Here's what you'll find in this section:
We have previously discussed methods of testing whether
To set our notation, let I be the number of populations or treatments being compared and let be the I means. Then the hypotheses for testing are
To test these hypotheses, we require a random sample from each population or treatment.
NOTE:\ For computational purposes, the ANOVA equations for the multiple population case and the multiple treatment on one population case are the same. However, the interpretation of hypotheses and results is slightly different. Thus,
Recall that we have I populations or I treatments on one population and we wish to test whether the means for all I groups are equal. The notation we will use for our random variables and observed data values is:
The mathematical model describing analysis of variance can be expressed in two different ways. First,
where is an overall mean, is the effect due to treatment i, and . Note that the treatment effects satisfy the condition . If we define the ith treatment or population mean as , our model can be expressed as
In this class, we will not be concerned with formulas for computing ANOVA quantities. Instead, we will let Stataquest do that for us. However, we will need to learn how to interpret and test using Stataquest output.
The traditional way to present ANOVA results is in an ANOVA table such as the one given below.
Applicable StataQuest Commands:
Labs Calculating One-Way ANOVA
Statistics ANOVA One-way
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