Paired t

Overview  |  How to  |  Data  |  Example

Overview

The Paired t conducts a hypothesis test of the difference between two population means when observations are paired.  It also calculates a confidence interval of the difference.

This procedure is based on the t-distribution which is derived from a normal distribution.  It is appropriate when the paired differences follow a normal distribution.  If the observations are dependent in a pairwise manner, the matching results in smaller variance and greater power of detecting differences than the 2-sample t.

Test	Null Hypothesis, H0	Alternate Hypothesis, H1
One-tailed	md = m0	md < m0 or md > m0
Two-tailed	md = m0	md ¹ m0

where m_d is the population mean of the differences and m₀ is the hypothesized mean of the differences.

How to

1. Choose ProcessMA > Basic Statistics > Paired t.

2. In Sample 1, select the column containing the first sample.

3. In Sample 2, select the column containing the second sample.

4. In Test mean difference, enter the hypothesised difference between the population means.

5. Click OK.

Optional

6. In Alternate, select the type of test.

7. In Confidence level, enter the desired confidence level for the confidence interval.

8. Check Plot dotplot, if you want to display the Dotplot of the data and the hypothesis test parameters.

Note       To select a column of data into a textbox, double-click on any of the column names shown in the list on the left of the dialog box while in the textbox.

Data

Sample 1: Numeric.

Sample 2: Numeric.

Test mean difference: Numeric.

Confidence level: Numeric; Between 0 and 100.

Example

A tire manufacturer wants to compare 2 types of tires, P and Q.  Twelve motorcycles were fitted with each type of tires in random (either front or back).  After 6 months, the amount of wear and tire on the tires were measured.  You want to use a Paired t procedure as it removes the variation due to difference between motorcycles. 

1. Open worksheet ProcessMA > Tools > Data Files > Stat.xls.

2. Choose ProcessMA > Basic Statistics > Paired t.

3. In Sample 1, select C – Tire-A.

4. In Sample 2, select D – Tire-B.

5. In Test mean difference, enter 0.

6. In Alternate, select Not equals.

7. In Confidence level, enter 95.

8. Check Plot dotplot.

9. Click OK.

Interpretation

For a desired a = 0.05, since p = 0.025 < a, we will reject H₀.  Therefore, we conclude that there is significant evidence that the two types of tires wear out differently.