为什么与excel和手动计算相比，使用R获得单向方差分析输出的方式有所不同？

Question

I'm new to R, so might be doing something wrong, but I've searched many different ways of doing the same thing, and still get the same results. I have the following data (15 measures, 3 factors, 5 measures in each): measures:

##factors: 1, 2, 3

         Y    Z
1     43.0    1
2     40.5    1
3     39.6    1
4     44.9    1
5     37.2    1
6     44.4    2
7     40.5    2
8     40.1    2
9     43.3    2
10    36.1    2
11    41.1    3
12    39.2    3
13    36.4    3
14    37.2    3
15    36.7    3

When I perform a one-way anova in R, using > anova(lm(Y~Z, data=data)) , I get F=2.7934, p=0.1185 and Df=1. I get the same result using aov and AOVModel functions too.

However, both Excel and the manual calculations (and Minitab, actaully) give me F=1.728 and p=0.219, with 2 degrees of freedom. I cannot understand this - what am I doing wrong?

Thanks

Answer 1

This is because you have the data$Z as a numeric variable. See Dason's comment above. So you'd want to convert Z to a factor (I renamed data to dat as data is the name of an R base object). Here's how:

dat$Z <- as.factor(dat$Z)

Yielding:

> anova(lm(Y~Z, data=dat))
Analysis of Variance Table

Response: Y
          Df Sum Sq Mean Sq F value Pr(>F)
Z          2 26.949 13.4747  1.7281  0.219
Residuals 12 93.568  7.7973  

Side note use str to see how your variables are stored. It's one of the most used R functions.

So...

str(dat) would have told you:

> str(dat)
'data.frame':   15 obs. of  2 variables:
 $ Y: num  43 40.5 39.6 44.9 37.2 44.4 40.5 40.1 43.3 36.1 ...
 $ Z: int  1 1 1 1 1 2 2 2 2 2 ...

And after the factor conversion:

> str(dat)
'data.frame':   15 obs. of  2 variables:
 $ Y: num  43 40.5 39.6 44.9 37.2 44.4 40.5 40.1 43.3 36.1 ...
 $ Z: Factor w/ 3 levels "1","2","3": 1 1 1 1 1 2 2 2 2 2 ...