Student's t-test

Student's t-test

• Background
• developed by Gusset working at Guinness Brewery
• Problems with the Normal Distribution
• Gossett discovers the t distribution
• Publishes it under an assumed name-student

Calculation of Z scores require knowledge of population parameter

• Population Mean
• Population Standard Deviation and Standard Error
• Small samples do not provide reliable enough estimates of population parameters

Characteristics of the t distribution 

• Leptokurtic
• As n and v (df=v=n-1) increased the t distribution begins to approach a normal distribution

Types of Student's t tests

• One-sample Student's t test
• Two independent (unpaired) Samples Student's t test
• Two dependent (paired) Samples Student't test

One-sample Student's t test

• Used to compare a population mean inferred from a sample with a hypothetical population mean 

Two Independent (unpaired) Sample Student's t test

• Used to compare two independent population mean inferred from two samples (independent indicated that the value from both samples are numerical independent of each- there is no correlation 

Two dependent (paired) Samples Student's t test 

• Used to compare two dependent populations inferred from two samples (dependent indicates that the value from both samples are numerically dependent upon each other- there is a correlation between corresponding values)

Two variations of all Student's t test

• Two-tailed test
• One-tailed test 

Two-tailed test- evaluates whether a difference exists between 2 samples, not the direction of the difference

One-tailed test- evaluates whether a difference exists between 2 samples, and specifically evaluates the direction of the difference