Thank you very much. If I get it right, the CI get wider, my test has less power and the probability of getting a significant relation decreases. What about the significant coefficients, are they reliable?
Message du 20/10/14 ? 11h30
De : "Roman Lu?trik"
A : "V. Coudrain"
Copie ? : "r-sig-ecology at r-project.org"
Objet : Re: [R-sig-eco] Regression with few observations per factor level
I think you can, but the confidence intervals will be rather large due to number of samples.
Notice how standard errors change for sample size (per group) from 4 to 30.
pg <- 4 # pg = per group> my.df <- data.frame(var = c(rnorm(pg, mean = 3), rnorm(pg, mean = 1), rnorm(pg, mean = 11), rnorm(pg, mean = 30)), + trt = rep(c("trt1", "trt2", "trt3", "trt4"), each = pg), + cov = runif(pg*4)) # 4 groups> summary(lm(var ~ trt + cov, data = my.df))
Call:lm(formula = var ~ trt + cov, data = my.df)
Residuals: Min 1Q Median 3Q Max -1.63861 -0.46080 0.03332 0.66380 1.27974
Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 1.2345 1.0218 1.208 0.252 trttrt2 -0.7759 0.8667 -0.895 0.390 trttrt3 7.8503 0.8308 9.449 1.3e-06 ***trttrt4 28.2685 0.9050 31.236 4.3e-12 ***cov 1.4027 1.1639 1.205 0.253 ---Signif. codes: 0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1
Residual standard error: 1.154 on 11 degrees of freedomMultiple R-squared: 0.9932,Adjusted R-squared: 0.9908 F-statistic: 404.4 on 4 and 11 DF, p-value: 7.467e-12
pg <- 30 # pg = per group> my.df <- data.frame(var = c(rnorm(pg, mean = 3), rnorm(pg, mean = 1), rnorm(pg, mean = 11), rnorm(pg, mean = 30)), + trt = rep(c("trt1", "trt2", "trt3", "trt4"), each = pg), + cov = runif(pg*4)) # 4 groups> summary(lm(var ~ trt + cov, data = my.df))
Call:lm(formula = var ~ trt + cov, data = my.df)
Residuals: Min 1Q Median 3Q Max -2.5778 -0.6584 -0.0185 0.6423 3.2077
Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 2.76961 0.25232 10.977 < 2e-16 ***trttrt2 -1.75490 0.28546 -6.148 1.17e-08 ***trttrt3 8.40521 0.28251 29.752 < 2e-16 ***trttrt4 27.04095 0.28286 95.599 < 2e-16 ***cov 0.05129 0.32523 0.158 0.875 ---Signif. codes: 0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1
Residual standard error: 1.094 on 115 degrees of freedomMultiple R-squared: 0.9913,Adjusted R-squared: 0.991 F-statistic: 3269 on 4 and 115 DF, p-value: < 2.2e-16
On Mon, Oct 20, 2014 at 10:53 AM, V. Coudrain wrote:
Hi, I would like to test the impact of a treatment of some variable using regression (e.g. lm(var ~ trt + cov)). However I only have four observations per factor level. Is it still possible to apply a regression with such a small sample size. I think that i should be difficult to correctly estimate variance.Do you think that I rather should compute a non-parametric test such as Kruskal-Wallis? However I need to include covariables in my models and I am not sure if basic non-parametric tests are suitable for this. Thanks for any suggestion.