Question

1.What is the relationship between the LSD and a Z score? (R programming Language)

Write a fragment of code comparing how both would be computed. Use the Z score for the standard error of a mean,

$z_i = (x_i - \mu)/(\sigma / \sqrt(n))$

2. How would you modify the calculations of LSD to produce Tukey's Honest Signficant Difference?

Answer 1

The main difference/relationship between LSD and z-score is that z score is used to assess that whether means of two samples (independent or paired) are statistically different or not but it does not tell us what is the exact difference. LSD is used when we have more than two groups and want to know that what is the exact difference between the means of all the samples.

For example - If you have 5 samples, you would not apply z test by taking two samples at a time. It will take a lot of time. Hence, you will apply LSD directly on it.

R programming code for LSD:

library(agricolae) #installing the library agricolae first

(LSD.test(model, "Group",
           alpha = 0.05,       
           p.adj="none"))

R programming code for Z-Score:

z.test(x, y = NULL, alternative = "two.sided", mu = 0, conf.level = 0.95)

2. How to modify the calculations of LSD to produce Tukey HSD:

LSD is calculated using the following formula in R:

LSD =

Here, MSE = Mean square Error

n* = number of scores used

To calculcate HSD: Modification can be done in the above formula, instead of t value, we have to use the q value to calculate HSD. Rest of the formula remains the same.

HSD = q *

q value is obtained using the q statistic table.