Question

In your own words, compare and contrast the purposes of each type of t-test (single, independent, and repeated). Under what conditions/circumstances should you use each type? Include in your discussion the types of samples, comparisons, variance, pooled variance, matched-pair, individual differences, # of samples involved, etc. This is not a simple question and requires a comprehensive response to cover all aspects. As it states above, the responses should be mostly in your own words, but you can cite sources to support your statements.

Answer 1

T-Test

Assumptions :

1. When we use T test we always assume data is normally distributed and (n < 30 ) that assumption can ignored.

2. Population standard deviation is not given.

Single T test : When single data or one set of observation is given , Standard deviation is not given and then we use Single T test.

In this test we use sample variance ( ) for calculation.

Independent Test : When two set of observation is given and two sets of conditions are different means one set do not depends on other then we use Independent T test.

When Population standard deviation or population variances is not equal ( ) and we assume that both variances or standard deviations are equation then we use variance as .

When Population standard deviation or population variances is equal ( ) Then we use pooled variances

Repeated T test : When two set of observation is given and two sets of conditions are not different means one set is depends on other then we use Repeated T test. (eg . After and before data)

Here individual differences can be computed ( X1 , X2 , D = X1 -X2 , We take average for D and variance of D )