Cohens d

I asked google: How to correct for small p-value due to very large sample size?

and I got suggestion to use Cohens d. Here are the results.

You can read more about Effect size.

FDR _עב made to correct something else. Not big sample, but many questions.

library(effsize)
ws = read.csv("P val for rotem.csv")

Examples

treatment = rnorm(5000,mean=11, sd = 5000)
control = rnorm(5000,mean=10, sd = 5000)
d = (c(treatment,control))
f = rep(c("Treatment","Control"),each=1000)
## compute Cohen's d
## treatment and control
cohen.d(treatment,control)

Cohen's d

d estimate: 0.005496748 (negligible)
95 percent confidence interval:
        inf         sup 
-0.03370735  0.04470085 

treatment = rnorm(5000,mean=11, sd = 1)
control = rnorm(5000,mean=10, sd = 1)
d = (c(treatment,control))
f = rep(c("Treatment","Control"),each=1000)
## compute Cohen's d
## treatment and control
cohen.d(treatment,control)

Cohen's d

d estimate: 0.975917 (large)
95 percent confidence interval:
      inf       sup 
0.9344449 1.0173891 

Formula

\[ Cohen.d = (\bar 1-\bar 2)\div \sqrt{\frac{(N_1-1)\times SD_1^2 + (N_1-1)\times SD_2^2}{N_1+N_2 -2 }} \]

mean_1 = mean(treatment)
mean_2 = mean(control)
sd_1 = sd(treatment)
sd_2 = sd(control)
n_1 <- length(treatment)
n_2 <- length(control)
mean_diff <- mean_1 - mean_2
pooled_sd_n <- ((n_1-1)*(sd_1**2)) + ((n_1-1)*(sd_2**2))
pooled_sd_d <- ((n_1 + n_2) - 2)
pooled_sd <- sqrt(pooled_sd_n/pooled_sd_d)
cohens_d <- mean_diff / pooled_sd
cohens_d

[1] 0.975917

# d_ci <- cohen.d.ci(d = cohens_d, n1 = n_1, n2 = n_2, a=a_level)
# d_ci

The small difference between this value and the previous is something about alpha = 0.05 that I don’t understand completly.

View(ws)

gfp10 = ws[,1:2]
colnames(gfp10) <-  c("a", "b")
gfp10 = gfp10[3:length(gfp10$a),]
gfp10 = as.matrix(gfp10)
gfp10 = apply(gfp10, 2, as.numeric)
gfp2 = ws[,7:11]
colnames(gfp2) = c("4", "8","GFP+AMP8", "24", "GFP+AMP24")
gfp2 = gfp2[4:length(gfp2$'4'),]
gfp2 = apply(gfp2, 2, as.numeric)
AlonaComment = ws[1:2,13]

Results

Explanation for values: Sign (+/-) is not significant and just sign the direction of the change.

• Numbers smaller than 0.2 considers small and the difference between group is small.
• Numbers below 0.8 are marginal with some diffrence between means.
• Numbers above 0.8 are high and group are differ each other.

ten = cohen.d(d = as.numeric(gfp10[,2]),f = as.numeric(gfp10[,1]), paired = F, na.rm = T)
ten$estimate

Treatment 
0.3148121 

amp = cohen.d(as.numeric(gfp2[,3]), as.numeric(gfp2[,5]), na.rm = T, paired = F)
amp$estimate

Treatment 
-1.799924 

foureight = cohen.d(as.numeric(gfp2[,1]), as.numeric(gfp2[,2]), na.rm = T, paired = F)
four24 = cohen.d(as.numeric(gfp2[,1]), as.numeric(gfp2[,4]), na.rm = T, paired = F)
eight24 = cohen.d(as.numeric(gfp2[,2]), as.numeric(gfp2[,4]), na.rm = T, paired = F)
foureight$estimate

Treatment 
-2.370494 

four24$estimate

Treatment 
-3.564258 

eight24$estimate

Treatment 
-1.506389 

citation("effsize")

To cite package ‘effsize’ in publications use:

  Marco Torchiano (2017). effsize: Efficient Effect Size Computation. R package version 0.7.1.
  https://CRAN.R-project.org/package=effsize

A BibTeX entry for LaTeX users is

  @Manual{,
    title = {effsize: Efficient Effect Size Computation},
    author = {Marco Torchiano},
    year = {2017},
    note = {R package version 0.7.1},
    url = {https://CRAN.R-project.org/package=effsize},
  }