Testing Hypotheses for Means

           

     

           

                 

                                         

                                             

   

                                               

                                                           

                         

                                                     

                                                                     

                                     

                                           

                 

                                                                               

                   

       

                                 

                                                                                                                       

The t Test for Related Samples

The t Test for Related  Samples Program Transcript

MATT JONES: As  its  name implies, the independent samples  t-­test has  the assumption of the independence of observations. But that's not always  the case. Sometimes  we take multiple observations  of the same unit of analysis, such as  a person, over  time. In this  case, we'll use a paired sample t-­test, sometimes   referred to as  the dependent sample t-­test. Let's go to SPSS  to see how we do this.

To perform  the paired sample t-­test in SPSS, we once again go to Analyze, Compare Means, and down to the Paired Sample T-­test. SPSS  doesn't require much information here;; only  the pair  of variables  of which we would like to test. We have a simulated data set here for  statistical anxiety  of students. Students   were provided with an instrument that measures  their  anxiety  around statistical topics  on a number  of different constructs-­-­ teachers, interpretation, asking for   help, worth, and self-­conceptualization.

They  were given the test at the beginning of the class  and at the conclusion of a class. Hence, why  in the value labels  we see pre-­test and post-­test. As  a teacher, I might have some interest in determining whether  students  felt more comfortable with me or  had lowering anxiety  over  time. This  is  perfect for  a paired sample t-­ test. To perform  this  paired sample t-­test, we'll go to Analyze, Compare Means, the Paired Sample T-­test.

SPSS doesn't ask  for  much information;; only  the pair  of variables  of which I would like to test. In this  case, teacher  pre-­test and teacher  post-­test. So this  is  a classic  before and after. The first piece of output I obtain from  the paired sample t-­test are some descriptive statistics, specifically  around the pairwise comparison I'm looking at, which is  the teacher  subscale pre-­test and post-­test.

I see that there is  mean on the pre-­test of 17.32 and on the post-­test, an 18.44. So it appears, at least from  a descriptive sense, that there is  a higher  mean on the post-­test than the pre-­test. On the instrument, higher  scores  on an item  or  the subscale indicate higher  levels  of anxiety  for  that specific  attitude. Except for  this   specific  subscale, fear  of statistics  teachers, where higher  scores  actually   indicate lower  levels  of anxiety.

So if post scores  are higher  than pre scores, that means  on average, students   feel lower  levels  of anxiety  and more positive attitude about their  statistics   teacher. I can see here, at least from  a descriptive sense, that that appears  to be the case. But from  the sample, I am  performing a test of statistical significance. Next to the mean, I'm provided with the sample size 25-­-­ 25 observations  pre-­test and 25 observations  post-­test, all the same person-­-­ the standard deviation for   the pre-­test and the post-­test, and the standard error  of the mean.

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The t Test for Related Samples

Next, let's go down and interpret the paired sample test itself. We can see that on average, there was  a difference of 1.12 units  on the scale with a standard deviation of 2.50. From  the 95% confidence interval, we see that the true difference is  somewhere between 2.15 and 0.085. We have a t-­statistic  of 2.235 and an associated p-­value of 0.035.

At the 0.05 level, the results  are statistically  significant and we can say  that there is  a significant difference between pre-­test scores  and post-­test scores. Therefore, we can reject the null hypothesis  that there is  no difference. On average, it appears  on the post-­test, students  had lower  levels  of anxiety  about their  statistics  teacher.

This  last example illustrated that students  felt more comfortable with statistics  as   time progressed and specifically  felt less  anxious  about their  statistics  instructor. I certainly  hope this  example rings  true for  you, and that you feel comfortable or  at least don't self-­identify  as  being anxious  about statistics  at the conclusion of this   course. I encourage you to review your  textbook, review the videos, ask  your   instructor  for  help, and also research the resources  here available at Walden University  to help you succeed.

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