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 $10.00 US
If you already purchased premium access you can login here.

Excerpts of the premium content have been displayed below.

Descriptive Statistics

The first step is to compute the descriptive statistics for each sample. . . .Purchase Access

Unequal Variances: Welch-Satterthwaite Procedure

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

Test Statistic

Standard Error of the Difference (se)

Test Statistic

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

Degrees of Freedom

The degrees of freedom for unequal variances are found using the following . . .Purchase Access

P-values

The p-value for this test is found using the student-t distribution. To fin. . .Purchase Access

95% Confidence Interval For the Difference

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

Equal Variances

When we assume equal variances we need to "pool" the two standard deviation. . .Purchase Access

Pooled Standard Deviation(se)

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

Test Statistic

The test statistic t, is found by dividing the difference between means by . . .Purchase Access

Degrees of Freedom

The degrees of freedom for equal variances are much more straight forward t. . .Purchase Access

P-values

To find the p-value associated with this test statistics we use the degrees. . .Purchase Access

95% Confidence Interval For the Difference

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

Test Considerations

1 or 2 Tailed Test

Now that we have the degrees of freedom and test statistics we can find the. . .Purchase Access

Equal or Unequal Variances?

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

Assumptions

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

References

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