Learning Objectives
In this chapter you will learn
about the t-test and its distribution
t-test for related samples
t-test for independent samples
hypothesis testing
how to use SPSS to test for
differences between means
t Distribution
In Chapter 6, you were introduced
to the Normal Distribution
In this chapter, we will explore
another distribution
– t distribution
t Distribution
If the sample size is less than 30
–use the t distribution
• to calculate confidence intervals
–as sample size increases
• t distribution approximates the
normal distribution
• the shape of t distribution is not fixed
Hypothesis Testing
Hypothesis testing
• based on sample evidence and
probability theory
• used to determine whether the
hypothesis should or should not
be rejected
Important Terms
Null Hypothesis
• A statement about the expected
value of a population parameter
Alternative Hypothesis
• Research statement that is accepted
– if the sample data suggest that the null
hypothesis should be rejected
Type I & Type II Errors
Type I Error
• Rejecting the null hypothesis
when it is actually true
Type II Error ()
• Accepting the null hypothesis
when it is actually false
Type I Errors
The chance of making a Type I error
is known as the level of
significance or the alpha level
()
– it is set by the researcher
– the convention is to use the .05 level
of significance as the probability of
committing Type I error
Steps in Hypothesis
Testing
S te p 1 : S ta te n u ll a n d a lte rn a tiv e h yp o th e s e s
O n e - ta ile d o r tw o - ta ile d te s t?
S tep 2: S ele ct a le v e l of sig n ific an ce
S te p 3 : Id e n tify a p p r o p r ia te sta tis tic
S te p 4 : C o lle c t a n d a n a lyz e d a ta
S te p 5 : R e a c h a d e c is io n
D o n o t r e je c t n u ll
R e je c t n u ll a n d a cc e p t a lte r n a tiv e
The Null Hypothesis
The research hypothesis is not tested
directly
– Instead, we test the null hypothesis
(H0): the hypothesis of no difference or no
relationship
– We can never prove a hypothesis to be
true
– Instead, we are searching for instance
when it is not true
Accept or Reject?
Compare the test statistic
(obtained value) to the alpha
level and decide if it is greater
or less than alpha
–if less than, reject H0
–if greater than, retain H0
Decisions Under the Null
Hypothesis
D e cisio n
H 0 is T ru e
H 0 is False
R e je ct
H0
T yp e I E rro r
C o rre ct
A cce p t
H0
C o rre ct
T yp e II E rro r
t Test
We frequently want to compare
means
–different tests based on sample
• paired t test for related sample
• independent t test when samples are
not related somehow
SPSS Procedure
The following slides demonstrate
the independent t test
–don’t forget to
• test for equality of variance
• define the group either by specifying a
group number (discrete variable) or by
using the cut point (perhaps the
median) if the variable is continuous
SPSS Step 1
Open data
set
SPSS Step 2
Select Compare Means
and then Independent
Samples T Test
SPSS Step 3
Select the test
variable and
then the
grouping
variable
SPSS Step 4
Define the
groups or use
the Cut Point to
divide a
continuous-level
variable
SPSS Step 5
Mouse Click
OK to obtain
results
SPSS Output