![]() ![]() So why do we inspect our sample sizes based on a means table? Why didn't we just look at the frequency distribution for fertilizer? Well, our ANOVA uses only cases without missing values on our dependent variable. Since our sample sizes are equal, we don't need the homogeneity assumption either. ![]() Our means table shows that each n ≥ 25 so we don't need to meet normality.Our plants seem to be independent observations: each has a different id value (first variable).So how to check if we meet these assumptions? And what to do if we violate them? The simple flowchart below guides us through. In this case, Levene's test can be used to see if homogeneity is met. Homogeneity is only needed for (sharply) unequal sample sizes. homogeneity: the variance of the dependent variable must be equal in each subpopulation.Normality is not needed for reasonable sample sizes, say each n ≥ 25. normality: the dependent variable is normally distributed in the population.Precisely, the assumption is “independent and identically distributed variables” but a thorough explanation is way beyond the scope of this tutorial. independent observations: each record in the data must be a distinct and independent entity.However, it requires some assumptions regarding our data. In this case, we may conclude that this null hypothesis probably wasn't true after all.ĪNOVA will basically tells us to what extent our null hypothesis is credible. However, very different sample means contradict the hypothesis that the population means are equal. If this is true, then our sample means will probably differ a bit anyway. But what do our sample means say about the population means? Can we say anything about the effects of fertilizers on all (future) plants? We'll try to do so by refuting the statement that all fertilizers perform equally: our null hypothesis. Now, this table tells us a lot about our samples of plants. “Biological” has a slightly higher standard deviation than the other conditions but the difference is pretty small.“None” performed worst at some 51 grams while “Biological” is in between. Second, the chemical fertilizer resulted in the highest mean weight of almost 57 grams.We have sample sizes of n = 30 for each fertilizer.means grams by fertilizer /cells count mean stddev. *Basic descriptives table for grams by fertilizer.
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