Investigate measured variation in penguins

Observe variation before explaining it

Open all species and all islands. The marks represent measured flipper length and body mass. A larger flipper value tends to accompany a larger body-mass value in this collection, but the display does not assign flipper sizes or manipulate mass. You are inspecting observations, not running an experiment on birds.

The source contains 344 records for three species from three islands in the Palmer Archipelago, observed during 2007–2009. This lesson uses a frozen copy of the simplified palmerpenguins dataset, distributed under CC0. Credit the data collectors as well as the people who prepared the teaching dataset. Source and citation information.

Reconstruct one summary from raw observations

The first two file rows have flipper lengths 181 and 186 mm and body masses 3,750 and 3,800 g. Their two-row mean flipper length is (181 + 186)/2 = 183.5 mm. Their mean mass is 3,775 g. These calculations describe those two rows, not a random sample drawn by this lesson.

Inspect file row 4. Its missing measurements contribute neither zero millimeters nor zero grams. The paired analysis excludes it from both means and the scatterplot, while retaining it in the selected-record count and raw table. There are two incomplete pairs in the full file, leaving 342 complete pairs. If a future dataset lacks only one measurement in a row, this paired analysis would still exclude that row from both means.

Before checking the summary: explain why dividing the sum of measured flipper lengths by all 344 records would bias this mean downward. State the correct denominator for this analysis.

Describe spread as well as a mean

Select Adelie and all islands. There are 152 selected records, of which 151 have both measurements. The sum of the retained flipper lengths is 28,683 mm, so their mean is 28,683/151, about 189.95 mm. This mean need not equal any individual measurement.

Capture that subset, then select Gentoo and capture again. Compare the means, ranges and clouds of individual points. A difference between species means does not imply that every individual from one species exceeds every individual from the other. The range is the observed minimum-to-maximum span; it is not a confidence interval or a measure of ruler precision.

Separate three kinds of uncertainty

Measurement uncertainty concerns how accurately a length or mass was recorded. Biological variation concerns real differences among the sampled birds. Sampling uncertainty concerns how these records relate to a population beyond the dataset. More decimal places in the computed mean do not eliminate any of these.

Your reflection should identify the evidence, describe an observed pattern, and name an alternative explanation or limitation. Possible influences include species composition, sex, season and sampling location. The frozen download contains additional fields for further analysis, but this workbench controls only species and island. It does not establish independent random sampling of all Antarctic penguins or a causal effect of flipper length on mass.