What Is an Effect Size, and Why Does It Matter More Than p < 0.05?

When an anxiety study reports that a treatment “significantly” reduced symptoms, the word can be misleading. Statistical significance (the famous p < 0.05) answers a narrow question: is the result unlikely to have appeared by chance alone? It says nothing about whether the result was large enough to matter to a person. That job belongs to the effect size.

What an effect size is

An effect size is a number that describes how large a difference or relationship is. If a therapy trial reports that treated participants improved more than controls with p < 0.01, you know the difference was unlikely to be chance. You don’t yet know whether it was the difference between feeling much better and feeling the same, or between feeling very slightly better and feeling the same.

The most common metrics

Three families of effect sizes appear regularly in anxiety research.

Standardized mean differences: Cohen’s d and Hedges’ g

These express a difference between two groups in standard deviation units. If a treatment group’s anxiety scores dropped one standard deviation more than a control group’s, d = 1.0. Cohen proposed rough benchmarks: d = 0.2 (small), 0.5 (medium), 0.8 (large) [1]. These were never meant to be rigid categories. Cohen called them conventions for use when no better frame of reference was available.

Hedges’ g applies a small correction for bias in small samples. For most studies the difference from Cohen’s d is trivial [4].

Correlation coefficients

An r of 0.10 is conventionally small, 0.30 medium, 0.50 large. A revised set of benchmarks, grounded in a survey of actual findings in personality and social psychology, suggested that r = 0.10 is actually a typical effect and r = 0.30 is already a “large” real-world effect [5]. This matters because many correlations in anxiety research fall in the 0.20–0.40 range, which sounds modest but may represent meaningful relationships.

Odds ratios and risk ratios

Binary outcomes (diagnosed or not, dropped out or not) use odds ratios or risk ratios. An odds ratio of 2.0 means the odds of the outcome are twice as high in one group. These are common in epidemiological studies and treatment response research.

Why the comparison group changes everything

The size of an effect depends on what the treatment is compared with. This is one of the most important things to check.

A comprehensive meta-analysis of psychological therapies for anxiety disorders found a pooled effect of g = 0.56 when compared with control conditions [2]. But the type of control mattered enormously. A separate meta-analysis restricted to trials where CBT for anxiety was compared with a placebo condition, either a pill placebo or a psychological placebo, found a smaller pooled effect of g = 0.33, and only g = 0.22 when compared with psychological placebo specifically [3].

The pattern is consistent: effects shrink with better comparison groups. Against a waiting list, the comparison group receives nothing, so the apparent treatment effect includes natural improvement, expectation of future help, and regression to the mean. When both groups receive something plausible, those shared factors cancel out and what remains is the specific effect of the treatment. Neither number is wrong; they answer different questions. For how comparison groups shape results more broadly, see how researchers separate correlation from causation.

From a number to a feeling

A Cohen’s d of 0.5 in GAD-7 terms might translate to roughly 3–4 points. Whether that changes how someone experiences their day depends on where they started. A drop from 18 to 14 may be noticeable; a drop from 6 to 2 may mean going from mild to minimal. One analysis estimated the minimal clinically important difference on the GAD-7 at about 4 points, though that needs confirming in anxiety-specific samples, as discussed in what an anxiety study actually measures.

Common mistakes in reading effect sizes

• Treating Cohen’s benchmarks as absolute standards. A d of 0.3 might be important for a cheap, widely available intervention and unimportant for an expensive, intensive one. Context matters.
• Ignoring the comparison group. A g of 0.8 against a waiting list is not the same as a g of 0.8 against an active treatment.
• Comparing effect sizes across different measures. A d of 0.5 on a self-report questionnaire and a d of 0.5 on a physiological measure don’t mean the same thing.
• Assuming an average effect applies to every person. An effect size is a summary across the group. Some people improve a lot, some don’t change, and a few may get worse.

Questions to ask when you see an effect size

1. What is the comparison group, and does it control for expectation?
2. Is the effect large enough to cross a clinically meaningful threshold?
3. Was the same measure used across the studies being compared?
4. Are the benchmarks (small/medium/large) appropriate for this field, or is there a better reference point?

What remains uncertain

There is no settled agreement on what counts as a “worthwhile” effect size in anxiety treatment. Different stakeholders may draw the line differently: a person living with severe anxiety may value a small improvement that a health-economic analysis would dismiss. The best reading combines the number with what it means in the units people experience.

Reading numbers about your own situation. An effect size describes an average across a study group, not a prediction for you. If you’re trying to decide between treatment options, a GP or mental health professional can help you weigh the evidence alongside your own circumstances. If anxiety is affecting your daily life, talk to a professional. If you are in crisis or thinking about harming yourself, contact emergency services or a crisis line now: in the US, call or text 988; in the UK and Ireland, Samaritans on 116 123.