Template-style statistics

Template-style statistics

Template-style statistics

Hypothesis testing as first topic

• Economics majors take one statistics course in the current curriculum.
• Emphasize that math is not the main skill in statistics – but they share abstraction as a device for thinking.
• We get a heterogeneous range of students: No exposure, some exposure, and mostly exposure to template-style statistics.
• Took the task of introducing hypothesis testing first on Term 1, AY 2024-2025 – with some objections from PLC

Hypothesis testing as first topic

• Why could it be the first topic?

  • Researchers in the Philippines have disproportionately used hypothesis testing as a way to answer research questions.
  • The way it is taught is via a template which students cannot understand but can actually do.
  • Usually squeezed at the end.

• Opportunity to hear students ask the question “If statistics are numbers subject to variation, then why should we believe them?”

How to teach it as a first topic

• Change the template and force the articulation of the logic and argumentation behind hypothesis testing
• Take the position that the null is true. Explore what sample means you observe.

sample <- rnorm(n = 35, mean = 63000, sd = 5250)
sample

 [1] 57086.34 72627.21 48546.54 63052.87 72791.96 63151.60 53419.70 64908.09
 [9] 53561.17 57810.03 65971.27 63011.76 67199.72 59631.00 63736.18 62351.57
[17] 76924.14 56000.74 61866.49 66153.03 69852.82 62351.09 62235.09 64212.20
[25] 54041.51 75258.45 61053.16 70627.81 60254.72 58670.50 67539.52 68700.45
[33] 67999.32 61274.68 66648.94

mean(sample)

[1] 63443.48

How to teach it as a first topic

• Rinse and repeat.

sample <- rnorm(n = 35, mean = 63000, sd = 5250)
sample

 [1] 69273.31 64171.88 58609.04 68721.18 56093.84 68617.21 58183.58 71168.63
 [9] 73891.26 62554.08 73408.62 58320.02 66985.84 64250.31 55322.43 61800.78
[17] 66886.80 69431.39 74194.31 65033.88 61517.14 71323.90 59063.35 58752.31
[25] 69672.25 58920.79 71801.98 56937.87 61865.53 67737.30 64352.25 78195.61
[33] 62665.85 59491.55 53984.81

mean(sample)

[1] 64662.88

Simulation-based inference

• Rinse and repeat an extremely large number of times.

collection.means <-
  replicate(10000,
            mean(rnorm(n = 35, mean = 63000, sd = 5250)))

• Sample means are subject to variation. What does the variation look like under the null?
• It might now make sense to think about the “standard deviation of the (sample) mean”.

Regular descriptive statistics applied to artificial data

• Apply descriptive statistics to the collection of simulated sample means.

mean(collection.means)

[1] 62984.66

sd(collection.means)

[1] 884.6135

# Compare with
5250/sqrt(35)

[1] 887.412

Visualize the sampling distribution

Draw that bell-shaped curve

Make a conclusion

Make a conclusion

• By any chance, would you know what this is?

mean(collection.means >= 65700)

[1] 0.0015

• Seeing the simulation should inspire you to ask better questions about what hypothesis testing is about.

• Absolutely no formulas! Replace formulas with code and a bit more thought.

• How come hypothesis testing was invented and have to look this way?

Competencies?

• Should you use hypothesis testing at all?
• Better appreciation of the need to quantify uncertainty – right at the very beginning
• Capacity for abstraction
• Use software in a less template-y fashion

Indirectly affect PLO6

Implement the scientific method on economic problems: developing hypotheses, envisioning data requirements, analyzing with mathematical and statistical tools.

CLO-PLO mappings

How to assess?

• Use vignettes and then determine if situation calls for hypothesis test
• Assess ability of student to change the relevant parts of R code to mirror other similar situations
• Find other similar examples in reality and in media
• Doing math without actually doing math – change the way math is perceived

How to spend time in classroom

• Focus on the topic which dominates choice of method in the Philippines
• Reduce template-y approach, reduce reliance on tables
• Provide more direct motivation than usual ways of motivating statistics – key is sampling variation and how to decide claims based on sampling variation
• Better clarifying questions from students
• High difficulties in exams: Defining what the parameter is, articulating the argument rather than the template

Summary

• Hypothesis testing first – the idea is not new, existed for the past 15 years!

• Can be implemented but require the instructor to actually understand hypothesis testing

• Need to pay the price for avoiding math and for moving away from the template

Take-aways

Are the innovations only for innovation’s sake?

• Will it reduce the invisible workload?
• Competencies? Should we think of the average rather than the ideal DLSU student?
• Contribution to CLOs and PLOs? Would students care about these.
• How to actually assess? Shouldn’t retention matter more?
• How to spend time in the classroom? Document time use