difference between means

Learning ObjectivesIn this chapter you will learn

about the t-test and its distributiont-test for related samplest-test for independent samples

hypothesis testinghow to use SPSS to test for differences between means

t DistributionIn Chapter 6, you were

introduced to the Normal Distribution

In this chapter, we will explore another distribution– t distribution

t DistributionIf 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 TestingHypothesis testing•based on sample evidence

and probability theory•used to determine whether

the hypothesis should or should not be rejected

Important TermsNull Hypothesis• A statement about the expected

value of a population parameterAlternative 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 trueType II Error () •Accepting the null hypothesis

when it is actually false

Type I ErrorsThe 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

One-tailed or two-tailed test?

Do not reject null Reject null and accept alternative

Step 5: Reach a decision

Step 4: Collect and analyze data

Step 3: Identify appropriate statistic

Step 2: Select a level of significance

Step 1: State null and alternative hypotheses

The Null HypothesisThe 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 HypothesisDecision H0 is True H0 is False

Reject H0

Type I Error Correct

Accept H0

Correct Type II Error

t TestWe 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 ProcedureThe 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