What's the difference between aov() and anova() in R? How are they used?
aov() performs 1 way ANOVA. The generic anova() is used to compute the analysis of variance (or deviance) tables for one or more fitted model objects (Type I). The anova() in the car package may be used to get the two way ANOVA table.To run an ANOVA using aov() run the function, store the output and use extraction functions to use what you need, e.g.: >aov.out = aov(count ~ spray, data=InsectSprays) >summary(aov.out)To produce an Analysis of Variance table for a model:>anova(plant.mod1) Analysis of Variance TableResponse: weight Df Sum Sq Mean Sq F value Pr(>F) group 2 3.7663 1.8832 4.8461 0.01591 * Residuals 27 10.4921 0.3886--- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
How is an ANOVA different from a t-test?
An ANOVA is a statistical method for determining the statistical significance of differences among a SET of 2 or more means. Whereas the t-test is a significance test that uses a theoretical distribution to determine the significance of experimental results based on small [single] samples. Basically a t-test is used when you have about 10 participants and you are using a pre and post-test; the t-test allows you to know to significant difference between the pre & post test. The ANOVA is used when there are a set of two or more groups to determine significance. For example, if you have 5 groups of college students in your study equaling 25 students to determine which beverage (mt dew, water, beer, coke, fruit juice) makes them pee more, you'd use an ANOVA to determine which beverage makes you pee more. The t-test is easier to do, but the ANOVA will show more statistical significance in your data. The chi square will allow even more than both the t-test and the ANOVA.
What is the difference between one-way ANOVA and two-way ANOVA?
An example of when a one-way ANOVA could be used is if you want to determine if there is a difference in the mean height of stalks of three different types of seeds. Since there is more than one mean, you can use a one-way ANOVA since there is only one factor that could be making the heights different. Now, if take these three different types of seeds, and then add the possibility that four different types of fertilizer is used, then you would want to use a two-way ANOVA. The mean height of the stalks could be different for a combination of several reasons: The types of seed could cause the change, the types of fertilizer could cause the change, and/or there is an interaction between the type of seed and the type of fertilizer. There are two factors here (type of seed and type of fertilizer), so, if the assumptions hold, then you can use a two-way ANOVA.
Is ANOVA a type of factor analysis, or are they completely different things?
They are answering different questions. In ANOVA, we have a "response variable" (for example, height) measured on some subjects who are divided into groups. We want to know how the response variable differs from group to group and whether the groups are different from each other in terms of the average response. (Are people's average heights significantly different by eye color?)In factor analysis, there is no single "response variable." Instead, we have several measurements on each subject, e.g. scores on a battery of tests. We want to know if there is a smaller number of variables (e.g. mathematical ability, verbal ability) which could explain the scores.
What is ANOVA?
Analysis of variance.That's not a very useful description though. There are many different levels that this question can be answered on.There's the practical description: It's a statistical test that's used when you have categorical predictor(s) of a continuous outcome variable in order to test for significance of difference of means.There's the historical description: It's the method, devised by Fisher, which allowed people to get least squares estimates of parameters (and their standard errors) with orthogonal and categorical predictor variables, without doing matrix algebra.There's the conceptual description: If you have three groups of individuals, each of which have a response on a continuous variable, you'll have some variance on that continuous measure. You can also calculate the variance within each of the groups, and the variance between each of the groups. Analysis of variance compares those variances - specifically, the more variance there is between the groups, relative to the variance within the groups, the larger the differences between the means of the groups, relative to the variance.There's a mathematical description too, but it's too late ...If you elaborate on what you're interested in, I (or someone else) can give a better answer.