Reporting a One-Sample t-Test in SPSS
Test Value, Difference and Interval
Reporting a one-sample t-test in SPSS starts with the test value: where it came from belongs in the sentence. The mean difference from that value, its interval, t with its df and an effect size follow, each with a printed source in the output.
IN SHORT
The Reference Value and the Distance From It
The test value is the part of a one-sample result that SPSS cannot supply: the output prints it as a bare number, and the report must say whether it is a norm, a benchmark or a scale midpoint, and where it came from. Around it sit the sample mean and SD, the mean difference with a 95% interval, t with its df, an exact p-value and an effect size. For reporting a one-sample t-test in SPSS, take these from the One-Sample Statistics and One-Sample Test tables (Analyze, Compare Means, One-Sample T Test; menu labels vary by release). Setting the sentence, the table and the cited source against the output is work done by an in-house PhD-level statistician at OnlineSPSS, a specialist statistical consultancy for academic, clinical and professional research, and whether the comparison suits the study is the researcher’s to argue.
In This Guide
ANALYSIS SUPPORT
Analysis Support for This Method
A fixed reference value is one kind of comparison among several. Two groups, or two measurements on the same cases, call for a different test, and that choice is made in the analysis before any reporting.
Comparative & Hypothesis Testing
The family of tests for comparing groups, measurements and benchmarks, analyzed for your design with the estimate and its interval reported.
Paired Samples t-Test
Two measurements on the same cases, for questions where the quantity of interest is the change and not the distance from a fixed value.
BEFORE YOU REPORT IT
What the Reference Value Settles
The output shows only the number that was tested against, so its source, its timing, its meaning and the direction of the test are matters for the text.
Where the Value Came From A norm, a published benchmark and a scale midpoint carry different weight. The sentence names the source, because the printed output shows only the number.
Fixed Before the Data A test value chosen after the sample mean was seen cannot be read as a test. The report says the value was set in advance, and in which document it was set.
What the Midpoint Means A scale midpoint is a property of the response format. A mean above it says little about attitude unless the midpoint has an agreed meaning, so the comparison is framed with that in view.
Direction in Advance A one-sided p-value is acceptable only when the direction was stated beforehand. Otherwise the two-sided value is the one reported, and the sentence says which was used.
IN SPSS
Which Output Table Holds Each Part of the Sentence
Choosing the reference value is covered in One-Sample t-Test in SPSS: Checks and Reporting, and the six values below come from the tables that IBM SPSS prints after that choice.
Record the Test Value
Note the Test Value shown above the columns of the One-Sample Test table and confirm it is the reference you meant to use.
Check: A value typed into the dialog by mistake still produces a clean-looking table. Compare it with the number in your source before anything else is copied.
Take the Sample Mean, SD and N
From the One-Sample Statistics table, take N, Mean and Std. Deviation, which describe the sample being compared.
Tip: Give the sample mean and SD in the sentence as well as the difference, so that a reader sees the level of the sample and not only its distance from the reference.
Read t, df and Which p Applies
From the One-Sample Test table, take t, df and the significance value (Sig. (2-tailed) in older releases, Two-Sided p in recent ones).
Watch: Every variable entered in one run is tested against the same value, so subscales with different benchmarks need separate runs, each with its own row in the table.
Copy the Gap From the Test Value and Its CI
In the same table, take Mean Difference and the 95% Confidence Interval of the Difference, Lower and Upper.
Watch: Mean Difference is the sample mean minus the test value, and the interval belongs to that difference, not to the mean. For an interval around the mean, add the test value to both limits.
Convert the Gap Into SD Units
In recent releases, take Cohen’s d with its interval from the One-Sample Effect Sizes table and read its Standardizer.
Check: In a one-sample test the standardizer is the sample SD, so d expresses the distance from the reference in SD units of this sample, and the text says so.
Add the Source of the Value
Enter the values in the sentence and the table shell below, with the source of the test value stated in the sentence itself.
Check: Read the finished sentence without the output beside it. If a reader cannot tell what the sample was compared with, or why, the source of the test value is missing.
READING THE OUTPUT
One-Sample Output Values and Their Place in the Report
The test value appears only as a heading above the columns, so the rows start from it and then run through the sample, the difference and the effect size.
| Output value | Where SPSS prints it | Where it goes and what to check |
|---|---|---|
| Test Value | Heading of the One-Sample Test table | The reference value in the sentence, with its source, checked against the number typed |
| N, Mean and Std. Deviation | One-Sample Statistics | The sample description: n, M and SD, in the sentence before the comparison |
| t and df | One-Sample Test | t(df) in the sentence; df is N minus 1, so it moves with missing data |
| Two-Sided p (Sig. (2-tailed) in older releases) | One-Sample Test | The exact p; a printed .000 becomes p < .001, and the sidedness is stated |
| Mean Difference | One-Sample Test | Sample mean minus test value, with its sign turned into higher or lower in words |
| 95% Confidence Interval of the Difference | One-Sample Test | Beside the mean difference; adding the test value gives an interval for the mean |
| Cohen’s d, Point Estimate and Standardizer | One-Sample Effect Sizes, recent releases | The effect size, named, with its interval, read against the units of the scale |
REPORTING
A Sentence That Names Its Reference, a Table Shell and d
The sentence carries the justification for the test value, and the table repeats the comparison for each scale reported.
In one-sample t-test APA format, the sentence gives the reference value and where it came from, the sample mean and SD, the mean difference with its 95% interval, t(df), the exact p-value and d. A one-sample t-test results sentence reads most clearly when the comparison is stated first and the statistics follow, so that the reader sees what the sample was set against before seeing how far it was from it.
Mean [outcome] in the sample (M = ___, SD = ___, n = ___) was compared with [the test value of ___, taken from the norm / published benchmark / scale midpoint, SOURCE] using a one-sample t-test. The sample mean was [higher / lower] than the reference value by ___ [units], 95% CI [___, ___], t(___) = ___, p = ___, d = ___, 95% CI [___, ___]. [One sentence on why this difference matters, or does not, in the terms of the study, with the sidedness of the test stated.]
| Table 1. [Scale] Scores Compared With [Reference Values] | |||
|---|---|---|---|
| Measure | n | M (SD) | Difference from [value] [95% CI] |
| [Measure 1] | ___ | ___ (___) | ___ [___, ___] |
| [Measure 2] | ___ | ___ (___) | ___ [___, ___] |
| [Measure 3] | ___ | ___ (___) | ___ [___, ___] |
| Note. Reference values: [value 1] from [source], [value 2] from [source]. Each comparison used a two-sided one-sample t-test, and t, df, p and d for each measure are given in the text. ___ cases with a missing value were excluded from [measure]. | |||
The effect size is the distance from the reference value in standard deviation units, Cohen’s d, and it is named as such with its interval. It answers a different question from the p-value: a large sample can make a very small distance significant, whereas a small sample can leave a large distance with a wide interval. Whether a distance matters is a substantive judgment, so the sentence relates the mean difference to the units of the scale and to what the field regards as meaningful, and does not lean on a label for d.
COMMON MISTAKES
What Undermines a Benchmark Comparison in the Text
A benchmark comparison is only as sound as its reference value, so most of these slips concern the value and not the arithmetic.
Value With No Source A test value that appears without its origin cannot be judged. The sentence names the norm, benchmark or midpoint, and cites the publication where the value comes from one.
Midpoint Treated as a Finding Finding that a mean exceeds a scale midpoint is not by itself a substantive result. The midpoint marks the middle of the response format, and the report says what, if anything, it represents.
Interval for the Wrong Quantity SPSS prints the interval of the difference. Placing it after the sample mean as though it were the interval of the mean misplaces it by the size of the test value.
Value Chosen After the Data Selecting the reference once the sample mean is known turns a test into a description. The report states when the value was fixed, and a post hoc comparison is labeled as one.
Many Scales, No Count Testing a dozen subscales against a dozen benchmarks produces chance findings in proportion to the number of tests. The report states the count and deals with the multiplicity it creates.
Direction Left Implicit Reporting that the sample differed from the reference without saying higher or lower omits the part a reader wants. The sign of the mean difference supplies the direction, and the sentence uses it.
Test value chosen, source still thin? Independent Statistical Review examines the reference value, the output and the sentence together.
FREQUENTLY ASKED QUESTIONS
Reference Values and Intervals in a One-Sample Result
A benchmark that is itself an estimate, a one-sided p printed beside the two-sided one, a table of several scales and a value with no traceable source each change what the sentence may claim.
Can I test against a published mean that has its own uncertainty?
The one-sample test treats the reference as fixed and exact, so a benchmark that is itself an estimate calls for a different comparison. When the published mean comes with an SD and an n, a two-sample comparison built from those summary values is more defensible, and the text says which comparison was used and why.
Do I report the one-sided p-value that SPSS prints?
Only if the direction was fixed before the data were seen; otherwise report the two-sided value. Recent releases print both, and choosing the smaller after looking at the sign of the difference doubles the false-positive rate for that comparison. State the decision in the methods.
How do I report several scales tested against benchmarks?
In one table, with a row per scale, the reference value and its source for each, and the difference with its interval. State how many comparisons were made. If the comparisons were not planned in advance, label them exploratory and treat the p-values accordingly, since each extra test adds a chance of a false positive.
What if my reference value cannot be traced to a source?
A value with no traceable source can be reported only as a descriptive comparison, not as a test against a stated benchmark, and the sentence says so. An in-house PhD-level statistician at OnlineSPSS can set the sentence and table beside the output, or prepare the results text, within Results Reporting & Interpretation.
How do you protect my research data and confidentiality?
Your data and project details are handled confidentially, and project information is not published. Researcher names and institutions are not used publicly without permission. An NDA is available where required and can be arranged before sensitive materials are shared. Read more about confidentiality and data security.
What happens when I request an assessment, and how long does it take?
You share your research question, design and relevant materials, such as the dataset or the output you have, and a statistically trained Research Coordinator reviews the request and responds the same day. The analysis, deliverables, timeline and one fixed project fee are then confirmed before any work begins, so the timeline follows from the agreed scope.
Still have a question? Find more answers in our full FAQ.
NEXT STEP
Will a Reader Know Where
Your Test Value Came From?
Whoever reads the result will ask what the sample was compared with and why. A sentence that cites its source answers the question before anyone has to put it.
No Commitment Required
Strictly Confidential
Fixed Project Fee
In-House PhD-Level Statisticians
Same-Day Response
Serving Researchers Since 2014