The Penguin Paradox: Real Data, Real Statistics
The Penguin Paradox: Real Data, Real Statistics
Clean a real field dataset, choose and run the right tests, and discover a result that reverses when you look closer.
Briefing
Between 2007 and 2009, Dr Kristen Gorman and the Palmer Station Long Term Ecological Research programme measured 344 penguins of three species on three islands in Antarctica.
The data is now one of the most used teaching datasets in statistics. It is real, it has missing values, and it hides a trap for anyone who analyses it carelessly.
Download it and answer every question with your own analysis. Unless a question says otherwise, ignore missing values only for the variables you are using.
Topics you practise
Evidence
penguins.csv
344 rows, 8 columns: species, island, bill_length_mm, bill_depth_mm, flipper_length_mm, body_mass_g, sex, year. Missing values are written as NA. (15 KB)
Source: palmerpenguins (Horst, Hill and Gorman, 2020), data from Gorman et al. (2014). CC0 1.0 (public domain).
Suggested tools: Excel or LibreOffice Calc, Python (pandas, scipy), R, JASP or jamovi.
How many rows have at least one missing value?
Format: a number.
After listwise deletion (dropping every row with any missing value), how many penguins remain?
Format: a number.
What is the mean body mass of Gentoo penguins, in grams?
Format: a number to 2 decimal places.
You want to compare mean flipper length across the three species. Which test do you use?
Format: the test name.
Run it. What is the F statistic?
Format: a number to 2 decimal places.
What are the degrees of freedom of that F test?
Format: between,within.
A Shapiro-Wilk test on body_mass_g gives p < 0.001. Which non-parametric test replaces one-way ANOVA for comparing body mass across species?
Format: the test name.
Run a chi-square test of independence on species by island. What is the chi-square statistic?
Format: a number to 2 decimal places.
What is the Pearson correlation between bill length and bill depth across all penguins?
Format: a number to 3 decimal places.
Now compute the same correlation for Gentoo penguins only.
Format: a number to 3 decimal places.
The sign of the correlation flips when you split the data by species. What is this phenomenon called?
Format: the name.
Compare body mass of male and female Gentoo penguins with Welch's t-test. What is the t statistic (male minus female)?
Format: a number to 2 decimal places.
Each task is worth 100 points: minus 15 per wrong answer and 25 for a hint (never below 40). Finish when you are done; 15 unsolved tasks score 0. Your progress is saved on this device.