STAT1070: Statistical Methods and Data Interpretation Assignment

Questions

1. A researcher is interested in comparing the education system in New South Wales (NSW) and Queensland (QLD). They randomly choose 20 high schools from NSW. For each of these schools they find the high school in QLD that most closely matches the school in NSW in terms of a number of socioeconomic indicators. This is done in an attempt to remove the effect that socioeconomic status might have on performance in the test.

For all 40 schools the Dux (the schools highest achiever) is chosen to complete a specialised quiz testing a range of topics. The scores for the students are collected in two data sets:

• education-independent.omv: this data set has the data in the format for an independent samples t-test.
• education-paired.omv: this data set has the data in the format for a paired samples t-test.

Choose the data set above that is most appropriate for the scenario described and create a screen capture recording of you using jamovi. (Do not demonstrate analysis with both data sets.) You should demonstrate the process of performing an appropriate hypothesis test to answer the question of whether there are differences in student outcomes between NSW and QLD.

The screen capture should include a voice over explaining the following:

• what test you have chosen and why 
• the null and alternative hypothesis of the test you are performing 
• the p-value you have found 
• the decision and conclusion you have reached for the test 
• the assumptions of the test and whether they have been met or not

Note: Your recording does not need to be polished and perfect. There are no marks for how the recording presents aesthetically. You simply need to present the steps you take using the software and communicate your answers to the above aspects of performing a hypothesis test. Ideally your recording should be around 2 to 3 minutes.

2. How do the train networks of Australia’s three most populous cities compare in terms of the distance between consecutive stations? To explore this, a random sample of 5 routes between consecutive stations was taken for the Brisbane, Melbourne, and Sydney train networks, and the corresponding interstation distances were recorded in the file Trains.omv. 

The file includes the following variables:

• Station 1: the name of the first station 
• Station 2: the name of the second station 
• City: the name of the city in which the route between the two stations is located 
• Interstation Distance: the distance between Station 1 and Station 2, in kilometres

(a) Is there evidence of a difference in average interstation distance among the three cities’ train networks? Conduct an appropriate hypothesis test at the 5% significance level. Be sure to state the null and alternative hypotheses, test statistic, null distribution, p-value, decision and an appropriate conclusion in plain language.

(b) If appropriate, perform post-hoc tests to determine which city train networks have significantly different average interstation distances. If post-hoc tests are not appropriate, explain the purpose of a post-hoc test and why it’s not appropriate in this case.

(c) What are the assumptions of the analysis performed in part (a)? State whether each assumption is reasonable with reference to appropriate jamovi output.

(d) A train enthusiast you know is adamant that there are differences in the average length between stops for the three cities. Based on your results in part (a), how would you respond to your friend? Explain your reasoning.

3. A hand grip dynamometer like the one shown in Figure 1 was used to measure grip strength in Newtons (N) for a random sample of 50 people. The cross-sectional area (cm2 ) of the forearm used in the test was also measured.

The data is available in file grip.omv:

(a) Test at the 5% significance level if there is a significant relationship between grip strength and forearm cross sectional area. Be sure to include the null and alternative hypotheses, the test statistic, the null distribution, the p-value, and an appropriate decision and conclusion.

(b) Provide a 95% confidence interval for the population slope parameter and interpret this interval.

(c) List the assumptions of your analysis. To what degree are these assumptions satisfied? Include output from jamovi where appropriate.

(d) Create a scatterplot of grip strength against against forearm cross sectional area. Does the scatter plot indicate that simple linear regression is appropriate?

Assessment Summary

This assessment evaluates the student’s ability to apply statistical hypothesis testing using the software jamovi to real-world data scenarios. The key requirements include selecting the appropriate statistical test, demonstrating analysis through a recorded screen capture, and interpreting results with correct reference to hypotheses, assumptions, and conclusions.

The assessment is divided into three main questions:

1. Comparing Education Systems (NSW vs QLD)

   • Select the appropriate dataset (paired or independent).
   • Perform a hypothesis test to determine if there is a difference in student outcomes between the two states.
   • Explain the choice of test, hypotheses, p-value, decision, and test assumptions.

2. Train Network Comparison (Brisbane, Melbourne, Sydney)

   • Conduct a hypothesis test to compare the average interstation distances between the three cities.
   • Present null and alternative hypotheses, p-value, and interpretation in plain language.
   • If applicable, perform post-hoc tests and discuss assumptions using jamovi output.
   • Explain how to respond to a claim about differences based on statistical evidence.

3. Grip Strength and Forearm Cross-Sectional Area

   • Use linear regression to test if there is a significant relationship between grip strength and forearm cross-sectional area.
   • Provide a 95% confidence interval for the slope and interpret it.
   • Discuss regression assumptions and evaluate their validity using graphical and statistical output.
   • Interpret a scatterplot to determine the appropriateness of the regression model.

The assessment aims to test practical data analysis skills, understanding of inferential statistics, and the ability to communicate statistical reasoning effectively.

Mentor’s Step-by-Step Guidance Approach

The Academic Mentor guided the student through a structured analytical process, ensuring conceptual clarity and technical accuracy at each stage:

Step 1: Understanding the Assessment Context

The mentor began by helping the student interpret each question, clarifying the difference between paired and independent samples, ANOVA and post-hoc tests, and regression analysis. The mentor emphasized how each test corresponds to a specific research question and dataset structure.

Step 2: Selecting Appropriate Statistical Tests

For Question 1, the mentor explained how the matched-pair design (NSW schools paired with similar QLD schools) required a paired samples t-test.
For Question 2, since three groups were being compared, the mentor guided the use of a one-way ANOVA.
For Question 3, the focus was on simple linear regression, examining the relationship between two continuous variables.

Step 3: Setting Up jamovi and Conducting Analysis

The mentor demonstrated:

• How to import .omv datasets into jamovi.
• Selecting the correct test from the Analyses → T-Tests / ANOVA / Regression menus.
• Checking assumptions (normality, homogeneity, linearity) using plots and test outputs.
• Interpreting jamovi output tables identifying test statistics, p-values, and confidence intervals.

Step 4: Formulating Hypotheses and Interpreting Results

The student was guided to:

• Clearly state null (H₀) and alternative (H₁) hypotheses before running each test.
• Compare the p-value to the 0.05 significance level.
• Write conclusions in simple, academic language, linking findings to the context (e.g., “There is no significant difference in average interstation distance among the three cities”).

Step 5: Discussion of Assumptions and Limitations

The mentor helped the student interpret diagnostic plots and test results (e.g., residual plots in regression, Levene’s test for ANOVA). The student learned to identify whether assumptions were met and to justify their reasoning.

Step 6: Communicating Findings

The final step involved training the student to present results concisely and coherently explaining what the results mean for each real-world scenario (education comparison, train distances, and grip strength relationship).

Outcome and Learning Achievements

By the end of the assessment, the student successfully:

• Applied appropriate statistical techniques (Paired T-test, ANOVA, Regression).
• Interpreted jamovi outputs and translated statistical results into meaningful conclusions.
• Understood and evaluated test assumptions for validity.
• Demonstrated improved confidence in using statistical tools for real-world problem-solving.
• Achieved key learning objectives aligned with course outcomes:
  • Applying statistical reasoning to research data.
  • Interpreting and communicating findings effectively.
  • Using analytical software (jamovi) proficiently.

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