What Is the Advantage of Using Anova to Test for Differences Among Treatment Means Rather Than Testing All Possible Pairs of Treatment

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What is the advantage of using ANOVA to test for differences among treatment means rather than testing all possible pairs of treatment means?  The advantages of using ANOVA is that (1) If two means are compared the ANOVA will provide the same result as the t-test. ANOVA is a statistical method for making simultaneous comparisons between two or more means. It therefore generalizes t- test to more than two groups. Doing multiple two sample t- tests would result in an increased chance of committing type 1 error. Type 1 error occurs when the null hypothesis, (Ho), when it is true but it is rejected. For example if you have four group (A,B,C,D,) and compare the pairs of mean then you will get six result such as (A vs B,A vs C,A vs D,B vs C,B vs D,C vs D). The probability of not obtaining a significant result is 1-(1-0.05)^6=0.265. This means that your chances of incorrectly rejecting the null hypothesis is about 1 in 4 instead of 1 in 20. ANOVA compares all means simultaneously and maintain the type 1 error probability at the designated level. (2) Also t-test for comparing two or more means are time consuming than ANOVA.(3) You can use the ANOVA for the three treatment condition but in order to compare the three conditions with the t-test you cannot do so. In research using a two-variable design offers many advantages over using a one-variable design. The first advantage is increased efficiency. The other advantage is that we can analyze the interaction of the two variables in the design. (4) ANOVA is used in the analysis of comparative experiments, those in which only the difference in outcomes is of interest. The statistical significance of the experiment is determined by a ratio of two variances. This ratio is independent of several possible alterations to the experimental observations: Adding a constant to all observations does not alter significance. Multiplying all observations by a constant does not alter significance. If we do an ANOVA test we can do two or...
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