How to calculate a p-value for an ANOVA F-Statistic using R or a TI-84
At the end of calculating an Analysis of Variance (ANOVA), you have an F-statistic. To get the p-value of the F-Statistic, you can use R or the TI-84:
For example, in an ANOVA with treatment degrees of freedom = 1 and error degrees of freedom = 10, you calculate the F-Statistic as 2.81 and want to know its p-value (that is, what is the probability of observing this F-Statistic under the Null Hypothesis?):
1) R
# The following calculates the p-value of an F-statistic
pf(q=2.81, df1=1, df2=10, lower.tail=FALSE)
You'll get the answer:
[1] 0.1246126
2) TI-84
The syntax for the Fcdf command is:
Fcdf(lower limit, upper limit, numerator degrees of freedom, denominator degrees of freedom).
Fcdf(2.81, 99999, 1, 10)
You'll get the answer:
[1] 0.1246126
I'm a student in the MS in Applied Statistics program and the University of the District of Columbia.
Thanks! It's always hard to find R help online, but this helped me answer part of a HW assignment
ReplyDeleteDear Timothy,
ReplyDeleteI hope you can help!
I have a model that reports as per summary below.
I need to obtain the F Statistic and Degrees of freedom values? How do I get these from this summary or per command?
> summary(modelnp)
Call:
lm(formula = data2, data = data2)
Residuals:
Min 1Q Median 3Q Max
-0.91777 -0.28089 0.03571 0.23273 0.82883
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 10.572610 8.862711 1.193 0.238760
Roi9 -0.105219 0.042237 -2.491 0.016244 *
Roi14 0.199637 0.033340 5.988 2.62e-07 ***
Roi38 0.023947 0.006492 3.689 0.000574 ***
Roi39 -0.012495 0.003821 -3.270 0.001991 **
Roi42 0.045623 0.018258 2.499 0.015940 *
Roi44 -0.027964 0.018030 -1.551 0.127476
Roi47 -0.133500 0.026998 -4.945 9.73e-06 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.3872 on 48 degrees of freedom
Multiple R-squared: 0.7737, Adjusted R-squared: 0.7407
F-statistic: 23.44 on 7 and 48 DF, p-value: 1.792e-13