T test workspace
Run one-sample, paired, Welch or Student t tests from raw CSV values or summary statistics. Get the confidence interval for the difference, Cohen's d and Hedges' g with intervals, normality and variance checks, and QQ and interval charts.
Runs locally in your browser in a background worker; nothing is uploaded. CSV up to 1,000,000 characters and 10,000 data rows, with dot-decimal numbers. Raw headers are group,value for two groups, before,after for paired data and value for one sample, or name your own columns. A summary CSV has the headers group,n,mean,sd with one row (one sample or paired differences) or two rows. Confidence level 0.5 to 0.9999. Setting numbers are plain decimals with a digit before the point, such as 0.95, without exponents. In CSV with two or more columns a blank line between rows is rejected, and in one-column CSV it is a blank cell; blank lines after the last row are ignored. Downloads: a JSON report, CSV tables (result, effect sizes, groups, checks and QQ points) and SVG charts. Paste raw values with a header row, or a summary CSV with group,n,mean,sd. Up to 1,000,000 characters. Review the settings before running.
Your result
How to use T test workspace
- Choose the design and whether you have raw values or a summary CSV.
- Paste the CSV and name the columns, or keep the default headers.
- Set the null value, the alternative and the confidence level. Tick equal variances only if you have a reason to.
- Run the test, review the interval, effect sizes and checks, and download the report.
Useful next steps
How the test works
Two independent groups use Welch's t test by default, which does not assume equal variances (Welch 1947, Biometrika 34:28). Student's pooled test is available when equal variances are justified. Paired data are tested as one sample of differences, first minus second. The confidence interval uses the t quantile; one-sided alternatives give one-sided intervals, as R t.test does.
Effect sizes
Cohen's d uses the pooled standard deviation for two groups and the SD of the differences (d_z) for paired or one-sample data (Cohen 1988, Statistical Power Analysis, 2nd ed.). Its interval inverts the noncentral t distribution (Steiger and Fouladi 1997) and is always two-sided at the chosen confidence level, even for a one-sided alternative, so it is labelled two-sided and can include zero when a one-sided test is significant. Hedges' g applies the exact small-sample factor J (Hedges 1981, Journal of Educational Statistics 6:107).
Checks and charts
Raw data get the D'Agostino K squared normality test for samples of at least 8 (D'Agostino, Belanger and D'Agostino 1990, The American Statistician 44:316) and, for two groups, the Brown-Forsythe test (Brown and Forsythe 1974, JASA 69:364) and the variance ratio. The Brown-Forsythe test is left out when each group holds two values equally often (for example two values per group), because the absolute deviations then do not vary and the test is undefined. The QQ chart pairs sorted values with normal quantiles at the R ppoints positions. These checks describe the sample; they should not decide which test to use on their own.
Limits
The t test assumes independent observations and is sensitive to strong outliers in small samples. A p-value is not the size of an effect, so read it with the interval and the effect size.