is interested in the effects of background noise on 4. A graduate student learning. noise. The students were given material to study for one hour under these conditions. After that one hour, each student took a 20-point multiple-choice test. The scores for each student were as follows: Constant Noise Random Noise No Noise 16 18 20 17 13 19 140 18 15 16 16 15 13 11 17 2521
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.
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 pair of means is unequal).
The main assumptions required to perform a one-way ANOVA are:
- The dependent variable (DV) needs to be measured at least at the interval level
- The groups must come from normally distributed populations
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- The groups must come from normal populations with equal population variances
If the results of the ANOVA are significant, this is, the null hypothesis is rejected, we can perform a Post-Hoc test to assess exactly which pairs differ significantly. Examples of Post-Hoc tests are Fisher's LSD, Tukey's test, Bonferroni correction, etc.
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