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Purpose
This procedure
compares two populations mean. Procedure uses t-criterion, Welch
criterion, Pagurova criterion,
Means difference G-criterion. The theoretical assumptions of these criteria is
that, the samples should be normally distributed. If these assumptions are
clearly not met, then one of the nonparametric alternative tests should be used. To check it use Normality Tests. See
also Why the "Normal distribution" is
important.
The
t-test is the most commonly used method to evaluate the differences in
means between two groups. For example, the t-test
can be used to test for a difference in test scores between a group of patients
who were given a drug and a control group who received a placebo. Theoretically,
the t-test can be used even if the
sample sizes are very small (e.g., as small as 10; some researchers claim that
even smaller n's are possible), as long as the variables are normally
distributed within each group and the variation of scores in the two groups is
not reliably different.
When analyzing
samples from populations with unknown variances which equality is not supposed
or if the ration of variances is not known arises so-called Behrens-Fisher
problem. Welch and Pagurova criteria are used to solve this problem.
Preparations
To run this procedure, select a range, and
then run the Statistics→Basic
Statistics and Tables→F-Test for Variances...
command.
From the T-Test Type drop-down list select t-test type.
t-Test: Two-Sample Assuming Equal Variances. This
t-test form assumes that the means of both data sets are equal; it is
referred to as a homoscedastic t-test. You can use t-tests to determine
whether two sample means are equal.
t-Test: Two-Sample Assuming Unequal Variances.
This t-test form assumes that the variances of both ranges of data are
unequal; it is referred to as a heteroscedastic t-test. You can use a t-test
to determine whether two sample means are equal. Use this test when the
groups under study are distinct. Use a paired test when there is one group
before and after a treatment.
t-Test: Paired Two Sample For Means.
This t-test form does not assume that the variances of both populations are
equal. You can use a paired test when there is a natural pairing of
observations in the samples, such as when a sample group is tested twice —
before and after an experiment.
Results
Count - analyzed sample size.
Mean -
analyzed sample mean. See
Elementary Concepts.
Standard Error of the Mean, p-level - See
Elementary Concepts.
T-criter. value -
test statistics.
P(T<=t)Probability, corresponding to Student criterion) -
represents the probability of error involved in accepting our research
hypothesis about the existence of a difference. Technically speaking, this is
the probability of error associated with rejecting the hypothesis of no
difference between the two categories of observations (corresponding to the
groups) in the population when, in fact, the hypothesis is true. Some
researchers suggest that if the difference is in the predicted direction, you
can consider only one half (one "tail") of the probability distribution and thus
divide the standard p-level reported
with a
t-test (a "two-tailed"
probability) by two. Others, however, suggest that you should always report the
standard, two-tailed t-test probability
Pagurova criterion.
Pagurova assumed, that distribution of criterion statistics essentially depends
on the ration of variances.Test statistics is computed as
v =
|µ1-µ2|/( 12/N1+22/N2)1/2
Ratio of variances parameter
ñ = 12/N1/(12/N1+22/N2).
However, critical values are taken
others.
p-level- represents the probability of error involved in accepting our research
hypothesis about the existence of a difference.
Means difference G-criterion.
This procedure is used to compare the mean of a single group to a target
value.
p-level- represents the probability of error involved in accepting our research
hypothesis about the non existence of a difference.
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