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Published byMelanie Elliott Modified over 3 years ago

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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

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t Distribution In Chapter 6, you were introduced to the Normal Distribution In this chapter, we will explore another distribution –t distribution

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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

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Hypothesis Testing Hypothesis testing based on sample evidence and probability theory used to determine whether the hypothesis should or should not be rejected

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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

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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

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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

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Steps in Hypothesis Testing

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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

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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

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Decisions Under the Null Hypothesis

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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

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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

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SPSS Step 1 Open data set

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SPSS Step 2 Select Compare Means and then Independent Samples T Test

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SPSS Step 3 Select the test variable and then the grouping variable

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SPSS Step 4 Define the groups or use the Cut Point to divide a continuous-level variable

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SPSS Step 5 Mouse Click OK to obtain results

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SPSS Output

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