T-Test

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T-Test
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T-Test

• A t-test is a type of inferential statistic used
  to determine if there is a significant
  difference between the means of two groups,
  which may be related in certain features.
• It is mostly used when the data sets, like the
  data set recorded as the outcome from flipping a
  coin 100 times, would follow a normal
  distribution and may have unknown variances.

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T-Test

• A t-test is used as a hypothesis testing tool,
  which allows testing of an assumption applicable
  to a population.
• A t-test looks at the t-statistic, the
  t-distribution values, and the degrees of
  freedom to determine the statistical
  significance.
• To conduct a test with three or more means, one
  must use an analysis of variance.

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Key takeways

• A t-test is a type of inferential statistic used
  to determine if there is a significant
  difference between the means of two groups,
  which may be related in certain features.
• The t-test is one of many tests used for the
  purpose of hypothesis testing in statistics.

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Calculating a t-test requires three key data
values. They include the difference between the
mean values from each data set (called the
mean difference), the standard deviation of each
group, and the number of data values of each
group. There are several different types of
t-test that can be performed depending on the
data and type of analysis required.
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Assumptions for Performing a t-test
The data should follow a continuous or ordinal
scale (the IQ test scores of students, for
example) The observations in the data should be
randomly selected The data should resemble a
bell-shaped curve when we plot it, i.e., it
should be normally distributed. You can refer to
this article to get a better understanding of
the normal distribution Large sample size should
be taken for the data to approach a normal
distribution (although t-test is essential for
small samples as their distributions are
non-normal) Variances among the groups should be
equal (for independent two-sample t-test)
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Types of t-tests
One sample t-test Independent two-sample t-test
Paired sample t-test
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One sample t-test
The one-sample t-test is a statistical hypothesis
test used to determine whether an unknown
population mean is different from a specific
value.
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Independent two-sample t-test
The two-sample t-test (also known as
the independent samples t-test) is a method used
to test whether the unknown population means of
two groups are equal or not.
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Paired sample t-test
The paired sample t-test, sometimes called the
dependent sample t-test, is a statistical
procedure used to determine whether the mean
difference between two sets of observations is
zero. In a paired sample t-test, each subject or
entity is measured twice, resulting in pairs of
observations
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