What T test is
A t-test is a statistical test used to compare the means of two samples or groups. It is commonly used to determine whether two samples or groups of data are statistically different from each other. It is also used to determine the significance of a correlation between two variables.
Steps for a T-test:
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State the null hypothesis: This is the hypothesis that there is no difference between the means of the two samples or groups being compared.
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Specify the alternative hypothesis: This is the hypothesis that there is a difference between the means of the two samples or groups being compared.
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Calculate the t-statistic: This is the statistic that is used to determine the probability that the difference between the two samples or groups is due to chance.
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Calculate the degree of freedom: The degree of freedom is the number of independent observations that have been used to calculate the t-statistic.
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Calculate the p-value: The p-value is the probability that the difference between the two samples or groups is due to chance.
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Interpreting the results: If the p-value is less than the predetermined significance level (usually 0.05), then the null hypothesis is rejected and the alternative hypothesis is accepted. This means that the difference between the two samples or groups is statistically significant.
Examples
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A T-test can be used to compare the means of two groups, to determine if the averages are significantly different.
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A T-test can also be used to compare the means of two dependent samples, to determine if the difference between them is statistically significant.
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A T-test can be used to test for the statistical significance of a correlation coefficient.
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A T-test can be used to determine the statistical significance of a regression coefficient.
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A T-test can be used to compare the means of three or more independent groups, to determine if any of the groups are significantly different from each other.