A t-test cannot cover more than one group. This has to do with the underlying method used to calculate the test value.
Explain about t-test?
The t-test is designed to compare the means of two populations based on the means of the two samples. (any sample from either population).
An estimate of the standard deviation of the mean, commonly called the standard error, is used to measure the magnitude of the difference between the means. Now that we have a means to compare the two quantities (and know their theoretical distribution), we can determine whether this difference is significant.
The most important observation is that the t-test computes the difference between two sample means.
If there are more than two groups (that is, the population is split or stratified into more than one group), there are further differences to consider. If you have 3 groups A, B, C, there are 3 possible differences.
μA-μB, μB-μC, μA-μC between population means and three differences between sample means. However, one measure is needed to determine whether these differences are significant.
A t-test can be used for each of the above three differences. But it doesn't answer the question whether there is a difference when looking at all three groups at once.
To achieve this, ANOVA uses a trick.
Rather than using the differences between pairs of groups directly (ask yourself how to summarize three differences in one measure), measure the variance of the mean between groups. If there are large differences in group means, variance captures those differences into a measure!
If you have trouble understanding 'variance', you can use the word standard deviation from the previous text to get your points.
In other words, there is more than one difference between the groups, but we want one measure of Total Difference Between Groups. The t-test cannot do that.
So the procedure for groups of three or more is: Run ANOVA first. As a second step, if you have reason to believe that differences exist (based on this test), you can use the t-test to determine where those differences lie.
A t-test cannot cover more than one group. This has to do with the underlying method used to calculate the test value.
To know more about test value, check out:
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