Detailed Calculations and Explanations using the Data You Entered

This section is premium content and can be purchased along with the
downloadable Excel Calculator for $19.99 US

If you already purchased premium access you can login here.

Descriptive Statistics

The first step is to compute the descriptive statistics for each sample. . . .Purchase AccessUnequal Variances: Welch-Satterthwaite Procedure

One assumption of the t-test is that both samples have the same variances. . . .Purchase AccessTest Statistic

Standard Error of the Difference (se)

Test Statistic

The standard error of the estimate and is our denominator for the test stat. . .Purchase AccessDegrees of Freedom

The degrees of freedom for unequal variances are found using the following . . .Purchase AccessP-values

The p-value for this test is found using the student-t distribution. To fin. . .Purchase Access95% Confidence Interval For the Difference

The confidence interval is calculated by adding and subtracting the margin . . .Purchase AccessEqual Variances

When we assume equal variances we need to "pool" the two standard deviation. . .Purchase AccessPooled Standard Deviation(se)

The estimate of the standard deviation of the difference is found by multip. . .Purchase AccessTest Statistic

The test statistic t, is found by dividing the difference between means by . . .Purchase AccessDegrees of Freedom

The degrees of freedom for equal variances are much more straight forward t. . .Purchase AccessP-values

To find the p-value associated with this test statistics we use the degrees. . .Purchase Access95% Confidence Interval For the Difference

The confidence interval is calculated by adding and subtracting the margin . . .Purchase AccessTest Considerations

1 or 2 Tailed Test

Now that we have the degrees of freedom and test statistics we can find the. . .Purchase AccessEqual or Unequal Variances?

This choice depends on what you’re testing. If for example you’ve given a d. . .Purchase AccessAssumptions

When using the t-test, it is assumed the data is normally distributed and t. . .Purchase AccessReferences

- Agresti, A., Franklin, C. (2007) Statistics: The Art and Science of Learning from Data (2nd Edition)
- G.E.P. Box (1953), "Non-Normality and test on variances.", Biometrika 40: p318–355
- Howell, D. (2002), Statistical Methods for Psychology
- Satterthwaite, F. E. (1946), "An Approximate Distribution of Estimates of Variance Components.", Biometrics Bulletin 2: 110–114
- Welch, B. L. (1947), "The generalization of "student's" problem when several different population variances are involved.", Biometrika 34: 28–35