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Because our t-table doesn’t include 78 degrees of freedom exactly,
we should round down to the next available degrees of freedom,
which in this case is 60. Therefore, our critical value cutoffs are
+ −2.001. Let’s include these cutoffs in our comparison distribution
/
(see Figure 10.13).

Distribution
of Means
µ M – M = 0
µ
2
1
S Difference = 0.2253

–2 –1 0 +1 +2

t-Cutoff t-Cutoff
–2.001 2.001

Figure 10.13 t Distribution with Critical
Value Cutoff

Step 4: Determine Sample Results We’re almost ready to convert
our sample results into a t-score. Before we do that, we need to make
sure that we’ve satisfied the four assumptions for the independent
samples t-test. The first of these assumptions says that the dependent
variable must be measured on the interval or ratio level. For our cur-
rent study, we must measure stress using the Perceived Stress Scale,
which qualifies as an interval-level variable, so we satisfied the first
assumption. The second assumption says that participants’ scores
are independent observations. We had participants complete the
study individually, so their scores are independent. Check. The third
assumption says that the population is normally distributed, or we
have large samples. For our current study, we recruited 40 participants
per condition (for a total of 80 participants), thus we should have a
sufficiently large sample such that we don’t need to worry about vio-
lating this assumption.
Testing the fourth assumption of the independent samples t-test
is a bit more complicated. Recall that the fourth assumption is the
equality of variances assumption, which states that the variances of
our two conditions should be approximately equal. Looking at our
current study results, we can see that the variance for the mindfulness
condition is 1.17 and the variance for the control condition is 0.86.

370 S TATIS TI c S F OR R ESEAR c H

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