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Critically Appraising Quantitative Evidence

The narration between entries paraphrases; it never reads an entry aloud before the entry plays. Every entry in this lecture plays exactly as it does on its own page — same file, same speed, nothing laid over it.

What you can do after this

  1. Build a two-by-two table from a reported result
  2. Express one result as an absolute reduction, a relative reduction and a number needed to treat
  3. Say why the same data produce two very different impressions
  4. Say when an odds ratio and a relative risk diverge
  5. Recompute a relative figure against a different baseline

What it covers

30 entries in 9 topics. Each number links to that entry on its own.

  1. 1. Why this strand exists

  2. 2. Data types, and the table

  3. 3. Absolute measures

  4. 4. Relative measures, and the same data twice

  5. 5. Odds, and where they mislead

  6. 6. Number needed to treat

  7. 7. Why the distinction matters

  8. 8. The canonical error

  9. 9. The numbers, read

Check yourself

A trial reports incidence falling from six percent to three percent. Express that three ways.

Absolute risk reduction is three percentage points. Relative risk is one half, so the relative risk reduction is fifty percent. Number needed to treat is the reciprocal of the absolute reduction — thirty-three patients treated for one to benefit.

Why do the same data produce two very different impressions?

Because a relative measure divides and an absolute measure subtracts. A halving sounds large; three fewer patients in a hundred sounds small. Both are correct descriptions of the identical result, and the relative one is the one that reaches abstracts and press releases.

Why do absolute measures travel between settings and relative ones not?

An absolute measure carries the baseline risk inside it, so it means the same thing wherever you read it. A relative measure is the same figure whether the baseline was six percent or one percent — which makes it portable and deceptive at once, because the context was dropped on the way.

When do an odds ratio and a relative risk diverge?

When the outcome is common. With a rare outcome the two are close enough to read interchangeably. With a common one they separate, and an odds ratio read as though it were a risk ratio overstates the effect.

Your unit's baseline incidence is one percent, not six. What does the trial's fifty percent reduction mean for you?

Recompute. Fifty percent of one percent is an absolute reduction of half a percentage point, and a number needed to treat near two hundred rather than thirty-three. The relative figure travelled unchanged and meant something entirely different on arrival.

Lecture transcript

The narration as recorded, in order. Where an entry plays, the transcript links to it rather than reprinting it — the entry plays from its own file, unaltered, and says the same thing on its own page.

This is the statistics strand, and it is the only place in the course where arithmetic is actually performed rather than described. It is short, and it changes how you read every result you will ever meet. The honest framing first: you do not need the formulas. You need to read what these numbers mean, and that is a real distinction rather than a lowered bar. The whole strand builds to one point — a fifty percent reduction and a three-point difference can be the same finding, and they land completely differently on whoever reads them. By the end you can build a two-by-two table from a reported result; express one result three ways; say why the same data produce two impressions; say when an odds ratio diverges from a relative risk; and recompute a relative figure against your own baseline.

Four videos to open. The second is the honest framing: you need to read what these numbers mean, not to derive them — a real distinction rather than a lowered bar. The fourth is a check that takes one second and catches missing patients.

Why this strand exists.

EBP 0821 Why an Appraiser Needs Statistics

You cannot judge whether a result matters without reading the numbers that express it.

What is and is not required.

EBP 0822 You Do Not Need the Formulas

You need to read what the numbers mean, not to derive them. That is a real distinction and not a lowering of the bar.

Two symbols worth knowing.

EBP 0823 N and n

Capital N is the whole sample; lowercase n is a subgroup within it.

A check that takes one second.

EBP 0824 Do the n Values Sum to N?

If the subgroups do not add up to the total, someone is missing and the paper should say where they went.

Five videos. Draw the two-by-two table first and every measure that follows becomes readable; skip it and they stay abstract.

The first data type.

EBP 0825 Dichotomous Data

Data with two categories: it happened or it did not. Most of this strand concerns these.

The second.

EBP 0826 Continuous Data

Data on a scale, like blood pressure or length of stay.

Why the distinction matters.

EBP 0827 Different Data, Different Tests

The data type determines which statistical tests are appropriate, so a mismatch is a flaw you can spot.

The quantity everything else expresses.

EBP 0828 Magnitude of Effect

How large the difference is between groups, which is what all the measures ahead are ways of expressing.

The instrument to draw first.

EBP 0829 The Two-by-Two Table

Four cells: outcome or not, in each group. Drawing it first makes every measure that follows readable.

Four videos on the measures that carry their own context. These are the ones that mean the same thing wherever you read them.

The base quantity.

EBP 0830 Absolute Risk

The proportion in a group who had the outcome. Everything else is built from these.

The first comparison.

EBP 0831 Risk Difference

One absolute risk subtracted from the other.

The measure that travels honestly.

EBP 0832 Absolute Risk Reduction

The risk difference when the intervention helped, expressed in percentage points. It carries the baseline with it.

The same thing, other direction.

EBP 0833 Absolute Risk Increase

The same quantity when the intervention harmed rather than helped.

Five videos, and the fourth is the entry this whole strand exists for. The same trial result, expressed two legitimate ways, lands completely differently on a reader.

The measure that dominates abstracts.

EBP 0834 Relative Risk

One absolute risk divided by the other. A ratio, and ratios hide their inputs.

Reading a ratio's direction.

EBP 0835 Reading Which Way a Ratio Points

Below one means less risk in the treated group, above one means more. Check which group is the numerator.

The number that reaches the headline.

EBP 0836 Relative Risk Reduction

The proportional reduction. This is the figure that appears in abstracts and press releases.

The load-bearing entry of the strand.

EBP 0837 Same Data, Two Impressions

Six percent to three percent is a fifty percent relative reduction and a three point absolute one. Same data. Neither is wrong, and they land completely differently.

When a small effect matters.

EBP 0838 When One Percent Is Worth Having

A one point absolute reduction can be well worth having when the outcome is severe and common.

Three videos on odds. The trap is that an odds ratio and a relative risk look alike when the outcome is rare, and diverge when it is common.

A different way to express chance.

EBP 0839 Odds

The ratio of events to non-events, which is not the same as a proportion.

The measure built from it.

EBP 0840 Odds Ratio

The odds in one group divided by the odds in the other.

The trap in reading them.

EBP 0841 Odds Ratio and Relative Risk Can Look Alike

When the outcome is rare the two are close. When it is common they diverge, and an odds ratio read as a risk ratio overstates the effect.

Two videos on the measure that speaks most directly in clinical terms.

The measure that speaks clinically.

EBP 0842 Number Needed to Treat

How many patients you must treat for one to benefit. The reciprocal of the absolute risk reduction.

How to read one.

EBP 0843 Reading a Number Needed to Treat

A small number means a large effect. Thirty-three means thirty-three treated for one to benefit.

Five videos putting it together. A relative figure is the same number whether the baseline was six percent or one, which is exactly what makes it portable and deceptive at once.

Why absolute measures travel.

EBP 0844 Absolute Measures Carry Baseline Risk

An absolute measure includes the starting risk, so it means the same thing wherever you read it.

And why relative ones mislead.

EBP 0845 Relative Measures Hide Baseline Risk

A relative measure is the same figure whether the baseline was six percent or one. That is what makes it portable and deceptive at once.

The contrast worked through.

EBP 0846 Two Patients, One Relative Reduction

The same fifty percent reduction, applied to two patients with different baseline risks, produces very different absolute benefit.

And what it does to the NNT.

EBP 0847 Same Relative Figure, Different Numbers Needed

The same relative reduction gives a number needed to treat of thirty-three at one baseline and near two hundred at another.

The other side of the ledger.

EBP 0848 Adverse Effects Enter the Same Judgement

Harms are counted the same way, and a number needed to harm sits beside the number needed to treat.

One video, and it is the error this entire strand was built to prevent.

The strand's canonical error.

EBP 0849 Misconception: The Bigger Number Is the Better Result

The larger-sounding figure is usually the relative one, and it is larger because it dropped the baseline rather than because the effect is bigger.

One procedure taking a single result through all three expressions with the baseline shown throughout.

The strand assembled.

EBP 0850 Reading the Numbers in a Study

One trial result expressed as absolute reduction, relative reduction and number needed to treat, with the baseline shown throughout.

That is the strand. Against the outcomes. Draw the two-by-two table first. Four cells — outcome or not, in each group — and every measure that follows is built from them rather than taken on trust. One result, three expressions. Six percent to three percent is an absolute reduction of three percentage points, a relative reduction of fifty percent, and a number needed to treat of thirty-three. The reason both are reported is that both are true. The reason it matters is that the relative figure is the same number whether the baseline was six percent or one — portable and deceptive at once, because it dropped the context on the way. An odds ratio and a relative risk look alike when the outcome is rare and diverge when it is common. Read as a risk ratio, an odds ratio on a common outcome overstates the effect. So when you meet a relative figure, find the baseline it came from and recompute against your own. The same fifty percent gives a number needed to treat of thirty-three on one unit and near two hundred on another. Unit 7 leaves numbers behind entirely, for the questions no trial can answer.

This is free, and stays free. If it helped, here is what keeps it running.