The State of Texas Assessments of Academic Readiness, commonly referred to as its acronym STAAR, is a series of standardized tests used in Texas public primary and secondary schools to assess a student’s achievements and knowledge learned in the grade level. Starting in third grade, Texas students are required to take the State of Texas Assessment of Academic Readiness test, or STAAR, every year.  This dataset contains test scores and demographic information for randomly selected third grade students from the Texoma region

 

This data set contains only data from randomly selected third-grade students in from the Texoma region in the 2023-2024 academic year. The data were collected for the purpose of identifying significant predictors in both the home environment and the scholastic setting that may influence educational outcomes. Of particular interest in this study is the evaluation of a new Prep Course designed to prepare children to be able to navigate and succeed on standardized tests.  This course was introduced to select schools on a trial basis to determine the efficacy of the program.  Also of interest is the family socioeconomic status, indicated by the highest education level of either parent (or guardian) and the indication whether the child qualifies for free or discounted lunch.  Test scores are percentile ranks relative to the statewide performance of third grade students in the three facets of the STAAR test: math, reading, and writing.  The following measures were included in the data:

 

Variables:

 

• StudentID– Participant’s identification number which looks strangely similar to the original row number of the dataset.
• Gender –The biological sex of the child, i.e. Female/Male.
• Testing Location – Represents the Independent School District in which the Prep Course and Testing were given Anna, TX and McKinney, TX
• Parental Level of Education –the highest education level completed by either parent (or guardian), categorized by: High School, Associates Degree, or Bachelors Degree.
• Lunch –Binary measure indicating whether or not the child is eligible for free or discounted lunch, indicated by free/reduced for qualifying students and standard for students paying the standard fees.
• Test Prep Course–Binary measure to indicate the completion of the newly introduced Prep Course before STAAR testing began in Spring 2024.  This measure is indicated as Complete for those whose schools were included in the initiative in time to complete the program or None if the student’s school was not included.

Research Question:

 

In this case we will be designing a study to determine if math test scores for all students differ significantly based on the highest education level of the parent.  Upon loading, examining, and cleaning your data, choose the correct analytical technique to test the following hypothesis:

where populations 1, 2, and 3 represent math exam scores for kids for kids whose parents highest education level is High School, Associates, and Bachelors, respectively.

 (You may use or quickly recreate the same Frequency and Descriptive Sections from Case 1 to satisfy Accuracy and Outliers if you easily remember what you did to clean the data.)

 Accuracy:

1. Check the data for out of range scores.
   1. Include a summary showing you do/do not have out of range scores.
   2. If necessary, fix the out of range scores.
      1. Indicate what the problems were in the dataset.
      2. Make all out of range values NA.

• Include a summary showing that you fixed the accuracy issues.

2. Fix the factored columns to have nice labels (i.e. Proper Case, Fully Spelled out). Only factor the IV, do not factor the DV.
   1. Use the data editor in JASP to change the Test Location so that the label for Group A shows Anna, TX and the label for Group B shows McKinney, TX.
   2. Use the data editor in JASP to change the Parent Education variable so that the value for High School, Associate, and Bachelor reads 1, 2, and 3.  This will ensure they line up correctly in your graphs.

Missing data:

3. Exclude all missing data using listwise deletion.  Use the filter function to eliminate any cases with missing data.

Outliers:

4. Use the boxplot feature to show that you have no outliers.
   1. Include a summary of those z-scores.
   2. Do you have any outliers?
   3. Exclude those outliers.

Normality:

5. Perform the proper test to show that the assumption of normality is met.

 

Linearity:

6. Include the multivariate QQ plot.

Homogeneity:

7. Include the multivariate residuals plot.
8. Interpret the graph. Does it indicate homogeneity?

Power:

9. Calculate the number of participants you would need for this study, assuming a medium effect size.
   1. Include a screen shot or summary of the numbers you typed into G*Power, so we can give you partial credit if you get a different sample size than us.

ANOVA and Levene’s:

10. Include the ANOVA and Levene’s test output.
11. Do you meet the homogeneity assumption given the results from Levene’s test?
12. Was the overall test significant?
    1. Include the APA/AMA style write up for F (just the statistics):
    2. Post Hocs:

13. Calculate the means, standard deviations, and group sizes for your levels.
14. Post hocs:
    1. What type of post hoc testdid you run?
    2. What type of post hoc correction did you run?
    3. Include the t-test output.
15. Effect size:
    1. Calculate the effect size for your pairwise comparisons.
    2. Include the effect size output or MOTE screen shot.
16. Fill in the table below with the information from the above calculations (like the one from the notes):

 

Mean 1	Mean 2	P-value	Explain?	Effect size

Graph:

17. Include a graph of the means and confidence interval for your ANOVA. Be sure to check the following:
    1. X-axis label
    2. Y-axis label
    3. X-axis group labels
    4. Error bars
    5. Cleaned up graph (no gray backgrounds)

Write up:

18. Write up an analysis of what you find in this data, including all the information you answered above. Use the example in the notes for a guide. This write up should include the following for credit:
19. Result section style (APA and AMA):
    1. Double space
    2. Times New Roman 12 point
    3. Two decimals
    4. Centered, bolded Results
20. Short description of the study/variables.
21. Data screening summary:
    1. Accuracy – did you have problems?  What did you do to fix it?
    2. Missing data – did you have problems?  What did you do to fix it?
    3. Outliers – did you have problems?  What did you do to fix it?
    4. Assumptions:
       1. Normality
       2. Linearity

• Homogeneity and Levene’s

22. ANOVA
    1. Overall F statistic
    2. Post hoc tests / corrections and results
    3. Effect size for all tests
23. Graph with reference to the figure in the text.
    

    Struggling with where to start this assignment? Follow this guide to tackle your assignment easily!

    Step-by-Step Guide to Structuring Your Paper

    1. Data Preparation & Cleaning

       • Accuracy Check: Review math test scores to ensure they fall between 0 and 100. Identify any scores outside this range, document them, and convert them to ‘NA’. Summarize the findings and corrections in your report.

       • Factor Variables: In JASP, relabel the “Testing Location” values to “Anna, TX” and “McKinney, TX”. Change “Parental Education” so that High School = 1, Associate Degree = 2, and Bachelor’s Degree = 3. Only the IV (Parental Education) needs this adjustment for graphing consistency.

       • Missing Data: Use the filter or data cleaning function in JASP to perform listwise deletion. This ensures only complete cases are included in your analysis.

    2. Outliers & Descriptives

       • Outlier Detection: Create a boxplot for math scores and calculate z-scores. Identify and exclude any outliers (typically ±3 SD from the mean). Report whether any were found and removed.

       • Descriptive Stats: Generate frequency tables and descriptive statistics (means, SDs) for math scores across the three parental education groups.

    3. Testing Assumptions for ANOVA

       • Normality: Conduct a Shapiro-Wilk test for each group. p-values > .05 indicate that the data are normally distributed.

       • Linearity: Use a multivariate Q-Q plot to visually confirm linearity between groups and math performance.

       • Homogeneity: Run a multivariate residuals plot and Levene’s Test. Non-significant Levene’s (p > .05) supports the assumption of equal variances.

    4. Power Analysis

       • Use G*Power with the following settings:

         • Test family: F tests

         • Statistical test: ANOVA: Fixed effects, omnibus

         • Effect size f = 0.25 (medium)

         • α = 0.05, Power = 0.80, Groups = 3

       • Record the required sample size and attach a screenshot or describe your input/output.

    5. ANOVA Execution

       • Run ANOVA: Use Parental Education as the IV and Math Score as the DV. Review the output for F-value, p-value, and degrees of freedom.

       • Levene’s Output: Confirm if the homogeneity of variance assumption is met.

    6. Post Hoc Analysis

       • If the ANOVA is significant, proceed with post hoc tests:

         • Run Tukey’s HSD or Bonferroni for multiple comparisons.

         • Provide output showing mean differences and significance levels.

       • Effect Sizes: Use Cohen’s d or partial eta squared. Include either screenshots or MOTE-calculated results.

       • Summary Table:

    Mean 1	Mean 2	P-value	Explain?	Effect Size

    7. Graph the Results

       • Create a bar chart showing group means with 95% confidence intervals.

       • Label:

         • X-axis: “Parental Education Level”

         • Y-axis: “Math Score (Percentile Rank)”

         • Add error bars, remove background, and use clear group labels (1 = High School, etc.)

    8. Writing the Results Section

       • Formatting: Use double-spacing, Times New Roman 12 pt, with a bolded and centered “Results” heading.

       • Content:

         • Begin with a brief description of your research purpose and variables.

         • Provide a summary of data cleaning:

           • Accuracy: Any out-of-range values addressed.

           • Missing data: Listwise deletion used.

           • Outliers: Presence and treatment.

         • List assumption checks (normality, linearity, homogeneity) and whether they were met.

         • Present ANOVA results with APA/AMA formatting, e.g.:
           F(2, 147) = 4.56, p = .013

         • Report post hoc results and effect sizes clearly.

         • Mention and refer to your graph in the text: “(See Figure 1)”

    This guide gives you a complete roadmap for conducting your statistical analysis and presenting your findings clearly and professionally. Make sure each section is grounded in evidence and formatted according to APA or AMA standards.

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