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18-6 Tests
The Z Test provides a variety of different standardization-based tests. They make
it possible to test whether or not a sample accurately represents the population
when the standard deviation of a population (such as the entire population of a
country) is known from previous tests. Z testing is used for market research and
public opinion research, that need to be performed repeatedly.
1-Sample Z Test tests for unknown population mean when the population
standard deviation is known.
2-Sample Z Test tests the equality of the means of two populations based on
independent samples when both population standard deviations are known.
1-Prop Z Test tests for an unknown proportion of successes.
2-Prop Z Test tests to compare the proportion of successes from two populations.
The t Test uses the sample size and obtained data to test the hypothesis that the
sample is taken from a particular population. The hypothesis that is the opposite of
the hypothesis being proven is called the
null hypothesis
, while the hypothesis
being proved is called the
alternative hypothesis
. The t-test is normally applied to
test the null hypothesis. Then a determination is made whether the null hypothesis
or alternative hypothesis will be adopted.
When the sample shows a trend, the probability of the trend (and to what extent it
applies to the population) is tested based on the sample size and variance size.
Inversely, expressions related to the
t test are also used to calculate the sample
size required to improve probability. The t test can be used even when the
population standard deviation is not known, so it is useful in cases where there is
only a single survey.
1-Sample t Test tests the hypothesis for a single unknown population mean when
the population standard deviation is unknown.
2-Sample t Test compares the population means when the population standard
deviations are unknown.
LinearReg t Test calculates the strength of the linear association of paired data.
In addition to the above, a number of other functions are provided to check the
relationship between samples and populations.
χ
2
Test tests hypotheses concerning the proportion of samples included in each of
a number of independent groups. Mainly, it generates cross-tabulation of two
categorical variables (such as yes, no) and evaluates the independence of these
variables. It could be used, for example, to evaluate the relationship between
whether or not a driver has ever been involved in a traffic accident and that
person’s knowledge of traffic regulations.
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