Read a t-test result in this order: identify the comparison, read the estimated difference, inspect its confidence interval, then use the t statistic, degrees of freedom, and p-value to understand the test. A p-value alone cannot tell you the direction, size, precision, or practical meaning of the difference.
First identify which t-test was run
The output should tell you whether the result comes from:
- a one-sample t-test, comparing one sample mean with a specified value;
- an independent two-sample t-test, comparing means from separate groups;
- a paired t-test, analyzing within-pair differences;
- a Welch two-sample t-test, which does not impose equal group variances in the same way as the pooled-variance test.
These tests can display similar fields while estimating different quantities. Do not interpret a paired result as if it compared unrelated groups. Do not assume every two-sample result uses pooled variance; R’s standard two-sample function, for example, defaults to Welch’s test unless equal variance is requested.[R Core Team (2026)]
The fields and what each one answers
| Field | What it tells you | What to check |
|---|---|---|
| Estimate or means | The observed center or mean difference | Group order and units |
| Standard error | Estimated sampling variability of the difference | Whether the reported model matches the design |
| t statistic | Difference from the null in standard-error units | Sign and null value |
| Degrees of freedom | Reference-distribution parameter | It may be fractional for Welch’s test |
| p-value | Tail probability under the null model and assumptions | One- or two-sided alternative |
| Confidence interval | Range of parameter values compatible with the method and data | Confidence level and null value |
| Effect size | Standardized or otherwise scaled magnitude | Which effect-size definition was used |
Official R output includes the t statistic, degrees of freedom, p-value, confidence interval, estimates, method, and alternative; other software can arrange or name these pieces differently.[R Core Team (2026)] [developers (2026)]
A worked reading
Suppose a two-group output reports:
Mean difference = 4.2; t = 2.31; df = 37.6; p = .026; 95% CI [0.52, 7.88].
Read it field by field:
- Difference: the first group’s observed mean is 4.2 units higher under the subtraction order used.
- Interval: compatible differences under the method run from 0.52 to 7.88 units. The range shows substantial uncertainty around 4.2.
- t statistic: the estimate is 2.31 estimated standard errors above the null difference of 0.
- Degrees of freedom: the fractional 37.6 is consistent with a Welch–Satterthwaite calculation, not a data-entry error.[R Core Team (2026)]
- p-value: under the null model and stated assumptions, the selected tail probability is .026.
For a matching two-sided procedure, a 95% confidence interval that excludes 0 corresponds to rejecting a zero-difference null at the 5% level.[NIST/SEMATECH (2012)] How to interpret a p-value explains why this is not the probability that the null is true.
What the sign of t means
The sign follows the direction of the estimated difference. If software calculates mean A minus mean B, a positive t generally points toward A having the higher mean; reversing the subtraction reverses the sign. The two-sided p-value normally stays the same.
This means “t = −2.4” is not a worse result than “t = 2.4.” It indicates direction under the coding and comparison order. Read the named groups or paired-difference definition before describing that direction.
Why degrees of freedom can be fractional
The classic pooled two-sample test uses a simple degrees-of-freedom expression when its variance assumptions apply. Welch’s test estimates degrees of freedom using the sample variances and sizes, so the result need not be a whole number.[R Core Team (2026)] Rounding it to an integer can erase a clue about the method actually used.
If the output gives no method label, the degrees of freedom, equal-variance setting, and software documentation can help identify the test. Degrees of freedom gives a fuller interpretation.
Check assumptions after identifying the estimand
A t-test does not become valid because its table is complete. The relevant checks depend on the design:
- observations or pairs should match the sampling and dependence structure;
- extreme observations can affect means, standard errors, and the test statistic;
- a paired test concerns the distribution of within-pair differences;
- a pooled two-sample test adds an equal-variance assumption;
- Welch’s test addresses unequal variances but not every design problem.
Use normality and distribution checks for the distributional evidence appropriate to the test. If group variance is central, inspect the variance model rather than selecting a test from a single preliminary p-value.
Effect size belongs beside the test
The t statistic is scaled by uncertainty and sample information; it is not a direct measure of practical magnitude. Two studies can have similar mean differences and different t values because their standard errors differ. Report the raw difference and interval, and add a clearly defined effect size when it helps readers compare scales.
P-value interpretation and confidence intervals answer inferential questions. Effect size answers a magnitude question. None replaces an explanation in the original units.
Common reading errors
- Reporting “t was significant” without naming the comparison or direction.
- Treating the p-value as the size of the difference.
- Assuming a fractional df is invalid.
- Ignoring whether the test was paired, pooled, or Welch.
- Reading a two-sided p-value as a directional probability.
- Omitting the estimate and confidence interval.
A defensible reporting sentence
“The first group’s mean was 4.2 units higher than the second group’s (95% CI [0.52, 7.88]); Welch’s t(37.6) = 2.31, p = .026.” Then describe the outcome units, design, assumptions, and practical meaning. The table fields should support that account, not replace it.