What Two-sided test is
A two-sided test is a statistical procedure used to determine whether two sets of data are significantly different from each other. It is also known as a two-tailed test or a two-sample test. This type of test is used to test hypotheses, such as whether two populations have the same mean.
The steps for a two-sided test are as follows:
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State the null and alternative hypotheses. The null hypothesis is that the two sets of data come from the same population, while the alternative hypothesis is that the two sets of data come from different populations.
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Calculate the test statistic. This involves calculating the difference between the means of the two sets of data, and then dividing by the standard error.
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Calculate the p-value. This is the probability that the observed difference in means is due to chance.
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Compare the p-value to the significance level. The significance level is the probability of rejecting the null hypothesis when it is true. Generally, a p-value less than 0.05 is considered statistically significant.
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Make a decision. If the p-value is less than the significance level, then the null hypothesis can be rejected, and the alternative hypothesis accepted.
Examples
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A two-sided test could be used to test if a coin is fair by comparing the proportion of heads and tails to the expected proportion of 50%.
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A two-sided test could be used to test whether the average credit score for a population is significantly different from 700.