Convergent Validity: Interpretation and APA Reporting

The Basics

When to Use It

Use it when you have a measure of a construct you can't observe directly, such as a new questionnaire, a short form or a translation, and want evidence that it measures that construct. You give it, alongside established measures of the same construct and at least one measure of a different construct, to the same people. Convergent validity isn't a single test: it's an argument built from correlations, their intervals and a comparison between them. For example:

Does a new 8-item mindfulness scale agree with established mindfulness measures more than with extraversion?
Does a 2-item screener for depression correlate strongly with the other seven PHQ-9 items in primary-care patients?
Does a smartphone reaction-time task track the same attention ability as a lab-based continuous performance test?

Convergence is half of the classic argument. The other half, showing the measure stays apart from different constructs, is discriminant validity; this page includes the simplest version of it, one contrast correlation.

Vocabulary You Need

Definition Construct Validity

How well a measure's scores can be interpreted as reflecting a construct: an attribute such as mindfulness, anxiety or working memory that can't be observed directly. It isn't a single number. It's built up from several kinds of evidence: what the items cover, how they hang together, and whether scores relate to other measures the way the theory of the construct predicts (convergent and discriminant evidence). It belongs to a particular interpretation of scores, in a particular population, rather than to the test itself, and it is never proved once and for all. Glossary →

Definition Convergent Validity

Evidence that a measure's scores agree with other measures of the same construct, usually shown by a substantial correlation with an established measure of it. Campbell and Fiske (1959) framed it as agreement between independent ways of measuring the same trait. It is one strand of construct validity, and it only persuades alongside discriminant evidence: a measure that correlates strongly with everything may be picking up something broad, such as a way of answering questionnaires. There is no agreed cutoff for a strong enough correlation; it depends on how close the comparison measure is to the construct and on how reliable both measures are. Glossary →

Definition Disattenuated Correlation (

r_c

)

An observed correlation divided by the square root of the two measures' reliabilities multiplied together, r_c = r / √(r_xx × r_yy). Random measurement error that is unrelated between the two measures pulls a correlation toward zero on average (Spearman, 1904, called this attenuation), so the corrected value estimates how strongly the underlying true scores would correlate if both measures were perfectly reliable. It is only as good as the reliabilities it uses: underestimated reliabilities overcorrect it, and it can even come out above 1. It describes true scores, not the agreement the two measures actually achieve. Also called the correction for attenuation. Glossary →

Definition Reliability

The extent to which a measure's scores can be replicated: measured again, by another rater or with other items, would people get the same scores? Formally, it's the share of the differences between people's scores that reflects real differences in what's measured rather than measurement error, so it runs from 0 (all noise) to 1 (no noise). It belongs to scores from a particular group of people under particular conditions, not to the test itself: the same test can be more reliable in a group whose scores vary widely. There are several kinds, each asking about a different source of noise: test-retest (occasions), inter-rater (raters) and internal consistency (items). A measure has to be reliable to be valid, but reliable scores can still measure the wrong thing. Glossary →

Definition Multitrait-Multimethod Matrix

A correlation table for several traits, each measured by several methods (self-report, an informant, an observer, a task), arranged so convergent and discriminant evidence can be read side by side (Campbell & Fiske, 1959). Each measure's reliability sits on the diagonal. Correlations between different methods measuring the same trait, the validity diagonal, should be substantial, and higher than correlations between different traits. When every measure shares one method, such as questionnaires filled in at one sitting, the table can only show part of that logic, because shared method can raise every correlation. Often shortened to MTMM. Glossary →

Assumptions

1. Valid Comparison Measures The established measures you compare against really measure the constructs you say they do.

What It Means: Validity evidence from correlations borrows its meaning from the measures used for comparison. If an established measure covers only part of the construct, or something else as well, a strong correlation shows that the new measure shares whatever that measure captures, not that it captures the construct. The contrast measure should tap a construct theory says is distinct. A close neighbor (for mindfulness, rumination or self-compassion) is a stronger test than a distant one like extraversion, the easy case this example uses.
Applies To: Variables
How to Check: By reasoning and the literature, not by a test. What does each comparison measure cover, how was it validated, and in samples like yours? Before collecting data, write down which measures should correlate strongly with the new one, which weakly, and roughly how strongly, so the results are judged against hypotheses rather than after the fact.
How Much It Matters: Completely, for what the result means. The correlation with the MAAS is evidence about mindfulness only as far as the MAAS measures mindfulness, and the MAAS covers attention and awareness, not the acceptance side of mindfulness that the new scale may also include (Brown & Ryan, 2003, left attitudinal items out on purpose). That's one reason to use two established measures and to expect less than a perfect correlation.

If It's Violated

Design Change Correlate the new measure with two or more established measures that cover the construct in different ways, as we did with the MAAS and the FFMQ-15.
Design Change Write down, before collecting data, which correlations should be high, which low and roughly how high, and judge the results against that.
Proceed with Caveat Report which part of the construct each comparison measure taps, so readers can judge what a strong or weak correlation shows.

2. Independent Methods Your measures don't share a way of measuring that could make them agree on its own.

What It Means: Two measures can correlate because they tap the same construct, or because they share a method: the same informant, the same questionnaire format, the same sitting, the same tendency to agree with statements. Campbell and Fiske (1959) treated agreement between independent methods as the core of validation. When every measure is a self-report questionnaire completed at once, part of every correlation may be shared method rather than shared construct.
Applies To: Design
How to Check: By design. List what the measures have in common besides the construct: who answered, in what format, on what occasion. Then look at the correlations between different constructs measured the same way. If those are high too, shared method is probably inflating all the correlations.
How Much It Matters: A lot, and it pushes correlations up. All four of our measures are self-report questionnaires completed in one sitting, so a general tendency to rate oneself favorably could raise every correlation, including the one with extraversion. The design can show that the new scale agrees with other questionnaires, not that it agrees with mindfulness measured another way: it gives only the single-method part of a multitrait-multimethod matrix.

If It's Violated

Design Change Measure the construct a second way as well, such as ratings by someone who knows the person well, an experience-sampling measure or a behavioral task, and check that the new scale converges with it too.
Design Change Give the measures on different occasions or in different formats, so they share less than a single sitting.
Proceed with Caveat Say plainly that all the measures share a method, and read the gap between convergent and discriminant correlations rather than the convergent correlation alone.

3. Independent Observations The people (or other units) in your study don't influence each other.

What It Means: Each person's data comes from a separate, unconnected source, so knowing one person's scores tells you nothing about anyone else's. In designs that measure people more than once, their own scores are meant to be related; it's different people who must be independent. Methods built for clustered data, such as multilevel models and GEE, also allow members of the same group to be related, as long as the analysis names the grouping; then it's the groups that must be independent.
Applies To: Observations
How to Check: By design, not by a test. Did each person contribute their own data, with no clusters such as roommates, couples, therapy groups or classrooms whose members influence each other? If there are clusters, does the analysis model every one of them?
How Much It Matters: A lot, for the intervals and the test. Scores that come in clusters, such as members of the same meditation group, make every standard error too small. The correlations themselves are still correct descriptions of this sample.

If It's Violated

Design Change Recruit people independently, with each person answering every measure once.
Alternative Test If people come in clusters, estimate the correlations with a multilevel model that accounts for them.

4. Linear Relationship The relationship between your variables follows a straight line, not a curve.

What It Means: As one variable goes up, the other tends to change by about the same amount across its whole range. A curved relationship, one that levels off or a U shape, breaks this.
Applies To: Relationship
How to Check: Look at a scatterplot of each pair of measures: a roughly oval cloud tilted one way is fine; a clear bend, a ceiling or a U is not.
How Much It Matters: A lot, for what r means. A correlation only captures the straight-line part of a relationship, so if the new scale levels off at the top (a ceiling), r will understate how closely the two measures agree. Look at the scatterplot for each pair; ours follow roughly straight trends.

If It's Violated

Alternative Test Spearman Correlation. If the relationship bends but always rises, a rank correlation measures that consistent trend without needing a straight line.
Proceed with Caveat If one measure hits a ceiling or floor, say so and show the scatterplot; a ceiling is a finding about the measure.

5. Bivariate Normality The pairs of scores form an oval cloud, with each variable roughly bell-shaped.

What It Means: Each variable is roughly normal and the scatterplot forms an oval cloud; two bell-shaped variables alone don't guarantee it. The p-value and confidence interval rely on it; r itself, as a description, doesn't. Large samples protect the p-value of a test against zero fairly well. They don't protect a test against any other value, a comparison of two correlations, or the Fisher-z interval, whose coverage can get worse with more data when the scores are strongly nonnormal.
Applies To: Joint distribution
How to Check: Look at a histogram of each variable and at the scatterplot for strong skew, heavy tails or a funnel shape. Don't rely on a normality test: with small samples it misses real problems, and with large ones it flags trivial ones.
How Much It Matters: Some, for the intervals and the test, not for r itself. Fisher-z intervals and Williams's t assume roughly normal scores. Totals of several rating items are usually close to symmetric; ours have skewness between −0.12 and 0.01 with 200 people, so it's fine here.

If It's Violated

Robust Estimation Resample people, recompute the correlations and their gap thousands of times, and use the middle 95% as the interval.
Alternative Test Spearman Correlation. Rank correlations are much less affected by skew and heavy tails. The question becomes whether the orderings agree.

6. No Extreme Outliers No single case is far enough from the rest to drive the result.

What It Means: A few points far from the rest can pull a statistic around on their own, so it describes those few points more than everyone else. In a test, that can create an effect that isn't there or hide one that is.
Applies To: Observations
How to Check: Plot the data and look for points far from the rest. With two or more variables, flag cases with large squared Mahalanobis distances across them: points can be ordinary on each variable but unusual in combination. Check each against the raw records, and compare the result with and without it.
How Much It Matters: A lot in small samples, less with 200 people. One person far from the rest on two measures can pull a correlation up or down on their own, and a careless responder can do it on several at once. Nobody in our data is more than 3.1 standard deviations from the mean on any total.

If It's Violated

Correction Check extreme or implausible response patterns, such as the same answer to every item, against attention checks, and remove data-entry errors.
Proceed with Caveat If an outlier is a real person, report the correlations with and without them.

7. Suitable Reliability Estimates The reliabilities you correct with describe these scores in this sample.

What It Means: The correction for attenuation divides by the reliabilities, so any error in them goes straight into the corrected correlation. An underestimate overcorrects: alpha, for example, runs low when some items reflect the construct more strongly than others. A reliability borrowed from a manual or a different population may not describe your sample. The correction also assumes the two measures' errors are unrelated, which shared wording or a shared sitting can break.
Applies To: Items
How to Check: Estimate reliability in your own sample and say which coefficient you used. Try other reasonable estimates (omega, test-retest) and see how much the corrected correlation moves. A corrected correlation above 1 means something in the inputs is off.
How Much It Matters: Only for the corrected correlations, and a lot for those. Dividing by √(.85 × .86) raises .55 to .64; if the true reliabilities were higher, the corrected value would be lower, and vice versa. The observed correlations don't depend on this assumption at all.

If It's Violated

Correction If the items reflect the construct unequally, use omega from a factor model instead of alpha, which then runs low.
Proceed with Caveat Report the observed correlation first and the corrected one second, with the reliabilities used, so readers can see how much the correction contributes.
Alternative Test Confirmatory Factor Analysis (CFA). A confirmatory factor model estimates the correlation between the constructs directly from the items, with measurement error modeled item by item.

Limitations

This Is Not Your Test If…

You want to know whether scores are consistent, not what they mean Agreement and Reliability →
You want to show the measure is distinct from other constructs Discriminant Validity →
You've fitted a factor model and want item-level evidence Average Variance Extracted (AVE) →
You want to check the items form the factors you intended Confirmatory Factor Analysis (CFA) →
You're checking the measure against a yes/no diagnosis Sensitivity and Specificity →
You're comparing one correlation across two separate groups Comparing Correlation Coefficients →

What It Doesn't Tell You

Whether it measures mindfulness. Agreeing with the MAAS and the FFMQ-15 shows the new scale captures what they capture. If they miss part of mindfulness, or share a bias, so does this evidence.
Whether it's more than shared method. All four measures are self-report questionnaires from one sitting, so part of every correlation, the one with extraversion included, may reflect how people fill in questionnaires rather than what they're like.
Whether it's good enough for your purpose. An r of .55 meets a common rule of thumb, but there's no agreed standard, and a scale meant to replace the MAAS would need to agree with it much more closely.
Whether a short form agrees, if it shares items. A short form's items are part of the full form, so their correlation is inflated by the overlap. Give the forms separately, or correlate the short form with the full form minus those items.
That it fails, if a correlation had come out weak. A weak correlation could mean the new scale misses the construct, or that the comparison measure does, or that one of them is unreliable, or that the sample's scores vary too little. The design alone can't say which.

Common Mistakes

Don'tCall a measure valid because it correlates well with one similar measure.

InsteadTreat convergence as one piece of evidence. Pair it with discriminant correlations and with evidence about content and structure.
Don'tSettle for a convergent correlation that is merely significantly above zero.

InsteadJudge its size against the range you expected. With 200 people, even r = .15 is significant.
Don'tReport only the disattenuated correlation.

InsteadReport the observed correlation first, then the corrected one, with the reliabilities used to correct it.
Don'tCompare convergent and discriminant correlations by their p-values, or with a test for independent groups.

InsteadTest the gap directly with a test for dependent correlations, such as Williams's t or Steiger's z, which allows for the shared measure.
Don'tDecide which measures count as the same construct after seeing the correlations.

InsteadState in advance which correlations should be strong and which weak, and report any that missed.
Don'tRead a p-value as the chance that the null hypothesis is true.

InsteadRead it as: if the null were true, how often data at least this extreme would turn up.

Result Decoder

Significance and Effect Size Guidelines

Benchmarks Significance (p Value)

p < .001
Very strong evidence against the null hypothesis.
.001 ≤ p < .01
Strong evidence against the null hypothesis.
.01 ≤ p < .05
Statistically significant at α = .05. Moderate evidence against the null hypothesis.
.05 ≤ p < .10
Not significant. Weak evidence; sometimes called a “trend.” Treat it as inconclusive.
p ≥ .10
Not significant. Little evidence against the null, which is not the same as evidence of no effect.

These evidence labels are one common convention for describing p in graded language rather than as significant or not; the boundaries are rough guides, not rules, and other authors draw them differently. Muff et al. (2022) argue for this kind of language of evidence over a single cutoff. α is chosen before the analysis, and p never says how big or important an effect is.

More about statistical significance ↓

Benchmarks Effect Size (Convergent

r

)

r < .50 Below Common Cutoffs
Short of the usual > .50 rule and in the range Carlson and Herdman (2012) say a stand-in measure should avoid. Weak evidence of convergence, if the comparison measure really targets the same construct.
.50 ≤ r < .70 Commonly Adequate
Meets the usual rule for a measure of the same construct (Abma et al., 2016), but short of the .70 that Carlson and Herdman (2012) recommend before one measure stands in for another.
r ≥ .70 Strong
The level Carlson and Herdman (2012) recommend, and the stricter expectation Abma et al. (2016) set when two instruments really measure the same construct.

There is no agreed benchmark for convergent validity. These ranges come from the two sources we read that name numbers, both about the observed correlation with a measure of the same construct: Abma et al. (2016) describe > .50 as the usual rule in reviews of patient-reported measures and call such cutoffs arbitrary, and Carlson and Herdman (2012) recommend above .70 and advise against proxies below .50. Abma et al. also count the share of hypotheses stated in advance that hold, with more than 75% counted as adequate. Campbell and Fiske (1959) asked only that convergent correlations be significant and large enough to encourage further examination. Any r is lower in a sample whose scores vary little, so compare yours with values from similar samples, and write down the range you expect before collecting data.

More about effect size ↓

How It's Reported

Equation Form

Example

r(198) = .55, 95% CI [.44, .64], r_c = .64; r_disc = .30; r_conv − r_disc = .25, 95% CI [.09, .40], t(197) = 3.12, p = .002

Table 1. Means, Standard Deviations, Reliabilities and Correlations of the Four Measures

Example

	$M$	$SD$	1	2	3	4
New mindfulness scale	25.39	5.67	.85
MAAS	3.88	0.68	.55	.86
FFMQ-15	45.15	8.54	.59	.52	.83
Mini-IPIP extraversion	12.04	3.66	.30	.12	.25	.81

Note. N = 200. Values on the diagonal are each measure's Cronbach's α, from its own items; values below it are Pearson correlations. Columns 2 and 3 of row 1 are the convergent correlations; row 4 holds the correlations with a different construct. All correlations are significant at p < .001 except MAAS with extraversion (p = .089). All four are self-report questionnaires, so this is a single-method table: it can show convergent and discriminant patterns, but not separate them from shared method.

Full Text (APA Style)

Example

Scores on the new mindfulness scale (M = 25.39, SD = 5.67, α = .85) correlated substantially with the MAAS, r(198) = .55, 95% CI [.44, .64], and with the FFMQ-15, r(198) = .59, 95% CI [.50, .68]. Corrected for measurement error in both measures (α = .86 for the MAAS and .83 for the FFMQ-15), the correlations were .64 and .71. The new scale correlated more weakly with Mini-IPIP extraversion (α = .81), r(198) = .30, 95% CI [.17, .42]. The convergent correlation with the MAAS exceeded the correlation with extraversion by .25, 95% CI [.09, .40] (Zou's method); Williams's test for dependent correlations showed the difference was statistically significant, t(197) = 3.12, p = .002. The FFMQ-15 correlation exceeded the correlation with extraversion by .30, 95% CI [.15, .44], t(197) = 4.15, p < .001.

Report the whole pattern, not one number: every convergent and discriminant correlation, with intervals, ideally in a table with the reliabilities on the diagonal.
Give the observed correlations first. If you correct for attenuation, say so, give the reliabilities you used and label the corrected values.
Say which expectations you set in advance (for example, "above .50 with the MAAS, below .30 with extraversion") and whether each was met.
Test convergent against discriminant correlations with a test for dependent correlations, and name it.

Reading Each Piece

The equation form above, piece by piece, in this order: how big, how certain, then how surprising.

r(198) = .55	People who scored higher on the new scale tended to score higher on the MAAS. That's past the usual > .50 rule for a measure of the same construct, short of the .70 some recommend. The 198 is the degrees of freedom, n − 2. Benchmarks ↑
95% CI [.44, .64]	The population correlation is plausibly anywhere from .44 to .64: from a little short of the usual .50 rule to comfortably past it.
r_disc = .30	The new scale's correlation with extraversion, 95% CI [.17, .42]. Not zero: the two traits may be somewhat related, or the shared questionnaire method may be raising it. But it's clearly lower than the correlations with the mindfulness measures. The benchmarks above are for convergent correlations and don't apply here; lower is what we hoped for.
r_c = .64	If both scales measured without error, the new scale and the MAAS would correlate about .64. It's an estimate about true scores, only as good as the alphas it divides by, and it still says nothing about shared method.
r_conv − r_disc = .25	The new scale's correlation with the MAAS is .25 higher than its correlation with extraversion.
95% CI [.09, .40]	The true gap is plausibly anywhere from .09 to .40. The whole range is above zero, but 200 people can't say precisely how much stronger the convergent correlation is.
t(197) = 3.12	The gap is 3.12 standard errors from zero, allowing for how the two correlations move together. The 197 is the degrees of freedom, n − 3.
p = .002	If the new scale were as closely tied to extraversion as to the MAAS, a gap at least this large, in either direction, would turn up about 0.2% of the time. That's below .05, so the convergent correlation is significantly higher. Benchmarks ↑

Calculations

The Running Example

Example

The mindfulness scale study: 200 adults, a new 8-item mindfulness scale correlated with two established mindfulness measures and, for contrast, with extraversion.

Null Hypothesis:: $\rho_{\text{conv}} = \rho_{\text{disc}}$
Alternative (Two-Sided):: $\rho_{\text{conv}} \neq \rho_{\text{disc}}$

$\rho_{\text{conv}}$ is the population correlation between the new scale and the MAAS, and $\rho_{\text{disc}}$ the population correlation between the new scale and extraversion. Our sample's .55 and .30 estimate them. The hypotheses are about the one comparison we test; the correlations themselves are estimated with intervals, not tested against zero.

What Your Data Should Look Like

One row per person, with a total score for every measure and, for estimating reliability, every item of every measure. Items should already be recoded so that a higher answer always means more of the trait. Everyone answers every measure.

Example

participant	new_scale	maas	ffmq	extraversion	new_1	new_2	new_3	new_4	new_5	new_6	new_7	new_8	maas_1	maas_2	maas_3	maas_4	maas_5	maas_6	maas_7	maas_8	maas_9	maas_10	maas_11	maas_12	maas_13	maas_14	maas_15	ffmq_1	ffmq_2	ffmq_3	ffmq_4	ffmq_5	ffmq_6	ffmq_7	ffmq_8	ffmq_9	ffmq_10	ffmq_11	ffmq_12	ffmq_13	ffmq_14	ffmq_15	ipip_e_1	ipip_e_2	ipip_e_3	ipip_e_4
1	17	3.0	38	9	3	2	2	3	3	1	1	2	4	3	3	3	3	2	2	4	3	4	4	3	2	3	2	3	3	2	2	2	3	2	3	2	2	1	3	4	3	3	3	2	3	1
2	19	2.87	36	10	2	2	2	3	3	2	3	2	3	1	2	4	3	3	4	2	4	4	2	2	2	3	4	3	1	2	2	3	3	3	3	2	2	3	2	3	3	1	2	2	3	3
3	30	4.0	49	8	4	4	4	4	4	2	5	3	3	3	5	4	3	4	3	5	5	6	4	3	3	5	4	1	4	4	2	1	5	2	4	4	4	4	2	4	3	5	3	2	1	2
4	19	3.27	40	16	2	1	2	3	4	2	4	1	4	3	3	2	2	4	4	3	1	4	4	3	5	2	5	3	3	3	4	3	2	2	3	4	2	1	2	3	3	2	4	3	4	5
5	22	3.67	51	12	3	1	4	2	4	3	4	1	4	5	3	2	4	4	3	4	3	4	3	5	5	2	4	3	4	4	3	3	4	3	4	3	4	2	3	3	4	4	3	2	3	4
6	19	3.53	47	8	3	3	2	1	3	2	2	3	4	3	3	4	3	3	4	3	3	5	4	2	3	4	5	4	2	4	4	2	2	3	5	3	2	2	4	2	4	4	2	2	2	2
… 194 more rows

	M	SD	1	2	3
1. New Mindfulness Scale	25.39	5.67
2. MAAS	3.88	0.68	.55
3. FFMQ-15	45.15	8.54	.59	.52
4. Mini-IPIP Extraversion	12.04	3.66	.30	.12	.25

N = 200.

Correlations are Pearson r.

Simulated data.

Download all 200 rows (data.csv)

Napkin Math

The whole test, one idea at a time. Under each heading, a line says why the step matters, and the green note reads the equation in plain English with the mindfulness scale study's numbers. Collapse all to read just the headings: they tell the whole story on their own.

1. Correlate the New Scale with an Established Measure of the Same Construct

The first question is whether people who score high on the new scale also score high on a trusted measure of mindfulness. A Pearson correlation measures how closely the two sets of scores move together.

$r = \dfrac{\text{cov}_{xy}}{s_x \, s_y}$ = $\dfrac{2.12}{5.67 \times 0.68}$

= .55

$r_{\text{FFMQ}}$ = .59

$\text{cov}_{xy}$ is how the new scale ( $x$ ) and the MAAS ( $y$ ) move together, 2.12 points × MAAS units, and $s_x$ = 5.67 and $s_y$ = 0.68 are their spreads. 2.12 ÷ 3.86 = .55. The same formula with the FFMQ-15 gives $r$ = .59.
2. Give a Range of Plausible Values for That Correlation

A sample of 200 pins a correlation down only roughly. Stretch it onto Fisher's z scale, where its uncertainty is the same size everywhere, build the range there, and convert both ends back.

$\tanh\!\left(z_r \pm 1.96 \times \dfrac{1}{\sqrt{n - 3}}\right)$ = $\tanh\!\left(0.613 \pm 1.96 \times \dfrac{1}{\sqrt{197}}\right)$

= [.44, .64]

$\text{CI}_{\text{FFMQ}}$ = [.50, .68]

Fisher's $z_r = \tfrac12 \ln\frac{1 + r}{1 - r}$ stretches our $r$ (.5465 before rounding) to 0.613. $1/\sqrt{n - 3}$ = 1 ÷ √197 = 0.071, and 1.96 × 0.071 = 0.14, so on the z scale the range is 0.613 ± 0.14, from 0.474 to 0.753. The tanh function turns a z back into a correlation: tanh(0.474) = .44 and tanh(0.753) = .64.
3. Correlate the New Scale with a Measure of a Different Construct

Agreement with other mindfulness measures means little if the new scale agrees just as well with everything. So correlate it with a construct it should relate to less closely. We use extraversion, a distant trait and so an easy test; a close neighbor such as rumination or self-compassion would be a harder one.

$r = \dfrac{\text{cov}_{xy}}{s_x \, s_y}$

= .30

$\text{CI}_{\text{disc}}$ = [.17, .42]

The same formula, with the Mini-IPIP extraversion scale as $y$ : $r$ = .30. People who scored higher on the new scale scored a little higher on extraversion, but the link is about half as strong as with the MAAS.
4. Check How Consistently Each Measure Measures

Every score carries some random error. Error that's unrelated between two measures pulls their correlation toward zero, on average. Cronbach's alpha estimates a measure's reliability, how much of each total score is consistent signal rather than error, from how strongly its items go together.

$\alpha = \dfrac{k}{k - 1}\left(1 - \dfrac{\sum s_i^2}{s_X^2}\right)$ = $\dfrac{8}{7}\left(1 - \dfrac{8.25}{32.12}\right)$

= .85

$\alpha_{\text{MAAS}}$ = .86
$\alpha_{\text{FFMQ}}$ = .83
$\alpha_{\text{E}}$ = .81

$k$ is the new scale's 8 items. Its items' variances add up to 8.25, while the total score's variance is 32.12, far more than its parts because the items rise and fall together. 1 − 8.25 ÷ 32.12 = 0.74, and 8/7 × 0.74 = .85. The same for the others: MAAS .86, FFMQ-15 .83, extraversion .81.
5. Estimate How Strongly the Constructs Would Correlate without Measurement Error

Spearman's correction for attenuation divides the observed correlation by how far measurement error could have pulled it down, estimating the correlation between people's true scores, the scores they'd get with no measurement error. It answers a different question from the observed r, so it's reported alongside it, not instead.

$r_c = \dfrac{r_{xy}}{\sqrt{r_{xx}\, r_{yy}}}$ = $\dfrac{.55}{\sqrt{.85 \times .86}}$

= .64

$r_{c,\text{FFMQ}}$ = .71
$r_{c,\text{disc}}$ = .36

$r_{xy}$ is our observed .55, and $r_{xx}$ = .85 and $r_{yy}$ = .86 are the two alphas. .85 × .86 = .73 and its square root is .855: the highest correlation two measures this reliable can be expected to reach, if their errors are unrelated. .55 ÷ .855 = .64, so the observed .55 is about two-thirds of the way to that ceiling. With the FFMQ-15 the corrected value is .71; with extraversion, .36.
6. Find the Gap between the Convergent and Discriminant Correlations

The heart of the argument is a contrast: the new scale should go with mindfulness measures more strongly than with a different construct. The plainest measure of that is one correlation minus the other.

$r_{xy_1} - r_{xy_2}$ = $.55 - .30$

= 0.25

$r_{\text{FFMQ}} - r_{\text{disc}}$ = .30

$r_{xy_1}$ is the new scale with the MAAS, .55, and $r_{xy_2}$ the new scale with extraversion, .30. .55 − .30 = .25. For the FFMQ-15, .59 − .30 = .30.
7. Compare the Gap with Its Uncertainty

Both correlations come from the same 200 people and share the new scale, so they wobble together from sample to sample. Williams's t allows for that, using the correlation between the other two measures, the MAAS and extraversion.

$t = (r_{xy_1} - r_{xy_2})\sqrt{\dfrac{(n - 1)(1 + r_{y_1y_2})}{2\,\dfrac{n - 1}{n - 3}\,|R| + \bar{r}^{\,2}(1 - r_{y_1y_2})^3}}$ = $0.248\sqrt{\dfrac{199 \times 1.121}{1.287 + 0.121}}$

= 3.12

$r_{y_1y_2}$ = .12
$df$ = 197
$t_{\text{FFMQ}}$ = 4.15

$r_{y_1y_2}$ , the MAAS with extraversion, is .12, so $(n - 1)(1 + r_{y_1y_2})$ = 199 × 1.121 = 223.0. On the bottom, $|R|$ = .637 sums up how the three measures overlap (1 minus the three squared correlations, plus twice their product), so 2 × 199/197 × .637 = 1.287. $\bar r$ = .423 is the average of the two correlations being compared, and .423² × (1 − .121)³ = 0.121. That gives 1.287 + 0.121 = 1.408, and √(223.0 ÷ 1.408) = 12.58. 0.248 × 12.58 = 3.12, judged against a t distribution with $n - 3$ = 197 df. The same test for the FFMQ-15 gap gives $t$ = 4.15.
8. Give a Range of Plausible Values for the Gap

Zou's method builds the range from each correlation's own interval, pairing how far one could fall with how far the other could rise, then allows for the two moving together.

$\left[\, d - \sqrt{(r_1 - l_1)^2 + (u_2 - r_2)^2 - 2c\,(r_1 - l_1)(u_2 - r_2)},\;\; d + \sqrt{(u_1 - r_1)^2 + (r_2 - l_2)^2 - 2c\,(u_1 - r_1)(r_2 - l_2)} \,\right]$ = $.25 - \sqrt{.105^2 + .121^2 - 2(.039)(.105)(.121)}$

= [.09, .40]

$\text{CI}_{\text{FFMQ}}$ = [.15, .44]

The MAAS correlation's interval reaches .105 below .55, and the extraversion correlation's reaches .121 above .30. $c$ = .039 is how closely the two correlations move together here, small because the MAAS and extraversion barely correlate. √(.0110 + .0147 − .0010) = .157, so the low end is .25 − .16 = .09. The high end works the same way: .25 + .16 = .40. The FFMQ-15 gap's range is .15 to .44.
9. Ask How Surprising the Gap Would Be If the Two Correlations Were Equal

Finally, ask how often a gap at least this wide, in either direction, would turn up if the new scale were equally closely tied to the MAAS and to extraversion in the population.

$p = 2 \times P(T_{df} \le -|t|)$ = $2 \times P(T_{197} \ge 3.12)$

= .002

$p_{\text{FFMQ}}$ < .001

$P(T_{197} \ge 3.12)$ is the chance a t with 197 df lands at or above 3.12, about .001. Doubling it counts both directions: .002, about 1 in 480. For the FFMQ-15 gap, $p$ = .00005.

Run It in Software

The code below reads the running example's data from data.csv; save it in the same folder you run the code from.

SPSS (version 30, as documented by IBM)

SPSS has no single convergent-validity procedure, so it's three steps: each measure's reliability, the correlations, then a few lines of syntax for the correction and the comparison.

Analyze → Scale → Reliability Analysis. Move the new scale's eight items (new_1 to new_8) into Items, leave Model on Alpha, and click OK. Repeat for the MAAS (maas_1 to maas_15), FFMQ-15 (ffmq_1 to ffmq_15) and extraversion (ipip_e_1 to ipip_e_4) items.
Analyze → Correlate → Bivariate. Move new_scale, maas, ffmq and extraversion into Variables, leave Pearson checked, ask for a 95% confidence interval, and click OK.
Paste the last block of syntax below into a syntax window, type in the three correlations, two alphas and n, and run it. It creates a one-row dataset and lists the results.

Or paste this syntax:

RELIABILITY /VARIABLES=new_1 TO new_8 /MODEL=ALPHA.
RELIABILITY /VARIABLES=maas_1 TO maas_15 /MODEL=ALPHA.
RELIABILITY /VARIABLES=ffmq_1 TO ffmq_15 /MODEL=ALPHA.
RELIABILITY /VARIABLES=ipip_e_1 TO ipip_e_4 /MODEL=ALPHA.

CORRELATIONS
  /VARIABLES=new_scale maas ffmq extraversion
  /PRINT=TWOTAIL NOSIG FULL
  /CI CILEVEL(95)
  /MISSING=PAIRWISE.

* Correction for attenuation, and Williams's t and Zou's (2007) interval for
* r12 (new scale with MAAS) minus r13 (new scale with extraversion).
DATA LIST FREE / r12 r13 r23 a1 a2 n.
BEGIN DATA
.5465396 .2986059 .1205961 .849299 .8561593 200
END DATA.
COMPUTE rc = r12 / SQRT(a1 * a2).
COMPUTE diff = r12 - r13.
COMPUTE det = 1 - r12**2 - r13**2 - r23**2 + 2 * r12 * r13 * r23.
COMPUTE rbar = (r12 + r13) / 2.
COMPUTE t = diff * SQRT((n - 1) * (1 + r23) / (2 * (n - 1) / (n - 3) * det + rbar**2 * (1 - r23)**3)).
COMPUTE df = n - 3.
COMPUTE p = 2 * (1 - CDF.T(ABS(t), df)).
COMPUTE h = IDF.NORMAL(0.975, 0, 1) / SQRT(n - 3).
COMPUTE l1 = (EXP(2 * (0.5 * LN((1 + r12) / (1 - r12)) - h)) - 1) / (EXP(2 * (0.5 * LN((1 + r12) / (1 - r12)) - h)) + 1).
COMPUTE u1 = (EXP(2 * (0.5 * LN((1 + r12) / (1 - r12)) + h)) - 1) / (EXP(2 * (0.5 * LN((1 + r12) / (1 - r12)) + h)) + 1).
COMPUTE l2 = (EXP(2 * (0.5 * LN((1 + r13) / (1 - r13)) - h)) - 1) / (EXP(2 * (0.5 * LN((1 + r13) / (1 - r13)) - h)) + 1).
COMPUTE u2 = (EXP(2 * (0.5 * LN((1 + r13) / (1 - r13)) + h)) - 1) / (EXP(2 * (0.5 * LN((1 + r13) / (1 - r13)) + h)) + 1).
COMPUTE c = ((r23 - 0.5 * r12 * r13) * (1 - r12**2 - r13**2 - r23**2) + r23**3) / ((1 - r12**2) * (1 - r13**2)).
COMPUTE ci_low = diff - SQRT((r12 - l1)**2 + (u2 - r13)**2 - 2 * c * (r12 - l1) * (u2 - r13)).
COMPUTE ci_high = diff + SQRT((u1 - r12)**2 + (r13 - l2)**2 - 2 * c * (u1 - r12) * (r13 - l2)).
FORMATS rc diff ci_low ci_high t p (F8.4) df (F8.0).
LIST rc diff ci_low ci_high t df p.

Reading the Output

Read the output as one pattern: reliabilities first, then the convergent correlations and their intervals, the corrected correlations, the discriminant correlation, and last the comparison.

Reliability Statistics (one table per measure)

	Cronbach's Alpha	N of Items
New scale	.849	8
MAAS	.856	15
FFMQ-15	.832	15
Extraversion	.811	4

Correlations (the new scale's row; the full matrix repeats every value twice)

	maas	ffmq	extraversion
new_scale Pearson Correlation	.547**	.594**	.299**
Sig. (2-tailed)	.000	.000	.000
95% CI Lower	.441	.497	.167
95% CI Upper	.637	.677	.420

MAAS with extraversion is .121 (Sig. .089), and MAAS with FFMQ-15 is .516. SPSS prints p < .001 as .000; report it as p < .001.

The syntax block lists:

rc	diff	ci_low	ci_high	t	df	p
.6409	.2479	.0904	.4049	3.1199	197	.0021

rc is the MAAS correlation corrected for attenuation; diff, its interval and t compare the convergent and discriminant correlations.

Output laid out from this page's computed results, not captured from a live run; labels and layout may differ slightly in your version.

R

# install.packages(c("psych", "cocor"))
library(psych)
library(cocor)

mind <- read.csv("data.csv")

# 1. Reliability of each measure from its own items
items <- function(prefix) mind[, grepl(paste0("^", prefix, "_[0-9]+$"), names(mind))]
alphas <- sapply(c(new_scale = "new", maas = "maas", ffmq = "ffmq",
                   extraversion = "ipip_e"),
                 function(p) alpha(items(p))$total$raw_alpha)
round(alphas, 3)

# 2. Correlations, with the convergent one's interval
scores <- mind[, c("new_scale", "maas", "ffmq", "extraversion")]
r <- cor(scores)
round(r, 3)
cor.test(mind$new_scale, mind$maas)

# 3. Corrected for attenuation
round(r["new_scale", -1] / sqrt(alphas["new_scale"] * alphas[-1]), 3)

# 4. Convergent vs discriminant (both share new_scale)
cocor(~ new_scale + maas | new_scale + extraversion, data = mind,
      test = c("williams1959", "zou2007"))

   new_scale         maas         ffmq extraversion
       0.849        0.856        0.832        0.811
             new_scale  maas  ffmq extraversion
new_scale        1.000 0.547 0.594        0.299
maas             0.547 1.000 0.516        0.121
ffmq             0.594 0.516 1.000        0.250
extraversion     0.299 0.121 0.250        1.000

	Pearson's product-moment correlation

data:  mind$new_scale and mind$maas
t = 9.1834, df = 198, p-value < 2.2e-16
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 0.4412581 0.6369801
sample estimates:
      cor
0.5465396

        maas         ffmq extraversion
       0.641        0.707        0.360

  Results of a comparison of two overlapping correlations based on dependent groups

Comparison between r.jk (new_scale, maas) = 0.5465 and r.jh (new_scale, extraversion) = 0.2986
Difference: r.jk - r.jh = 0.2479
Related correlation: r.kh = 0.1206
Data: mind: j = new_scale, k = maas, h = extraversion
Group size: n = 200
Null hypothesis: r.jk is equal to r.jh
Alternative hypothesis: r.jk is not equal to r.jh (two-sided)
Alpha: 0.05

williams1959: Williams' t (1959)
  t = 3.1199, df = 197, p-value = 0.0021
  Null hypothesis rejected

zou2007: Zou's (2007) confidence interval
  95% confidence interval for r.jk - r.jh: 0.0904 0.4049
  Null hypothesis rejected (Interval does not include 0)

psych's alpha() also prints a long item-by-item table, left out here. Read it in order: the alphas, the correlation matrix, the convergent r with its interval, the corrected correlations, then cocor's comparison: the difference, Zou's interval, and Williams's t. r.kh is the MAAS–extraversion correlation the test needs. Add "steiger1980" to test for Steiger's z (3.08, p = .002).

Output from a real run: R 4.6.1 (psych 2.6.5, cocor 1.1.4), run 2026-10-03.

Python

import numpy as np
import pandas as pd
from scipy import stats

mind = pd.read_csv("data.csv")

def alpha(items):
    k = items.shape[1]
    return k / (k - 1) * (1 - items.var().sum() / items.sum(axis=1).var())

prefixes = {"new_scale": "new", "maas": "maas", "ffmq": "ffmq", "extraversion": "ipip_e"}
rel = {m: float(alpha(mind.filter(regex=f"^{p}_[0-9]+$"))) for m, p in prefixes.items()}

r = mind[list(prefixes)].corr()
res = stats.pearsonr(mind["new_scale"], mind["maas"])
ci = res.confidence_interval()                      # Fisher z interval
corrected = {m: float(r.loc["new_scale", m] / np.sqrt(rel["new_scale"] * rel[m]))
             for m in ["maas", "ffmq", "extraversion"]}

# Williams's t: new scale with MAAS (r12) vs with extraversion (r13)
n = len(mind)
r12, r13, r23 = r.loc["new_scale", "maas"], r.loc["new_scale", "extraversion"], r.loc["maas", "extraversion"]
det = 1 - r12**2 - r13**2 - r23**2 + 2 * r12 * r13 * r23
rbar = (r12 + r13) / 2
t = (r12 - r13) * np.sqrt((n - 1) * (1 + r23) / (2 * (n - 1) / (n - 3) * det + rbar**2 * (1 - r23)**3))
p = 2 * stats.t.sf(abs(t), n - 3)

print("alpha:", {m: round(a, 3) for m, a in rel.items()})
print(f"r = {res.statistic:.4f}, 95% CI [{ci.low:.4f}, {ci.high:.4f}]")
print("corrected:", {m: round(v, 3) for m, v in corrected.items()})
print(f"difference = {r12 - r13:.4f}, Williams t({n - 3}) = {t:.4f}, p = {p:.4f}")

alpha: {'new_scale': 0.849, 'maas': 0.856, 'ffmq': 0.832, 'extraversion': 0.811}
r = 0.5465, 95% CI [0.4413, 0.6370]
corrected: {'maas': 0.641, 'ffmq': 0.707, 'extraversion': 0.36}
difference = 0.2479, Williams t(197) = 3.1199, p = 0.0021

scipy has no functions for alpha or for comparing dependent correlations, so both are written out.

Output from a real run: Python 3.9.6 (scipy 1.12.0, pandas 2.3.3, numpy 1.26.4), run 2026-10-03.

Impact

Effect Size

The convergent correlation is its own effect size: how closely the new measure's scores track an established measure of the same construct, on a scale from −1 to 1 that doesn't depend on either measure's units. Two companions complete the picture: the correlation corrected for measurement error, and the gap between the convergent and discriminant correlations.

r = .55 \qquad r_c = \dfrac{.55}{\sqrt{.85 \times .86}} = .64 \qquad r_{\text{conv}} - r_{\text{disc}} = .55 - .30 = .25

The new scale agrees with the MAAS about as well as the usual .50 rule asks, and would agree at about .64 if both were measured without error. It tracks the MAAS noticeably more closely than it tracks extraversion.

The corrected correlation carries more sampling error than the observed one, because the reliabilities it divides by are estimates too, so don't read .64 as precise. For an interval, fit the two measures as correlated factors in a confirmatory factor analysis, or bootstrap the corrected r.

There is no agreed benchmark for convergent validity, and the numbers in circulation are rules of thumb: > .50 is common in reviews of patient-reported measures (Abma et al., 2016), and Carlson and Herdman (2012) recommend above .70 before one measure stands in for another. What counts as strong depends on how close the comparison measure is to your construct. The MAAS measures attention and awareness only, so a mindfulness scale that also covers acceptance shouldn't be expected to match it perfectly, while a short form of the MAAS, given separately, should correlate far above .55 with the full version. It also depends on your sample: in a group whose scores vary little, such as experienced meditators only, the same two scales correlate lower than in a broad adult sample. Compare your r with values from samples like yours.

Benchmarks Convergent

r

at a Glance

Below Common Cutoffs

r < .50

Commonly Adequate

.50 ≤ r < .70

Strong

r ≥ .70

Full benchmarks and caveats ↑

Statistical Significance

The one p on this page answers a narrow question: if the new scale were equally closely tied to the MAAS and to extraversion in the population, how often would a sample of 200 show a gap at least this wide, in either direction? Below the conventional α = .05, the gap is called statistically significant.

If the two correlations were really equal, a gap of .25 or more, in either direction, would turn up about 0.2% of the time, roughly 1 in 480. That's well below .05, so the new scale goes significantly more closely with the MAAS than with extraversion.

Testing each convergent correlation against zero is a much lower bar. Campbell and Fiske (1959) asked for convergent correlations that are significantly different from zero and large enough to be worth taking further; with 200 people, a correlation of .15 would clear the first hurdle and fail the second. p is not the probability that the correlations are equal, and it says nothing about whether the scale is valid. That's a judgment built from the sizes, the intervals and the design.

Benchmarks p at a Glance

Very Strong

p < .001

Strong

.001 ≤ p < .01

Significant

.01 ≤ p < .05

Weak

.05 ≤ p < .10

Little

p ≥ .10

Strength of evidence against the null hypothesis.

Full benchmarks and caveats ↑

Power and Sample Size

Power is the chance that a study detects an effect that's really there. In a validity study, though, the correlations are rarely in doubt; what matters is how precisely you can say how large they are. So the planning question here is mostly about precision: how many people you need for the interval around the convergent correlation to be narrow enough to judge against your expectation.

With a convergent correlation around .55, the 95% interval runs from about .32 to .72 with 50 people, .40 to .67 with 100, .44 to .64 with our 200 and .48 to .61 with 400. With 50 people, the data couldn't tell a correlation well below the usual .50 rule from one well above it.

The comparison with extraversion does need power. In simulations with population correlations of .55 and .30 (and .12 between the MAAS and extraversion), Williams's t came out significant 34% of the time with 50 people, 59% with 100, 81% with 165 and 88% with our 200. A smaller gap needs many more.

Plan the sample size for the interval you need. For a correlation near .55, about 190 people give a margin of roughly ±.10. That is, an interval about .20 wide, stretching a little further below the estimate than above it, as intervals for a positive correlation do. The planner below uses the Fisher-z interval from the Napkin Math. Try it:

Other Info

Follow-Up and Post Hoc Tests

Planned Contrasts

Tests for Dependent Correlations: Used on this page to compare the convergent correlation (new scale with the MAAS, .55) with the discriminant one (new scale with extraversion, .30). The two share the new scale and come from the same 200 people, so the test also needs the correlation between the MAAS and extraversion. We report Williams's t, one of the two tests that performed best overall in Hittner, May and Silver's (2003) simulations, with Zou's (2007) interval for the gap; Steiger's (1980) z gives almost the same answer (z = 3.08, p = .002). Run the same comparison for every convergent–discriminant pair you report; here the FFMQ-15 pair is tested too (see the write-up).

Related Methods

Related DesignDiscriminant Validity: the other half of the same argument. Convergent validity asks whether the new measure agrees with measures of its own construct; discriminant validity asks whether it stays clearly apart from measures of other constructs. The extraversion comparison on this page is the simplest discriminant check; that page covers fuller ones.
Related DesignAverage Variance Extracted (AVE): the factor-analytic route to convergent evidence. Instead of correlating total scores with other measures, it asks how much of the items' variance a confirmatory factor model attributes to the construct they're meant to measure.
Related DesignPearson Correlation: the building block. Every convergent and discriminant correlation here is an ordinary Pearson r with its Fisher-z interval; this page adds the reliabilities, the correction for attenuation and the comparison between correlations.
Related DesignComparing Correlation Coefficients: a related comparison for a different design. That page compares one correlation across two separate groups of people. Our convergent and discriminant correlations come from the same people and share the new scale, so they need a test for dependent correlations instead (see Follow-Up Tests).
Related DesignConfirmatory Factor Analysis (CFA): the model behind the latent-variable version of this question. Fitting the new scale and an established measure as two correlated factors estimates the correlation between the constructs with measurement error modeled item by item, instead of correcting one correlation afterward.
Related DesignMaximum Shared Variance (MSV): A factor-analytic discriminant check. It asks whether a construct shares more variance with its closest neighbor than it explains in its own items.
AlternativeSpearman Correlation: An alternative if “Linear Relationship” doesn't hold. If the relationship bends but always rises, a rank correlation measures that consistent trend without needing a straight line.

References

Campbell, D. T., & Fiske, D. W. (1959). Convergent and discriminant validation by the multitrait-multimethod matrix. Psychological Bulletin, 56(2), 81–105. https://doi.org/10.1037/h0046016
Carlson, K. D., & Herdman, A. O. (2012). Understanding the impact of convergent validity on research results. Organizational Research Methods, 15(1), 17–32. https://doi.org/10.1177/1094428110392383
“Convergent validities above r = .70 are recommended, whereas those below r = .50 should be avoided.” (Abstract)
Abma, I. L., Rovers, M., & van der Wees, P. J. (2016). Appraising convergent validity of patient-reported outcome measures in systematic reviews: Constructing hypotheses and interpreting outcomes. BMC Research Notes, 9, 226. https://doi.org/10.1186/s13104-016-2034-2
“Convergent validity is generally considered adequate if >75 % of hypotheses are correct, or if a correlation with an instrument measuring the same construct is >0.50.” (Background)

“The exact values of these cut-off points may be arbitrary, but they provide guidance when judging whether convergent validity is adequate.” (Background)

“when two instruments really measured the same construct we considered a more challenging hypothesis (correlation above >0.70) more adequate” (Constructing the hypotheses)

“take an active role in judging the suitability of the comparator instruments of validation articles” (Abstract)
Spearman, C. (1904). The proof and measurement of association between two things. The American Journal of Psychology, 15(1), 72–101. https://doi.org/10.2307/1412159
“To ascertain the amount of this attenuation, and thereby discover the true correlation, it appears necessary to make two or more independent series of observations of both p and q.” (p. 90)

“which is always in the direction of "attenuating" the apparent correspondence” (p. 89)
Diedenhofen, B., & Musch, J. (2015). cocor: A comprehensive solution for the statistical comparison of correlations. PLOS ONE, 10(4), e0121945. https://doi.org/10.1371/journal.pone.0121945
Brown, K. W., & Ryan, R. M. (2003). The benefits of being present: Mindfulness and its role in psychological well-being. Journal of Personality and Social Psychology, 84(4), 822–848. https://doi.org/10.1037/0022-3514.84.4.822
“Because our intent was to capture the central, subjective experience of mindfulness as present attention and awareness, items containing attitudinal components (e.g., patience, trust, acceptance) were excluded” (p. 825)
Gu, J., Strauss, C., Crane, C., Barnhofer, T., Karl, A., Cavanagh, K., & Kuyken, W. (2016). Examining the factor structure of the 39-item and 15-item versions of the Five Facet Mindfulness Questionnaire before and after mindfulness-based cognitive therapy for people with recurrent depression. Psychological Assessment, 28(7), 791–802. https://doi.org/10.1037/pas0000263
“a 15-item version (FFMQ-15) has been developed, which includes three items for each of the five facets” (The Five Facet Mindfulness Questionnaire)
Donnellan, M. B., Oswald, F. L., Baird, B. M., & Lucas, R. E. (2006). The Mini-IPIP scales: Tiny-yet-effective measures of the Big Five factors of personality. Psychological Assessment, 18(2), 192–203. https://doi.org/10.1037/1040-3590.18.2.192
“The Mini-IPIP scales, with four items per Big Five trait, had consistent and acceptable internal consistencies across five studies” (Abstract)
Cronbach, L. J., & Meehl, P. E. (1955). Construct validity in psychological tests. Psychological Bulletin, 52(4), 281–302. https://doi.org/10.1037/h0040957
“Construct validation is involved whenever a test is to be interpreted as a measure of some attribute or quality which is not "operationally defined."” (p. 282)
Koo, T. K., & Li, M. Y. (2016). A guideline of selecting and reporting intraclass correlation coefficients for reliability research. Journal of Chiropractic Medicine, 15(2), 155–163. https://doi.org/10.1016/j.jcm.2016.02.012
“Reliability is defined as the extent to which measurements can be replicated.” (Introduction)
Aldridge, V. K., Dovey, T. M., & Wade, A. (2017). Assessing test-retest reliability of psychological measures: Persistent methodological problems. European Psychologist, 22(4), 207–218. https://doi.org/10.1027/1016-9040/a000298
Muff, S., Nilsen, E. B., O'Hara, R. B., & Nater, C. R. (2022). Rewriting results sections in the language of evidence. Trends in Ecology & Evolution, 37(3), 203–210. https://doi.org/10.1016/j.tree.2021.10.009
“we suggest language of evidence that allows for a more nuanced approach to communicate scientific findings as a simple and intuitive alternative to statistical significance testing” (Abstract)
Bishara, A. J., & Hittner, J. B. (2012). Testing the significance of a correlation with nonnormal data: Comparison of Pearson, Spearman, transformation, and resampling approaches. Psychological Methods, 17(3), 399–417. https://doi.org/10.1037/a0028087
Bishara, A. J., & Hittner, J. B. (2017). Confidence intervals for correlations when data are not normal. Behavior Research Methods, 49(1), 294–309. https://doi.org/10.3758/s13428-016-0702-8
Steiger, J. H. (1980). Tests for comparing elements of a correlation matrix. Psychological Bulletin, 87(2), 245–251. https://doi.org/10.1037/0033-2909.87.2.245
Meng, X.-L., Rosenthal, R., & Rubin, D. B. (1992). Comparing correlated correlation coefficients. Psychological Bulletin, 111(1), 172–175. https://doi.org/10.1037/0033-2909.111.1.172
Hittner, J. B., May, K., & Silver, N. C. (2003). A Monte Carlo evaluation of tests for comparing dependent correlations. The Journal of General Psychology, 130(2), 149–168. https://doi.org/10.1080/00221300309601282
“the findings suggested that O. J. Dunn and V. A. Clark's (1969) z and E. J. Williams's (1959) t have the best overall statistical properties” (Abstract)
Zou, G. Y. (2007). Toward using confidence intervals to compare correlations. Psychological Methods, 12(4), 399–413. https://doi.org/10.1037/1082-989X.12.4.399