropriate conclusions.
UNIT III
1. Given a research problem and summary calculations for a study involving two
independent variables, complete the analysis and interpret the results.
2. Given the results of a research study involving two independent variables
provide an appropriate interpretation of the results.
3. Given summary calculations test hypotheses for specific contrasts and provide
interval estimates for differences between specific populations
4. Estimate the minimum sample size needed to test main effects or an interaction
for a factorial ANOVA.
5. Given a specific research context estimate the statistical power for detecting
main effects in a factorial ANOVA
6. Given a description of a research study and a computer printout or facsimile
interpret the results of the analysis and draw appropriate conclusions.
7. Interpret the results for an interaction effect as well as suggesting
appropriate follow-up analyses.
8. Illustrate the meaning of an interaction, simple effect and main effect by
numerical examples or graphs
9. Given a description of a research study and a computer printout or facsimile
interpret the results of the analysis and draw appropriate conclusions.
UNIT IV
1. Given a description of a research problem involving a continuous independent
variable and the regression equation interpret the following: intercept, slope,
R2.
2. Given the results of an ANOVA summary for a regression analysis interpret the
findings in terms of the hypothesis of interest.
3. Given a description of a research study and the data analysis results for a
simple linear regression/correlation as reported on a computer output or
facsimile interpret the results completely and draw conclusions supported by the
data.
4. Given descriptive statistics including means, standard deviations and
correlation compute the regression equation and ANOVA summary table.
Unit V
1. Given a description of a research study and the data analysis results as
reported on a computer output or facsimile interpret the results completely and
draw conclusions supported by the data. Data analysis strategies which might be
reported include: ANOVA for gain scores, analysis of covariance.
2. Given the results of analysis of covariance correctly interpret the meaning and
significance for the following tests: equality of regression slopes,
relationship between the covariance and dependent variable, treatment effect
including confidence intervals.
Unit VI
1. Given descriptive data complete the ANOVA summary table
2. Describe the effect of violating the assumption of sphericity.
3. Determine the necessary sample size for a repeated measures design.
4. Determine appropriate tests for specific contrasts of interest to a researcher.
5. Given a computer printout or facsimile interpret the results of the analysis.
Unit VII
1. Given a description of a research study and summary calculations for a mixed
model design, complete an ANOVA summary table.
2. Given research question determine which F-ratio is relevant for the question
and test specific hypotheses of interest through contrast analyses.
3. Given a computer printout or facsimile interpret the results of the analysis. |
Topical Outline: | Unit I. Review Statistical Hypothesis Testing
A. Comparing two populations
a. t-test statistic
b. errors in inference
c. statistical power
d. confidence interval
e. assumptions
Unit II. Analysis of Variance
A. Single factor
a. ANOVA summary
b. Identifying specific differences
c. assumptions
d. statistical sample size/power
e. structural model
Unit III. Analysis of Variance
A. Two Factors
a. structural model
b. sample size/power
c. ANOVA summary table
d. assumptions
e. effect size
f. contrasts
g. interaction
h. simple effects
i. identifying specific differences
Unit IV. Simple linear regression
A. quantitative independent variable
a. correlation
b. linear functions
c. ANOVA summary table
Unit V. Analysis of Covariance
A. Overview
B. Structural model
C. ANCOVA summary table
a. equality of regression slopes
b. relationship between covariate and dependent measure
c. treatment effects
d. identifying specific differences
D. Compared with Gain scores
Unit VI. Repeated Measures Design
A. related samples t-test
B. ANOVA summary table
C. assumptions
D. sample size/power
F. identifying specific differences
Unit. VII. Mixed Model Design
A. ANOVA summary table
B. assumptions
C. identifying specific differences |