Describing data honestly
In this lesson
By the end, you’ll be able to
- Choose a summary statistic that matches the data's shape, and know when the mean lies
- Report a center with the spread and sample size a reader needs to interpret it
- Treat every drop, impute, and exclude as a reportable scientific choice, not housekeeping
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Before a single test of significance, a study makes dozens of quiet choices about how to describe its data: which number stands in for hundreds, and what to do with the messy rows. These choices decide what the reader sees, and they are where honesty either starts or fails. A summary is a compression: it throws information away on purpose. The only question is whether it throws away the right information.
The mean balances every value, so a few extremes drag it toward the tail; the median marks the middle case and shrugs off outliers. On skewed data the median is usually the honest headline, and the gap between mean and median is itself a skew detector. But a center alone is never enough: report the spread (a standard deviation, an interquartile range, or the raw distribution) and the sample size, because '3.4 out of 5' could be near-universal agreement or a war between 1s and 5s. Two datasets can share a mean and standard deviation and still look nothing alike; only looking at the distribution reveals which you have.
Exercise
A survey of 200 households reports annual incomes. Most cluster around $50,000, but a handful earn several million. A report says 'the average household earns $141,000.' What is the honest headline number here?
A few millionaires among ordinary earners: which center do they drag?
Real data arrives dirty: impossible values, outliers, missing rows. How you handle them is not housekeeping; it is a chain of scientific decisions, each of which can change the result. The danger is the garden of forking paths: with many defensible-looking ways to drop, keep, or impute, a researcher who decides after seeing the result can walk to almost any conclusion, often without feeling dishonest. The safeguard is simple and strict: fix your cleaning rules before you look at the outcome, and report every decision: what you dropped, why, and what the result looks like with and without it. Removing a physically impossible value is defensible; deleting a real, inconvenient value because it weakens your finding is a bias wearing the costume of tidying.
Signature interactive
Cleaning Room
You measured reaction times (ms) for 13 participants and want to report the average. Ten rows are clean. Three are not. Decide how you would treat each, then reveal the mean your choices produce.
A 4 ms reaction time
Faster than a human nerve can fire: physically impossible.
An 1180 ms reaction time
Slow, but a real person could plausibly be that slow once.
One blank row
The value is missing; the participant's time was never recorded.
Constructed example. The point is the reasoning, not these specific numbers.
Categorize
Sort each data-cleaning move into how it should be treated. The line is not 'is it allowed', it is whether the choice was made by a rule set in advance, or by looking at how it changes your result.
Ask of each: was the rule set before looking at the result, and is it reported?
Written response
Lab. A study measured how long 40 users spent on a new feature (in seconds). Most spent 20–90 seconds; three left it open for over an hour, and one row is blank. Write two or three sentences describing this data honestly for a results section: which summary you would report, what spread and n you would give, and exactly how you would handle the three long sessions and the blank.
Median + IQR + n; then a stated, pre-specifiable rule for the long sessions and the blank.
0/60 words
Checkpoint · item 1 of 5
Which situation most calls for reporting the median instead of the mean?
Which shape drags the mean away from the typical value?
Reflection