Chapter 11 t(ea) for Two:

Tests Between the Means of Different Groups

Part IVSignificantly Different:

Using Inferential Statistics

What you will learn in Chapter 11

When to use a t testHow to compute the observed t valueInterpreting the t value and what it means

t Test for Independent SamplesDetermining the correct statistic

Computing the Test Statistic

Numerator is the difference between the means

Denominator is the amount of variation within and between each of the two groups

2 2

D

D ( D)1

tn

n

Degrees of Freedom

The degrees of freedom approximates the sample size

Degrees of freedom can vary based on the test statistic selected

For this procedure…n1 – 1 + n2 – 2

So How Do I Interpret…

t (58) = -.14, p > .05

t represents the test statistic used58 is the number of degrees of freedom-.14 is the obtained value (from the formula)p > .05 indicates the probability

Special Effects…

Effect size is a measure of how different two groups are from one another

Standardized difference between two group means

Jacob Cohen

Computing Effect Size

Small = 0.0 - .20Medium = .20 - .50Large = .50 and above

1 2ES

X X

SD

Effect Size Calculator

http://web.uccs.edu/lbecker/Psy590/escalc3.htm

Using the ComputerComputing a t Test using SPSS

SPSS OutputWhat does it all mean?

Glossary Terms to Know

Degrees of freedomt Test

Independent t TestObtained valueCritical value

Effect size

Chapter 12 t(ea) for Two (Again):

Tests Between the Means of Related Groups

Part IVSignificantly Different:

Using Inferential Statistics

What you will learn in Chapter 12

When to use a t test for dependent meansHow to compute the observed t valueInterpreting the t value and what it means

t Test for Dependent SamplesDetermining the correct statistic

Computing the Test Statistic

Numerator reflects the sum of the differences between two groups

1 2

2 21 1 1 2 1 2

1 2 1 2

,( 1) ( 1)

2

X Xt

n s n s n n

n n n n

Degrees of Freedom

The degrees of freedom approximates the sample size

Degrees of freedom can vary based on the test statistic selected

For this procedure…n – 1 (where n is the number of observations)

So How Do I Interpret…

t (24) = 2.45, p > .05

t represents the test statistic used24 is the number of degrees of freedom2.45 is the obtained value (from the formula)p > .05 indicates the probability

Using the ComputerSPSS and Paired Samples t Test

SPSS OutputWhat does it all mean?