Two Sample t-Test and Confidence Intervals

[#1]

Use to Estimate via a confidence interval and perform a hypothesis test for the difference between two population means. If more than two means (more than two levels of the categorical X variable), refer to the One-Way ANOVA guide.

Comparison of Two Population Means                      

1. From an open JMP^® data table, select Analyze > Fit Y by X.
2. Click on a continuous variable from Select Columns, and click Y, Response.
3. Click on a two-level categorical variable and click X, Factor.
4. Click OK. The Oneway Analysis output window will display.
5. Click on the red triangle and select Means/Anova/Pooled t.

Some of the additions to the report include:

• Mean diamonds (95% Confidence Intervals) added to the graph.
• T-test Statistic and p-values for testing the hypotheses:
  H₀: m₁ = m ₂ vs. H_A: m ₁ ≠ m ₂ ; or H_A: m ₁ > m ₂ ; or H_A: m ₁ < m ₂
• Confidence Interval for (m₁ - m ₂).
• Individual Confidence Intervals for m₁ and m ₂.                    

Note: Means/Anova/Pooled t is the test under the assumption of equal variances.

For a test without the assumption of equal variances, select t Test under the red triangle instead.

Results
• Upper CL Dif and Lower CL Dif give the 95% CI for (μ1 - μ 2), the difference between the two population means. Here we estimate that difference to be (-6.89 , 21.64). Since the 95% CI contains zero, we conclude that there is not the statistical evidence needed to conclude a significant difference between the means.
• Prob > |t| is the p-value for the two-tailed test. The null hypothesis is that means are equal (the mean difference is zero). Since Prob > |t| is greater than 0.05, cannot reject the null hypothesis (i.e., we cannot conclude that there is a significant difference between the two population means).
• 95% Confidence Intervals for the Individual Means are shown in the Means for OneWay Anova table. We estimate, with 95% confidence, that the population mean Weight for Females to be between 90.4 and 111.5 and to be between 98.7 and 117.9 for Males.

Note: The default confidence level is 95% (i.e., significant level of 0.05.) Select Set α Level under the red triangle to change.

This analysis can also be performed using the Hypothesis Test for Two Means and Confidence Intervals for Two Means Calculators under Help > Sample Index > Calculators or Student > Calculators in JMP Student Subscription.

Visit Discovering JMP > Analyze Your Data > Analyze Relationships and Basic Analysis > Oneway Analysis in JMP Help to learn more.