Iranian researchers studied factors affecting patients’ likelihood of wearing orthodontic appliances, noting that orthodontics is perhaps the area of health care with the highest need for patient cooperation (Behenam &amp; Pooya, 2007). Among their analyses, they compared students in primary school, junior high school, and high school. The data that follow have almost exactly the same means as the researchers found in their study, but with far smaller samples. The score for each student is his or her daily hours of wearing the orthodontic appliance. Did age of students impact how long they wore the orthodontic appliance for? Use alpha of .05. Primary school: 16,13,18(M=15.67,s=2.52) Junior high school: 8,13,14,12(M=11.75,s=2.63) High school: 20,15,16,18(M=17.25,s=2.22)

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Iranian researchers studied factors affecting patients’ likelihood of wearing orthodontic appliances, noting that orthodontics is perhaps the area of health care with the highest need for patient cooperation (Behenam &amp;amp; Pooya, 2007). Among their analyses, they compared students in primary school, junior high school, and high school. The data that follow have almost exactly the same means as the researchers found in their study, but with far smaller samples. The score for each student is his or her daily hours of wearing the orthodontic appliance. Did age of students impact how long they wore the orthodontic appliance for? Use alpha of .05.   Primary school: 16,13,18(M=15.67,s=2.52)           Junior high school: 8,13,14,12(M=11.75,s=2.63)   High school: 20,15,16,18(M=17.25,s=2.22)

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Step 1   ANOVA or Analysis of Variances is one of the most important fields in Statistic. The reason for this is that is goes into the core of analyzing the variation exhibited samples, by breaking down the total variation into various different sources of variation.   The most basic use of ANOVA is to test for the difference between the populations for several groups (2 or more). Let us recall that a t-test is used to compare the means of two groups, so then ANOVA is some sort extension that allows to perform comparisons for two or more groups.  Step 2   As with any other hypothesis test, ANOVA uses a null and the alternative hypothesis. The null hypothesis is a statement that claims that all population means are equal, and the alternative hypothesis is the hypothesis that not all means are equal (observe that this does NOT imply that all means are unequal, it implies that al least one mean is equal.

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