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 = mD | md < mD or md > mD |
| Two-tailed | md = mD | md <> mD |
where md is the population mean of the differences and mD is the hypothesized mean of the differences
At the Excel Menu (For Excel 2007, go to Add-ins first)
Choose ProcessMA > Statistics > Basic Statistics > Paired-t
In Variable 1, select the column containing the data for the first sample (Numeric)
In Variable 2, select the column containing the data for the second sample (Numeric, same number of data points as Variable 1)
In Test Mean Difference, enter hypothesized difference between the population means (Numeric)
In Alternate, select the appropriate alternate test
In Confidence Level, enter value for confidence level (Numeric, >0 & <1)
Click OK
A tire manufacturer wants to compare 2 types of tires, A and B. Ten 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.
Open data worksheet by choosing ProcessMA > Tools > Data
Choose ProcessMA > Statistics > Basic Statistics > Paired-t
In Variable 1, select BL - Tire-A
In Variable 2, select BM - Tire-B
Click OK
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.
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