Evaluating importance: An overview

(emphasis on Cohen’s d)• Measures size and direction of an

effect (attempts to address practical significance)• Cohen’d (sometimes equated to a

correlation r)

• Functional significance or clinical significance• e.g., change in blood pressure,

weight, etc.• Remember CI’s for the estimated

effect can also be used for this!

Practical vs statistical significance• Statistical significance (alpha

level; p-value) reflects the odds that a particular finding could have occurred by chance.

• If the p-value for a difference between two groups is 0.05, it would be expected to occur by chance just 5 times out of 100 (thus, it is likely to be a “real” difference).

• If the p-value for the difference is 0.01, it would be expected to occur by chance just one time out of 100 (thus, we can be even more confident that the difference is real rather than random).

Practical significance

Reflects the magnitude, or size, of the difference, not the probability that the observed result could have happened by chance.

Arguably much more important than statistical significance, especially for clinical questions

Measures of effect size (ES) quantify practical significance of a finding

Effect size The degree to which the null

hypothesis is false, e.g., not just that two groups differ significantly, but how much they differ (Cohen, 1990)

Several measures of ES exist; use “whatever conveys the magnitude of the phenomenon of interest appropriate to the research context” (Cohen, 1990, p. 1310)

IQ and height example (Cohen, 1990)

The height-IQ correlation: Cohen’s (1990) example on statistical and

practical significance A study of 14,000 children ages 6-17

showed a “highly significant” (p < .001) correlation of r = .11) between height and IQ

What does this p indicate? What’s the magnitude of this

correlation? – Accounts for 1% of the variance– Based on an r this big, you’d expect that

increasing a child’s height by 4 feet would increase IQ by 30 points, and that increasing IQ by 233 points would increase height by 4 inches (as a correlation, the predicted relationship could work in either direction)

2 main types of ES measures Variance accounted for

– a squared metric reflecting the percentage of variance in the dependent variable explained by the independent variable

– e.g., squared correlations, odds ratios, kappa statistics

Standardized difference– scales measurements across studies into

a single metric referenced to some standard deviation

– d the most common and the easiest conceptually: our focus today

Effect size

APA (2001) Publication Manual mandates: . . .it is almost always necessary to include some index of effect size or strength of relationship…provide the reader not only with information about statistical significance but also with enough information to assess the magnitude of the observed effect or relationship (pp. 25-26).

APA guidelines (2001) mandate inclusion of ES information (not just p-value information) in all published reports.

Until that happy day, if ES information is missing, readers must estimate ES for themselves.

When group means and SDs are reported, you often can estimate effect size quickly and decide whether to keep reading or not.

Finding, estimating, & interpreting d in group

comparison studies d = Difference between the

means of the two groups, divided by the standard deviation (SD).

Interpret as size of group difference in SD units.

When average mean difference between tx and control groups is 0.8 to 1 SD, practical significance has been defined as “high”.

Estimating d Find group means, subtract

them, and divide by the standard deviation.

When SDs for the groups are identical, hooray. When not, arguments have been made for using the control group SD, or the average of the two SDs.– My preference is the second,

which is more conservative and strikes me as more appropriate when dealing with the large variability we see in many groups of patients with disorders

Exercise 1: Calculating effect size, given group means and

SDs Data from Arnold et al. (2004) study

comparing scores on SNAP composite test after four types of treatment for ADHD

(Scores on SNAP composite; lower = better):

Treatment group Mean (SD)

Combined 0.92 (0.50)

Medical management 0.95 (0.51)

Behavioral 1.34 (0.56)

Community care 1.40 (0.54)

http://www.minddisorders.com/Kau-Nu/Kaufman-Short-Neurological-Assessment-Procedure.html (Link to the SNAP Assessment)

d demonstration, comparing SNAP performance in Combined and Medical Management groups

Combined 0.92 (0.50)Medical management 0.95 (0.51) d = 0.92-0.95/0.505 = -.03/.505 =

-.0594Interpretation: The Combined

group scored about 6/100s of a standard deviation better (lower) than the Medical Mgt group (an extremely tiny difference; these treatment approaches resulted in virtually the same outcomes on the SNAP measure)

d for Combined vs. Community Care treatment groups

Combined 0.92 (0.50)Community care 1.40

(0.54) d = 0.92-1.40/0.52 = -0.48/.52 = -

0.92Interpretation: The Combined

group scored nearly a whole standard deviation better than the Community care group; this is a large effect size. Combined treatment is substantially better than Community care.

d for Medical Management vs.

Behavioral treatmentMedical management

0.95 (0.51)Behavioral 1.34

(0.56) d = ?Interpretation?Assuming equal sample sizes the pooled

variance is average of the sample variances, from which we can calculate the pooled SD estimate (spooled).

d = (1.34 - .95)/.536 = .39/.536 = .728

d for Medical Management vs.

Behavioral treatmentMedical management 0.95

(0.51)Behavioral 1.34

(0.56) d = 0.95-1.34= -.39/.535 =

-.72897 = -.73:Interpretation: The Medical Mgt

group scored about 3/4s of a SD better than the behavioral group. This is a solid effect size suggesting that Medical Mgt treatment was substantially more effective than Behavioral treatment.

Exercise 1: Interpreting d in the happy cases when it’s

reported Treatment-difference effect sizes

(Cohen’s d) from Arnold et al., 2004 (Table II, p. 45)Combined vs Medical Management

0.06Combined vs Behavioral

0.79Combined vs Community Care

0.92Medical Management vs Behavioral

0.728Medical Mgt vs Community Care

0.85Behavioral vs Community Care

0.11 Note that our calculated d’s

match these.

An Overview of Evaluating Precision

Precision is reflected by the width of the confidence interval (CI) surrounding a given finding

Any given finding is acknowledged to be an estimate of the “real” or “true” finding

CI reflects the range of values that includes the real finding with a known probability

A finding with a narrower CI is more precise (and thus more clinically useful) than a finding with a broader CI

The standard error (SE) is the key.

Evaluating Precision CI’s are calculated by adding and

subtracting a multiple of the standard error (SE) for a finding/value (e.g., estimate + 1.96xSE(estimate) to determine the 95% CI)

As we have seen the standard error depends on sample size and reliability/variability; larger samples and higher reliability (smaller variability) will result in narrower CIs, all else being equal.

Finding and interpreting evidence of precision

CI’s for difference between means of 206 children receiving early TTP and 196 receiving late TTP for OME (Paradise et al. 2001)

Early Late 95% CI

PPVT92 (13) 92 (15) -2.8 to 2.8

NDW 124 (32) 126 (30) -7.6 to 4.8

PCC-R 85 (7) 86 (7) -2.1 to 0.7

CI’s are narrow thanks to large sample

Contrast with risk estimates for low PCC-R from smaller samples of children with (n=15) and without (n=47) OME-associated hearing loss. (Shriberg et al., 2000)

Estimated risk was 9.60 (i.e., children with hearing loss were 9.6 times more likely to have low PCC-R at age 3 than children without.

But 95% confidence interval was 1.08-85.58 – meaning that this increased risk was somewhere between none and a lot. Not very precise!

Predict precision In one study, children with

histories of OME (n=10) had significantly lower scores on a competitive listening task than children without OME histories (n=13)OME+ OME- p-6.8 (2.8) -9.7 (2.6) .016

How could you quantify importance?

What would you predict about precision?

When multiple studies of a question are available, meta-

analysis Quantitative summary of

effects across a number of studies addressing particular question, usually in the form of a d (effect size) statistic

In EBP evidence reviews, the highest quality evidence comes from meta-analysis of studies with strong validity, precision, and importance

A meta-analysis of OME and speech and language (Casby,

2001) Casby (2001) summarized results

of available studies of OME and children’s language.

For global language abilities, the effect size for comparing mean language scores from children with and without OME histories was d = -.07.

Interpretation and a graphic representation.

An informative graphic for meta-analyses

Shows d from each study as well as associated 95% CI.

d and 95% CI boundaries for OME and vocabulary comprehension (Casby, 2001)

-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5

Teele 84

Lous 88

Teele 90

Roberts 91l

Roberts 91m

Lonigan 92

Black 93

Paradise 00

Upper 95% CI

dLower 5% CI

Worse with OME

Better with OME

Study

Overall d = .001

Evidence levels for evaluating quality of

treatment studiesBest Ia Meta-analysis of >1 randomized

controlled trial (RCT)

Ib Well-designed randomized controlled study

IIa Well-designed controlled study without

randomization IIb Well-designed quasi-experimental

study III Well-designed non-experimental

studies, i.e., comparative, correlational,

and case studies Worst IV Expert committee report,

consensus conference, clinical experience of

respected authorities

Summary of Effect Size Cohen’s d can be “equated” to a correlation. Provides a standardized measure of effect

size. Best way to discern practical significance

from statistical significance is direct quantification of effect size using a CI.

For meta-analysis however, we need a standardized ES in order to combine study results.