T
- TEST
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Definition of 'T-Test'
A statistical examination of two population means. A two-sample t-test
examines whether two samples are different and is commonly used when the
variances of two normal distributions are unknown and when an experiment uses
a small sample size. For example, a t-test could be used to compare the
average floor routine score of the U.S. women's Olympic gymnastic team to the
average floor routine score of China's women's team.
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The test statistic in the t-test is known as the t-statistic. The
t-test looks at the t-statistic, t-distribution and degrees of freedom to
determine a p value (probability) that can be used to determine whether the
population means differ. The t-test is one of a number of hypothesis tests.
To compare three or more variables, statisticians use an analysis of variance
(ANOVA). If the sample size is large, they use a z-test. Other hypothesis tests
include the chi-square test and f-test.
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Example
Let’s
say you’re interested in whether the average New Yorker spends more than the
average Kansan per month on movies.
You
ask a sample of 3 people from each state about their movie spending. You
might observe a difference in those averages (like $14 for the average Kansan
and $18 for the average New Yorker). But that difference is not statistically
significant; it could easily just be random luck of which 3 people you
randomly sampled that makes one group appear to spend more money than the
other. If instead you ask 300 New Yorkers and 300 Kansans and still see a
big difference, that difference is less likely to be caused by the sample being
unrepresentative.
Note
that if you asked 300,000 New Yorkers and 300,000 Kansans, the result would
likely be statistically significant even if the difference between the group
was only a penny. The t-test’s effect size complements
its statistical significance, describing the magnitude of the difference,
whether or not the difference is statistically significant.
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