t-Tests · General Linear Model
Paired-Samples t-Test
A paired-samples t-test compares two measurements from the same people.
A paired-samples t-test takes one continuous outcome measured twice in the same people and tests whether the average change between the two measurements differs from zero.
Do students' anxiety scores drop over a four-week mindfulness program? Thirty-two college students completed the GAD-7, a 0-to-21 anxiety questionnaire, before and after the program, so each student has two scores.
- Tests
- Population mean difference
- Observations
- Related
- Parametric
- Yes
- Headline Statistic
- t
- Effect Size
- Cohen's d_z
- Groups
- 2
The Basics
When to Use It
Use it when the same people are measured twice on one continuous outcome, before and after something or under two conditions (in counterbalanced order), and you want to know whether the average changed. Pairs of closely matched people, such as twins, work the same way: each pair is one row, and n is the number of pairs. For example:
- Do students' anxiety scores drop over a four-week mindfulness program?
- Do people recall more words after a night's sleep than after the same hours awake?
- Are people slower to name ink colors on the Stroop task when the word and color don't match?
Vocabulary You Need
Definition Difference Score (D)
One person's score in the second condition minus their score in the first. It turns each person's pair of scores into a single number, so stable differences between people cancel out and only the change is left. Glossary →
Definition Standard Deviation (s)
How spread out individual scores are around their mean. For roughly bell-shaped scores, about two-thirds fall within one standard deviation of the mean. Its square, s², is the variance: the average squared distance from the mean (dividing by n − 1). Glossary →
Definition Standard Error (SE)
How much a statistic, such as a mean, a proportion or a difference between two of them, would vary from one sample to the next. SD asks how much individuals vary; SE asks how sure we are about the estimate. It shrinks as the sample grows. Glossary →
Definition Degrees of Freedom (df)
How much independent information is left for estimating variability, after the quantities estimated from the same data are accounted for. Each estimated quantity uses one up: with a single mean, deviations from it always sum to zero, so once you know n − 1 of them the last is fixed; two group means use up two (N − 2), and a regression with k predictors and an intercept uses k + 1. Degrees of freedom pick which t, F or χ² distribution a result is judged against, and fewer of them mean heavier tails (more extreme values), so a result needs a bigger statistic to count as significant. Some tests, such as Welch's t or a sphericity-corrected F, use fractional values. In a table of counts, it's the number of cells free to vary once the row and column totals are fixed. Glossary →
Definition Significance Level (\alpha)
The false-positive rate a researcher accepts, chosen before the analysis. By convention it is usually .05. Glossary →
Assumptions and Inference
1. Independent Pairs (for the p-Value and Intervals) Each person's two scores belong together, but the people (or pairs) are independent of one another.
- 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. If people's changes influence each other, as in a therapy group, the standard error comes out too small and so does p.
What to Do
- Alternative Test Multilevel Regression (HLM). A multilevel model, which accounts for the clustering.
- Design Change Collect one pair of scores per independent unit, such as one person per group.
2. Normality of the Differences (for the p-Value and Intervals) The test is exact when the change scores come from a normal population. Bigger samples tolerate moderate departures, but strong skew, extreme changes or heavy tails can still throw off p and the intervals. Look at the change scores themselves, not just the before and after scores.
- What It Means
- The test's model assumes the scores it relies on are roughly normal: the scores within each group (or the scores themselves, for a one-sample test), the difference scores in a paired design, or the residuals (the errors left around a model's predictions) in a regression. For p-values and confidence intervals, what really matters is that the estimates (such as a mean, a difference between means or a model's coefficients) are roughly normal across repeated samples. A large enough sample usually provides that; how large depends on how skewed the scores are and how extreme their outliers.
- Applies To
- Differences
- How to Check
- Compute each person's change (second score minus first) and look at a histogram or Q–Q plot of those changes for strong skew or extreme values. The before and after scores can each be skewed without harming the test, and well-behaved before and after scores don't guarantee well-behaved changes. 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
- Only the difference scores need to be roughly normal, not the before and after scores themselves. With 32 pairs, moderate skew usually matters little; a few extreme changes in a small sample can. Here the 32 changes run from −8 to +4, with almost no skew (−0.07) and no change more than 1.9 standard deviations from the average.
What to Do
- Robust Estimation Bootstrap a confidence interval for the mean difference.
- Alternative Test Wilcoxon Signed-Rank Test. It ranks the difference scores instead of averaging them, so it tests a slightly different question: whether rises and drops balance. That matches the median change only if the changes are roughly symmetric; a sign test compares the median change with 0 without that assumption.
Limitations
This Is Not Your Test If…
- Your outcome is yes/no, measured twice McNemar's Test →
- Your two groups are different people Independent-Samples t-Test →
- You measured the same people three or more times One-Way Repeated-Measures ANOVA →
- You also have a control group measured twice Mixed Factorial ANOVA →
- You randomized groups and want after scores adjusted for before ANCOVA →
- You're comparing one group with a fixed value One-Sample t-Test →
What It Doesn't Tell You
- Why. With no control group, the drop could come from the program, or from time passing, taking the questionnaire twice, or very anxious students drifting back toward average.
- Whether it matters. Significance doesn't make a point and a half on the 0–21 scale something students would notice in their lives.
- Who else. The result describes students like these 32, who took part in a mindfulness study, and only as well as a self-report questionnaire measures anxiety.
- That there's no change, if p had been above .05. A non-significant result would have meant the data were inconclusive, not that scores don't change.
Common Mistakes
-
Don'tSwitch to a one-sided p because the result went the way you hoped.
InsteadUse a one-sided test only if you specified the direction before collecting data and have a defensible reason why an effect in the opposite direction wouldn't count toward your claim. Otherwise, use a two-sided test.
-
Don'tAnalyze before and after scores with an independent-samples t-test.
InsteadPair each person's scores. Treating them as separate groups ignores the pairing and usually throws away power.
-
Don'tRead a before-and-after change as the effect of the program.
InsteadAdd a control group measured twice. If groups were randomized, compare after scores adjusted for before scores (ANCOVA).
-
Don'tReport “Cohen's d” for paired data without saying which one.
InsteadName it (d_z, d_{av} or d_{rm}) and give its formula; they can differ a lot for the same data.
-
Don'tIgnore order effects when the same people experience two experimental conditions.
InsteadCounterbalance the order where the design allows it, half doing each condition first, so practice and fatigue aren't mistaken for a condition effect. A before-and-after study can't counterbalance time; add a control group measured twice to separate the program from practice, maturation and other change over time.
-
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.
Benchmarks Effect Size (Cohen's d_z)
-
|d| < 0.2
Below Small
Smaller than the conventional small benchmark. Whether an effect this size matters depends on the setting.
-
0.2 ≤ |d| < 0.5
Small
A relatively modest standardized difference
-
0.5 ≤ |d| < 0.8
Medium
A moderate standardized difference
-
|d| ≥ 0.8
Large
A relatively substantial standardized difference
These benchmarks were written for a d scaled by the spread of scores, not of change scores, so d_z isn't directly comparable to them. Treat them as a rough guide.
How It's Reported
Equation Form
Mdiff = −1.50, 95% CI [−2.76, −0.24], dz = −0.43, 95% CI [−0.79, −0.06], t(31) = −2.42, p = .021
Full Text (APA Style)
Students' anxiety scores fell from before the program (M = 9.50, SD = 4.03) to after it (M = 8.00, SD = 4.02), a mean change of −1.50 points, 95% CI [−2.76, −0.24], dz = −0.43, 95% CI [−0.79, −0.06]. A paired-samples t-test showed the change was statistically significant, t(31) = −2.42, p = .021.
- Give both means and SDs, and say which direction the difference runs (after minus before), so readers know what the minus sign means.
- Name the effect size you used. For paired data, d_z, d_{av} and d_{rm} can differ noticeably; here d_z = −0.43 and d_{av} = −0.37.
- Give the size and interval before the significance test.
- Italicize statistical symbols (M, SD, d, t, p) and report exact p to three decimals.
Reading Each Piece
The equation form above, piece by piece, in this order: how big, how certain, then how surprising.
| Mdiff = −1.50 | Anxiety scores dropped by an average of one and a half points on the 0–21 scale. With no control group, the drop could reflect the program, time passing, retaking the questionnaire, or very anxious students drifting back toward average. |
| dz = −0.43 | The average drop is 0.43 standard deviations of the change scores. Negative means anxiety went down. Cohen's labels were written for a d scaled by the spread of scores, like d_{av}; here d_{av} = −0.37, small by those labels. Whether a point and a half on the GAD-7 matters to a student is a clinical question, not a statistical one. Benchmarks ↑ |
| 95% CI [−2.76, −0.24] | The true average drop is plausibly anywhere from about a quarter of a point to nearly three points. The whole range is below zero, but only just. |
| 95% CI [−0.79, −0.06] | The true effect is plausibly anywhere from a small fraction of a standard deviation of the change scores to about eight tenths of one. Software finds it with a variant of the t distribution; SPSS prints it in the effect-size table. |
| t(31) = −2.42 | The average change is 2.42 standard errors below zero. The 31 is the degrees of freedom: the number of students minus 1. |
| p = .021 | If students' scores didn't change on average, an average change at least 2.42 standard errors from zero (each sample judged by its own SD of the changes), in either direction, would turn up about 2.1% of the time. That's below .05, so the result is statistically significant. It can't say the program caused the drop. Benchmarks ↑ |
Calculations
The Running Example
The mindfulness study: 32 students, each measured twice on the GAD-7 anxiety scale (0 to 21), before and after four weeks of mindfulness practice.
- Null Hypothesis:
- \mu_D = 0
- Alternative (Two-Sided):
- \mu_D \neq 0
D is a student's change, after minus before. \mu_D (“mu D”) is the average change for all students who could take the program, which the sample's −1.50 estimates. The null hypothesis is the starting point the test looks for evidence against: here, \mu_D = 0, scores don't change on average from before to after. The two-sided alternative is that the average changed, in either direction.
What Your Data Should Look Like
One row per person and two numeric columns, one for each measurement. The test pairs scores by row, so both scores in a row must belong to the same person; anyone missing one of the two drops out.
| participant | anxiety_before | anxiety_after |
|---|---|---|
| 1 | 6 | 7 |
| 2 | 17 | 14 |
| 3 | 7 | 2 |
| 4 | 11 | 12 |
| 5 | 9 | 5 |
| 6 | 14 | 13 |
| … 26 more rows | ||
| n | M | SD | |
|---|---|---|---|
| Anxiety Before | 32 | 9.50 | 4.03 |
| Anxiety After | 32 | 8.00 | 4.02 |
| Difference | 32 | −1.50 | 3.50 |
Difference = Anxiety After − Anxiety Before.
Pearson correlation between the two: r = .62
Simulated data.
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 study's numbers. Collapse all to read just the headings: they tell the whole story on their own.
-
1. Turn Each Person's Two Scores into One Change Score
The two scores from one person belong together, so we subtract them. Each person now has a single number, their change, and the rest of the test is a one-sample t-test on those changes against 0.
D_i = x_{2i} - x_{1i} =14 - 17= −3 points
x_{1i} and x_{2i} are one student's scores before and after. Student 2 went from 17 to 14, so D_2 = 14 − 17 = −3 points. Negative means less anxious.
-
2. Find the Average Change
Everything starts with how much people changed on average. It's the same as the after mean minus the before mean.
\bar{D} = \dfrac{\sum D_i}{n} =\dfrac{-48}{32}= −1.50 points
\sum D_i adds up all 32 changes, which total −48 points. −48 ÷ 32 = −1.50 points, the same as 8.00 − 9.50.
-
3. Figure Out How Much People's Changes Naturally Vary
Some students improved a lot, some not at all, some got worse. Before we can judge the average change, we need to know how much the changes bounce around.
s_D = \sqrt{\dfrac{\sum (D_i - \bar{D})^2}{n - 1}}= 3.50 points
Find each student's distance from the average change of −1.50, square it, add up all 32, divide by n - 1 = 31, and take the square root. That's s_D = 3.50 points. The changes vary less than the scores themselves (about 4.0 points before and after), because each student's own level cancels out. Students who start anxious tend to stay anxious, and their before and after scores correlate at .62.
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4. Figure Out How Precisely Our Sample Estimates the Average Change
An average of many people's changes is steadier than any one person's. The standard error measures how much the average change would wobble from sample to sample.
SE = \dfrac{s_D}{\sqrt{n}} =\dfrac{3.50}{\sqrt{32}}= 0.619
s_D is that 3.50-point spread and n is our 32 students. 3.50 ÷ √32 (about 5.66) = 0.619 points.
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5. Compare the Average Change with That Uncertainty
A change only means something relative to that wobble. t says how many standard errors the average change is from no change at all.
t = \dfrac{\bar{D} - 0}{SE} =\dfrac{-1.50 - 0}{0.619}= −2.42
Our −1.50-point average change, minus the 0 we're testing against, divided by the 0.619-point SE puts the change 2.42 standard errors below zero.
-
6. Account for How Much Information We Had
Once each person is one change score, we have one score per person, and estimating their mean uses up one piece of information. df tells us which t distribution to judge t against. The t distribution is the spread of t values you'd get by chance if the null hypothesis were true; with fewer df, its tails are heavier.
df = n - 1 =32 - 1= 31
n is our 32 students, not the 64 scores. 32 − 1 = 31.
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7. Measure How Big the Change Actually Is
t grows with sample size; d doesn't. Dividing the average change by the spread of the changes, instead of the standard error, gives a size you can compare across studies with the same design.
d_z = \dfrac{\bar{D}}{s_D} =\dfrac{-1.50}{3.50}= −0.43
\text{CI}_{d_z} = [−0.79, −0.06]
The same −1.50-point change, divided by the 3.50-point spread of the changes s_D, is 0.43 of a standard deviation.
-
8. Give a Range of Plausible Values for the True Average Change
Instead of a single best guess, give the range of true average changes that fit the data.
\bar{D} \pm t^{*}_{df} \times SE =-1.50 \pm 2.040 \times 0.619= [−2.76, −0.24]
t^{*}_{31} = 2.040 is the cutoff that holds the middle 95% of a t distribution with 31 df. 2.040 × 0.619 = 1.26 points, so the range is −1.50 ± 1.26, from −2.76 to −0.24 points.
-
9. Ask How Surprising the Result Would Be If There Were No Real Change
Finally, ask how often a t at least this far from zero, in either direction, would turn up if scores didn't change on average.
p = 2 \times P(T_{df} \le -|t|) =2 \times P(T_{31} \le -2.424)= .021
P(T_{31} \le -2.424) is the chance that a t with 31 df lands at or below −2.424 (t to three decimals, since rounding it to −2.42 would nudge p up to .022). Doubling it counts both directions, .021, about 1 in 47.
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)
- Analyze → Compare Means and Proportions → Paired-Samples T Test.
- Click
anxiety_after, thenanxiety_before, and move them into Paired Variables as Pair 1. SPSS subtracts Variable2 from Variable1, so this order gives after minus before. - Leave Estimate effect sizes checked, with Standardizer set to Standard deviation of the difference, and click OK.
Or paste this syntax:
T-TEST PAIRS=anxiety_after WITH anxiety_before (PAIRED) /ES DISPLAY(TRUE) STANDARDIZER(SD) /CRITERIA=CI(.95) /MISSING=ANALYSIS.
Reading the Output
SPSS prints four tables. Take the means and SDs from Paired Samples Statistics, then in Paired Samples Test read the Mean difference and its 95% Confidence Interval, then Cohen's d from Paired Samples Effect Sizes, then t, df and Two-Sided p. Use the one-sided p only if you specified the direction before collecting data and have a defensible reason why a change in the opposite direction wouldn't count toward your claim.
Paired Samples Statistics
| Mean | N | Std. Deviation | Std. Error Mean | ||
|---|---|---|---|---|---|
| Pair 1 | anxiety_after | 8.00 | 32 | 4.016 | .710 |
| anxiety_before | 9.50 | 32 | 4.032 | .713 |
Paired Samples Correlations
| N | Correlation | One-Sided p | Two-Sided p | ||
|---|---|---|---|---|---|
| Pair 1 | anxiety_after & anxiety_before | 32 | .622 | <.001 | <.001 |
Paired Samples Test (Paired Differences)
| Mean | Std. Deviation | Std. Error Mean | 95% CI Lower | Upper | t | df | One-Sided p | Two-Sided p | ||
|---|---|---|---|---|---|---|---|---|---|---|
| Pair 1 | anxiety_after − anxiety_before | -1.500 | 3.501 | .619 | -2.762 | -.238 | -2.424 | 31 | .011 | .021 |
Paired Samples Effect Sizes
| Standardizer | Point Estimate | 95% CI Lower | Upper | ||
|---|---|---|---|---|---|
| Pair 1 | Cohen's d | 3.501 | -.428 | -.788 | -.063 |
| Hedges' correction | 3.589 | -.418 | -.768 | -.061 |
SPSS's “Cohen's d” here is d_z: the Standardizer, 3.501, is the SD of the differences from the table above. “Hedges' correction” adjusts it for small-sample bias. The Correlations table tests whether the before and after scores are related, which isn't the question; a high correlation is simply why pairing helps.
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
mindfulness <- read.csv("data.csv")
t.test(mindfulness$anxiety_after, mindfulness$anxiety_before, paired = TRUE)
# Cohen's d_z
d <- mindfulness$anxiety_after - mindfulness$anxiety_before
mean(d) / sd(d)
Paired t-test
data: mindfulness$anxiety_after and mindfulness$anxiety_before
t = -2.4236, df = 31, p-value = 0.0214
alternative hypothesis: true mean difference is not equal to 0
95 percent confidence interval:
-2.7622999 -0.2377001
sample estimates:
mean difference
-1.5
[1] -0.4284304
Put the after scores first so the difference is after minus before. t.test(d, mu = 0) on the difference scores gives exactly the same result, because it's the same test.
Output from a real run: R 4.6.1, run 2026-09-29.
Python
import pandas as pd
from scipy import stats
mindfulness = pd.read_csv("data.csv")
result = stats.ttest_rel(mindfulness["anxiety_after"], mindfulness["anxiety_before"])
result.statistic # -2.4236
result.pvalue # 0.0214
result.df # 31
result.confidence_interval() # (-2.7623, -0.2377)
# Cohen's d_z
d = mindfulness["anxiety_after"] - mindfulness["anxiety_before"]
d.mean() / d.std() # -0.4284
Output from a real run: Python 3.9.6 (scipy 1.13.1, pandas 2.3.3), run 2026-09-29.
Impact
Effect Size
Cohen's d expresses the average change relative to a chosen standard deviation. For paired data there's more than one choice, and they can give quite different numbers for the same data, so always say which you used; results from different studies are comparable only if they used the same kind of d. This page reports d_z: the average change divided by the standard deviation of the difference scores. It's the one that matches the t-test, and the one power analyses for paired designs use (Lakens, 2013).
Students' anxiety dropped 1.50 points, which is 0.43 of the usual spread in how much students changed. Cohen's labels fit d_{av} better; at −0.37 (below), it's small.
The alternatives divide by the spread of the scores themselves rather than the changes. d_{av} uses the average of the before and after SDs, and d_{rm} also accounts for the correlation between the two measurements. They sit closer to the d from a study comparing two separate groups, so use one of them when comparing with such studies (Lakens, 2013). When the before and after SDs are similar, d_z comes out larger than d_{av} if the two measurements correlate above .5, and smaller if they correlate below .5.
Our before and after scores correlate at .62, so d_{av} = −1.50 ÷ 4.02 = −0.37, a bit smaller than d_z = −0.43.
Benchmarks are conventions. For scale, the GAD-7's authors suggest cut points of 5, 10 and 15 for mild, moderate and severe anxiety (Spitzer et al., 2006), but those cut points classify scores; they don't say whether a 1.50-point change is clinically meaningful. A small change can carry one student across a cut point while a bigger one leaves another in the same band. Judge the change against a criterion validated for change on the scale; whether it matters to a student is a clinical question, not a statistical one.
Benchmarks Cohen's d_z at a Glance
Statistical Significance
p answers one narrow question: if the average change were really zero, how often would t land at least this far from zero, in either direction? That is, how often would a sample's average change land at least this many of its own standard errors from zero? Below the conventional α = .05, the result is called statistically significant.
If scores didn't change on average, 32 students would show an average change at least 2.42 standard errors from zero, in either direction, about 2.1% of the time, roughly 1 in 47. That's below .05, so it's significant.
p is not the probability that the null hypothesis is true, it says nothing about how large or important the change is, and it can't say the program caused the change. That's what the effect size, the interval and the design are for.
Benchmarks p at a Glance
Strength of evidence against the null hypothesis.
Power and Sample Size
Power is the chance that a study detects an effect that's really there. A real effect doesn't guarantee a significant result: with too few people, it can easily come out non-significant. Power depends on four things: how big the true effect is, how many pairs you have, α, and whether the test is one- or two-sided. For a paired test, the effect size is d_z, so a d from a study of two separate groups isn't the same number. To convert one, divide it by \sqrt{2(1 - r)}, where r is how strongly the two measurements correlate. With our r = .62 that's dividing by about 0.87, which turns our d_{av} of −0.37 into the d_z of −0.43. The conversion assumes the before and after SDs are about equal, as ours are (4.03 and 4.02). If they differ a lot, it's only approximate; work out d_z directly from the SD of the change scores instead.
Suppose, before collecting any data, we thought anxiety might drop by half a standard deviation of the change scores (d_z = 0.5). With 34 students, the study would come out significant about 81% of the time. With our 32, it's about 78%.
Pairing is what gives this design its power: each person's stable level cancels out of their change, so the standard error shrinks.
Analyzed as if they were two separate groups, the same scores give SE = 1.01, t(62) = −1.49, p = .14. Pairing shrinks the standard error from 1.01 to 0.62, and the same change becomes significant.
Researchers usually aim for at least 80% power. Plan it before collecting data, using the smallest effect that would matter. Try it:
Other Info
Follow-Up and Post Hoc Tests
None needed. This test answers a single question, so there are no planned contrasts or post hoc tests to run.
References
- Student. (1908). The probable error of a mean. Biometrika, 6(1), 1–25. https://doi.org/10.2307/2331554
- Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Lawrence Erlbaum Associates.
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Lakens, D. (2013). Calculating and reporting effect sizes to facilitate cumulative science: A practical primer for t-tests and ANOVAs. Frontiers in Psychology, 4, 863.
https://doi.org/10.3389/fpsyg.2013.00863
“The standardized mean difference effect size for within-subjects designs is referred to as Cohen's dz, where the Z alludes to the fact that the unit of analysis is no longer X or Y, but their difference, Z” (section “Cohen's d in one-sample or correlated samples comparisons”)
- Spitzer, R. L., Kroenke, K., Williams, J. B. W., & Löwe, B. (2006). A brief measure for assessing generalized anxiety disorder: The GAD-7. Archives of Internal Medicine, 166(10), 1092–1097. https://doi.org/10.1001/archinte.166.10.1092
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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)
Spot an error? Something still confusing? Tell us at support@statsforpsychology.com.