Question

when calculating the related samples t statistic, what is the effect of an increase in the standard deviation for a sample of difference scores, assuming n is held comstant?

a an increase in the standard error and an increase in the value of t

b a decrease in the standard error and a decrease in the value of

c an increase in the standard error and a decrease in the value of t

d a decrease in the standard error and an increase in the value of t

Answer 1

Ans : c an increase in standard error and a decrease in the value of the .

Let X represents a set of values with size n, with mean m and with standard deviation S. The comparison of the observed mean (m) of the population to a theoretical value μ. So test statistic given as ,

t=(m−μ) / (s/√n )

So clearly standard error = s/√n

As s increases standard error increases. assuming n is fixed.

And as standard error increases the value of test statistic t is decrease.