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Test the mean difference between two samples of continuous data using the 2-sample t-test. The calculator uses the probabilities from the student t distribution.
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 Enter Summarized Data Sample 1 43 52 36 37 136 38 37 39 42 39 52 Sample 2 99 52 36 37 136 180 150 39 42 39 250 Clear Sample Data
NMeanStDevSE Mean
Sample 11150.09129.04648.758
Sample 21196.36473.298422.1
2 Sample t Tutorial
Observed difference (Sample 1 - Sample 2): -46.273
Standard Deviation of Difference : 23.7723

Unequal Variances
DF : 13
95% Confidence Interval for the Difference ( -97.6307 , 5.0847 )
Test Statistic t = -1.9465
Population 1 ≠ Population 2: P-Value = 0.0736
Population 1 < Population 2: P-Value = 0.9632
Population 1 > Population 2: P-Value = 0.0368

Equal Variances
Pooled Standard Deviation: 55.751
Pooled DF: 20
95% Confidence Interval for the Difference ( -95.862 , 3.316 )

Test Statistic t= -1.9465
Population 1 ≠ Population 2: P-Value = 0.0658
Population 1 < Population 2: P-Value = 0.9671
Population 1 > Population 2: P-Value = 0.0329

Detailed Calculations and Explanations using the Data You Entered

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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)

 = = = = 23.7723

Test Statistic

So 23.7723 is the standard error of the estimate and is our denominator for. . .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, -1.9465, we use t. . .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