6.4 Comparing Means From Two Independent Samples: Two-Sample t-Test 75null hypothesis is true. There is a relationship between p - values and
the level of the test. The p - value is the lowest level at which the test
will reject the null hypothesis. Therefore, it is more informative about
the evidence against the null hypothesis. A p - value can be one sided or
two sided, depending whether or not the test is one or two tailed.
6.4 COMPARING MEANS FROM TWO
INDEPENDENT SAMPLES: TWO - SAMPLE T - TEST
We start out by considering comparison of capture thresholds from two
treatment groups as a way to introduce the t - test for two independent
samples. In a clinical trial where pacing leads are implanted along with
a pacemaker, we want to show that the treatment, a steroid - eluting lead
attached in the heart, provides a 1 V lower capture threshold than a
nonsteroid lead, the control treatment. The test hypothesis is that the
difference in mean capture threshold at 6 months postimplant is zero.
This is the uninteresting result that we call the null hypothesis. For
the trial to be successful, we need to reject the null hypothesis in favor
of the alternative hypothesis that the difference: Treatment Group
Average — Control Group Average is negative.
We then choose the sample size to be large enough that we are very
likely to reject the null hypothesis when the mean threshold for the
treatment group is at least 1 V lower than for the control group. This
we call a clinically signifi cant difference.
If we reject the null hypothesis, we say the difference is statistically
signifi cant. We use the Neyman – Pearson approach discussed earlier.
In the clinical trial, we can determine a value for the test statistic
called the critical value such that we reject the null hypothesis if
the test statistic is as negative, or even more negative than the critical
value.
We set α = 0.05 and do a one - sided test (i.e., only reject for large
negative values, since we are only interested in showing statistically
signifi cantly lower thresholds and not signifi cantly higher ones). This
determines, based on the chosen signifi cance level and the sample size,
a critical value for the test statistic: The mean threshold difference
normalized by dividing by an estimate of the standard deviation of the
difference. This test statistic may be assumed to have a Student ’ s
t - distribution with 2 n − 2 degrees of freedom ( df ) when the null