When the LATD/NIP gene in Medicago truncatula is made inactive the root lengths of the plants are shorter.

The expected primary root lengths of the wild type (A17) plants are 17 cm with a standard deviation of 2. The expected primary root lengths of the mutant (latd) plants are 6 cm with a standard deviation of 2.

Simulation 1

Mean: Control = 17, latd = 6

control <- rnorm(n = 28, mean = 17, sd = 2) 
latd <- rnorm(n = 28, mean = 6, sd = 2)
df <- data.frame(control, latd)
t_test <- t.test(latd, control)
print(t_test)
## 
##  Welch Two Sample t-test
## 
## data:  latd and control
## t = -21.6, df = 53.218, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -11.847582  -9.834431
## sample estimates:
## mean of x mean of y 
##  6.460088 17.301095
boxplot(control, latd, 
        names = c('Control', 'latd'),
        ylab = 'Primary Root Length',
        title = 'Primary root Length: latd vs. Wild')

Mean: Control = 17, latd = 10

control <- rnorm(n = 28, mean = 17, sd = 2) 
latd <- rnorm(n = 28, mean = 10, sd = 2)
df <- data.frame(control, latd)
t_test <- t.test(latd, control)
print(t_test)
## 
##  Welch Two Sample t-test
## 
## data:  latd and control
## t = -11.855, df = 51.316, p-value = 2.592e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -6.918344 -4.914833
## sample estimates:
## mean of x mean of y 
##  10.15134  16.06793
boxplot(control, latd, 
        names = c('Control', 'latd'),
        ylab = 'Primary Root Length',
        title = 'Primary root Length: latd vs. Wild')

Mean: Control = 17, latd = 15

control <- rnorm(n = 28, mean = 17, sd = 2) 
latd <- rnorm(n = 28, mean = 15, sd = 2)
df <- data.frame(control, latd)
t_test <- t.test(latd, control)
print(t_test)
## 
##  Welch Two Sample t-test
## 
## data:  latd and control
## t = -3.1819, df = 52.851, p-value = 0.002451
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -3.2792661 -0.7433688
## sample estimates:
## mean of x mean of y 
##  15.22433  17.23565
boxplot(control, latd, 
        names = c('Control', 'latd'),
        ylab = 'Primary Root Length',
        title = 'Primary root Length: latd vs. Wild')

The lowest that I am able to go with the mean of the latd group is 15 before I get above a p-value of 0.05.

Sample size: 15

control <- rnorm(n = 15, mean = 17, sd = 2) 
latd <- rnorm(n = 15, mean = 6, sd = 2)
df <- data.frame(control, latd)
t_test <- t.test(latd, control)
print(t_test)
## 
##  Welch Two Sample t-test
## 
## data:  latd and control
## t = -15.036, df = 27.833, p-value = 6.885e-15
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -12.648396  -9.614523
## sample estimates:
## mean of x mean of y 
##  5.504394 16.635854
boxplot(control, latd, 
        names = c('Control', 'latd'),
        ylab = 'Primary Root Length',
        title = 'Primary root Length: latd vs. Wild')

Sample size: 5

control <- rnorm(n = 5, mean = 17, sd = 2) 
latd <- rnorm(n = 5, mean = 6, sd = 2)
df <- data.frame(control, latd)
t_test <- t.test(latd, control)
print(t_test)
## 
##  Welch Two Sample t-test
## 
## data:  latd and control
## t = -8.1239, df = 5.6633, p-value = 0.0002502
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -14.694755  -7.815734
## sample estimates:
## mean of x mean of y 
##   6.60823  17.86347
boxplot(control, latd, 
        names = c('Control', 'latd'),
        ylab = 'Primary Root Length',
        title = 'Primary root Length: latd vs. Wild')

Sample size: 2

control <- rnorm(n = 2, mean = 17, sd = 2) 
latd <- rnorm(n = 2, mean = 6, sd = 2)
df <- data.frame(control, latd)
t_test <- t.test(latd, control)
print(t_test)
## 
##  Welch Two Sample t-test
## 
## data:  latd and control
## t = -6.1375, df = 1.8583, p-value = 0.03037
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -21.844784  -3.051624
## sample estimates:
## mean of x mean of y 
##  5.325928 17.774132
boxplot(control, latd, 
        names = c('Control', 'latd'),
        ylab = 'Primary Root Length',
        title = 'Primary root Length: latd vs. Wild')

If I make the sample size 2 I still get a p-value that is below 0.05. 2 Is the lowest that I can go without getting an error in the t.test.