Select the analysis options for Paired t (Options tab)

On the Options tab of the Paired t dialog box, specify the confidence level for the confidence interval or define the alternative hypothesis.

Alternative hypothesis

From Alternative hypothesis, select the hypothesis that you want to test:
Mean difference < 0

Use this one-sided test to determine whether the difference in paired means between sample 1 and sample 2 is less than 0, and to get an upper bound. This one-sided test has greater power than a two-sided test, but it cannot determine whether the difference is greater than 0.

For example, a baker tests uses this one-sided test to determine whether bread that is baked at a lower temperature for more time contains less moisture. The baker divides samples from a single batch of dough in half and bakes each half at different temperatures for different times. This one-sided test has greater power to determine whether the bread baked at a lower temperature has less moisture, but it cannot determine whether the bread contains more moisture.

Mean difference ≠ 0

Use this two-sided test to determine whether the difference in paired means is different from 0, and to get a two-sided confidence interval. A two-sided test can detect differences that are less than or greater than the hypothesized value, but it has less power than a one-sided test.

For example, an engineer compares the difference in measurements of the same bearings made with 2 different calipers. Because any difference in the measurements is important, the engineer uses this two-sided test to determine whether the difference is greater than or less than 0.

Mean difference > 0

Use this one-sided test to determine whether the difference in paired means between sample 1 and sample 2 is greater than 0, and to get a lower bound. This one-sided test has greater power than a two-sided test, but it cannot determine whether the difference is less than 0.

For example, a quality analysis uses this one-sided test to determine whether treated wood beams are stronger than untreated beams. Each beam is cut in half; one half is treated and the other half is untreated. This one-sided test has greater power to determine whether the treated wood beams are stronger than the untreated beams, but it cannot determine whether the treated beams are less strong than the untreated beams.

For more information on selecting a one-sided or two-sided alternative hypothesis, go to About the null and alternative hypotheses.

Confidence level

From Confidence level, select the level of confidence for the confidence interval.

Usually, a confidence level of 95% works well. A 95% confidence level indicates that, if you take 100 random samples from the population, the confidence intervals for approximately 95 of the samples will contain the population parameter.

For a given set of data, a lower confidence level produces a narrower confidence interval, and a higher confidence level produces a wider confidence interval. The width of the interval also tends to decrease with larger sample sizes. Therefore, you may want to use a confidence level other than 95%, depending on your sample size, as follows:
  • If your sample size is small, a 95% confidence interval may be too wide to be useful. Using a lower confidence level, such as 90%, produces a narrower interval. However, the likelihood that the interval contains the population mean difference decreases.
  • If your sample size is large, consider using a higher confidence level, such as 99%. With a large sample, a 99% confidence level may still produce a reasonably narrow interval, while also increasing the likelihood that the interval contains the population mean difference.
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