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Assumptions of the t-Test for Two Independent Samples The
t-test for independent samples works only if we satisfy the following
four assumptions:
1. The dependent variable must be interval or ratio. We must measure
our outcome variable at interval or ratio levels of measurement,
and we cannot use nominal- or ordinal-level data.
2. The scores for participants must be independent. This assumption
states that the scores for one participant do not influence the
scores for another participant. To satisfy this assumption, we
should carefully consider our study design. Is it possible for the
participants to interact with each other such that their scores
are no longer independent? If, for example, we run our study
in groups, is it possible for one participant to affect another?
If so, we should redesign our study so that the scores are inde-
pendent, or we should perform a different analysis.
3. The population’s scores on the dependent variable are normally dis-
tributed, or we have large samples. To satisfy this assumption, we
need either to know that our dependent variable is normally
distributed within the population or to have sufficiently large
samples so that the distribution of means is approximately
normal. Recall that the Central Limit Theorem states that the
shape of the distribution of means will be approximately nor-
mal as the sample size increases (N > 30). Note that a sample size
of 30 is not large or sufficient with respect to statistical power.
It is merely the sample size at which our distribution of means
approaches normality, even if the population is non-normal
in shape.
4. The variances of our two populations are equal. This assumption
equality of variances is called the equality of variances assumption (also called the
assumption (also called the homogeneity of variances assumption) and reflects the fact that our
homogeneity of variances independent variable should affect our groups’ means, but not
assumption) an assumption their variances. For this reason, we can pool our two samples’
that two population variances together when we estimate the populations’ variance.
variances are equal. Used in Now, we should point out that it is unlikely that our two samples
the t-test for independent will have exactly equal variances. This fact can make it hard
samples to justify the sometimes to determine whether we have satisfied or violated
pooling of samples’
variances to estimate the this assumption. We will come back to this issue in a moment.
population’s variance. For now, we just need to know that we are going to assume that
the variances of our samples are equal to each other.

Step by Step: Hypothesis Testing with the t-Test for Two
Independent Samples We are now ready to conduct our formal
hypothesis test.

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

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