ANOVA

Analysis of Variance
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Question One
One-way ANOVA is a data analysis technique used to test the equality of population means in three or more independent groups by sample variances of one independent factor or variable. The null hypothesis states that there is no significant difference in means, whereas the alternative hypothesis states that the means are statistically different. One-way ANOVA can only be used appropriately if the population groups have a distribution close to the normal one (Triola, 2006).
Question Two
To test the equality of two means at a time in three populations, we will need to carry out three different hypothesis tests. Suppose the means for the three populations are µ1, µ2, and µ3 respectively. The three tests we will need to conduct are H0: µ1= µ2, H0: µ2= µ3 and H0: µ1= µ3 against their respective alternatives H1: µ1≠ µ2, H1: µ2≠ µ3 and H1: µ1≠ µ3. Suppose further that the tests’ significance level is 0.1 each. The overall level of confidence for the test will be 0.93, which is equal to 0.729. As observed, an increase in the number of individual tests increases the probability of an error of type I (caused when the null hypothesis is rejected when it is not supposed to be). The one-way ANOVA, therefore, helps to maintain the intended level of confidence for a particular test (Triola, 2006).
Question Three
The major difference between the two ANOVA approaches is that the one-way ANOVA tests for equality of means by examining the variance of three or more levels of one factor (variable) only whereas a two-way ANOVA examine the effect of multiple levels of two factors (variables) simultaneously (Triola, 2006).

References
Triola, M. F. (2006). Elementary statistics. Reading, MA: Pearson/Addison-Wesley.