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A t-test is the comparison

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of average values
between two groups.

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For example, you could be
comparing whether teaching

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evaluations of male instructors

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is the same for
female instructors.

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You can either assume
that the variance or

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standard deviation
is equal or unequal.

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How do we determine this?

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We have the teaching
evaluation data.

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We calculated the average
teaching evaluation

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for female instructors to be

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3.9 with a standard
deviation of 0.53.

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The average teaching
evaluations for

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male instructors
on the other hand,

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was calculated as 4.06 with a
standard deviation of 0.55.

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When we conduct a t-test,

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we are faced with
whether to assume

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equal or unequal variances.

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We have a t-test called

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Levene's test to determine
the equality of variances.

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The null hypothesis of

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the Levene's test is that
population variances

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are equal if the p-value
of the test is less 0.05,

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reject the null hypothesis of

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equal variances and assume

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that the variances are unequal.

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Let us look at the example
for that of teaching

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evaluation scores for male
and female instructors.

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We will use the Levene's function

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in the psi pi.stats package.

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We will run it against
both samples and we will

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specify the center
argument as mean.

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Since our t-tests, we test
for mean differences,

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we will get a p-value of 0.66,

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which is greater than 0.05.

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That means we will fail to reject

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the null hypothesis
and we will assume

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equal variances when
conducting our t-test.

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When you run your t-test,

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you set the equal
underscore var option to

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true and if you got a
p-value less than 0.05,

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you set that option to false.

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If you were to do
a t-test by hand,

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the formula would
be different for

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calculating equal versus
unequal variances.

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You must calculate the pooled
variance as shown here.

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Then calculate the
standard deviation

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that you will use in the t-test.

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If the variances were unequal,

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calculate the t-test with each of

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the individual standard
deviations and sample size.

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You will need to
find the degree of

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freedom to check
the t-test table.

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With this formula the
rule of thumb for

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assuming equal variance
when calculating by hand,

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is defined by the ratio
of the larger groups

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variance to the smaller groups

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variance to be less than 1.5.