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

The Null Hypothesis The research hypothesis is not tested directly –Instead, we test the null hypothesis (H 0 ): 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 H 0 –if greater than, retain H 0

Decisions Under the Null Hypothesis

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