## Null-hypothesis for a Factorial Analysis of Variance (ANOVA).ANOVA.

### The one way analysis of variance (ANOVA) Write the null hypothesis:.

Two population testing in statistics can be performed using an test. While the compares means, ANOVA compares the variance between the populations. A Two way ANOVA in Excel without replication can compare a group of individuals performing more than one task. For example, you could compare students’ scores across a battery of tests. If you have more than one group (say, from two different colleges), use the .

### Two-way factorial ANOVA in PASW (SPSS)

In the olden days, when people looked up *P* values in printed tables, they would report the results of a statistical test as "*P**P**P*>0.10", etc. Nowadays, almost all computer statistics programs give the exact *P* value resulting from a statistical test, such as *P*=0.029, and that's what you should report in your publications. You will conclude that the results are either significant or they're not significant; they either reject the null hypothesis (if *P* is below your pre-determined significance level) or don't reject the null hypothesis (if *P* is above your significance level). But other people will want to know if your results are "strongly" significant (*P* much less than 0.05), which will give them more confidence in your results than if they were "barely" significant (*P*=0.043, for example). In addition, other researchers will need the exact *P* value if they want to combine your results with others into a .

If you are using SAS to do a two-way anova without replication, do not put an interaction term in the model statement (sex*genotype is the interaction term in the example above).

## Two-way ANOVA determines how a response is affected by ..

A two-way anova with replication tests three : that the means of observations grouped by one factor are the same; that the means of observations grouped by the other factor are the same; and that there is no interaction between the two factors. The interaction test tells you whether the effects of one factor depend on the other factor. In the amphipod example, imagine that female amphipods of each genotype have about the same MPI activity, while male amphipods with the SS genotype had much lower MPI activity than male FF or FS amphipods (they don't, but imagine they do for a moment). The different effects of genotype on activity in female and male amphipods would result in a significant interaction term in the anova, meaning that the effect of genotype on activity would depend on whether you were looking at males or females. If there were no interaction, the differences among genotypes in enzyme activity would be the same for males and females, and the difference in activity between males and females would be the same for each of the three genotypes.

## anova - What is the null hypothesis of a MANOVA? - …

**Randomized blocks:** Another experimental design that is analyzed by a two-way anova is randomized blocks. This often occurs in agriculture, where you may want to test different treatments on small plots within larger blocks of land. Because the larger blocks may differ in some way that may affect the measurement variable, the data are analyzed with a two-way anova, with the block as one of the nominal variables. Each treatment is applied to one or more plot within the larger block, and the positions of the treatments are assigned at random. This is most commonly done without replication (one plot per block), but it can be done with replication as well.

## The null hypothesis $H_0$ of a one-way ANOVA is that the means of ..

Another way your data can fool you is when you don't reject the null hypothesis, even though it's not true. If the true proportion of female chicks is 51%, the null hypothesis of a 50% proportion is not true, but you're unlikely to get a significant difference from the null hypothesis unless you have a huge sample size. Failing to reject the null hypothesis, even though it's not true, is a "false negative" or "Type II error." This is why we never say that our data shows the null hypothesis to be true; all we can say is that we haven't rejected the null hypothesis.