How it works
The hypothesised difference is subtracted from the mean difference, then divided by the standard error from separate group variances. This form solves for first group mean; enter the known quantities in Standardised test statistic, Second group mean, Hypothesised mean difference, First group sample deviation, First group size, Second group sample deviation, Second group size.
Inputs and units
| Input | Example value | What to enter |
|---|---|---|
| Standardised test statistic | 1 | Formula symbol: t. Enter a numeric value. |
| Second group mean | 10 | Formula symbol: m2. Enter a numeric value. |
| Hypothesised mean difference | 0 | Formula symbol: null. Enter a numeric value. |
| First group sample deviation | 4 | Formula symbol: s1. Enter a numeric value. Must be greater than zero. |
| First group size | 8 | Formula symbol: n1. Enter a numeric value. Use a whole number. Must be greater than zero. |
| Second group sample deviation | 4 | Formula symbol: s2. Enter a numeric value. Must be greater than zero. |
| Second group size | 8 | Formula symbol: n2. Enter a numeric value. Use a whole number. Must be greater than zero. |
Worked example
Show example inputs and results
This example is generated by the same calculation engine using the starting values in the form. Your own inputs produce your own result.
- Standardised test statistic
- 1
- Second group mean
- 10
- Hypothesised mean difference
- 0
- First group sample deviation
- 4
- First group size
- 8
- Second group sample deviation
- 4
- Second group size
- 8
Complete example results
- First group mean
- 12
Reading the result
The result solves for first group mean from the entered quantities. Check the result unit and the formula conditions before using it.
Questions and answers
Can I use the example values for my own calculation?
The example values illustrate the calculation. Replace every input with your own information, especially dates, rates and the selected operation.
When can I use the first group mean result?
Independent observations and matching units are required. Only a Welch-style statistic is calculated; degrees of freedom, p-value and rejection decisions are excluded. Paired data need another model.
Why are some results rounded?
Results display up to 8 decimal places. Calculations use the unrounded values; very small values use scientific notation. JavaScript floating-point arithmetic can introduce tiny rounding differences.
Are my inputs sent to a server?
The calculator processes inputs in your browser. Its code does not send your values to a server.
Method sources: itl.nist.gov