The "R-Word"

 

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People with disabilities have abilities too and that is what this course is all about - making sure those abilities blossom and shine so that all the dreams you have can come true.

Mary McAleese
Data                        Graphs
 

 Sampling Method

Our population of interest was all of the teachers and students in North Olmsted High School. To obtain our sample we put two comprehensive lists (one of all of the teachers at North Olmsted High School and one of all of the students at North Olmsted High School) into Minitab. We then used Minitab to generate a random list of 100 students and 11 teachers. We then looked up the students schedules to find a class to send the survey to, and for the teachers we put in their mailboxes at the school. Each survey was labeled with a post-it note, which stated the student’s name, class period, and teacher’s name. Therefore, the student could receive the survey then remove the post-it note, to keep their identity anonymous. Once completing the survey they would give the survey to their teacher, and the teachers would return them to the statistics class. The sample space contained only North Olmsted high school students, and teachers.   

 

  Sample Survey
Please circle a choice for each of the following questions:

1. How often do you use the word “retard” or “retarded”?
Everyday     A Few Times a Week Once Every Few Months       Never Not Sure

2. When you use “retard” or “retarded” do you use it as a medical term?
Yes                 No

3. Do you personally know someone with a mental or physical disability?
Yes              No
 Hypothesis Tests

1.)  H0: There is no association between whether or not a student has a personal relationship with someone with an intellectual disability and how frequent they use the r-word.

2.)  Ha: There is an association.

3.)    α = 0.05

4.)  Assumptions: The cell count was based on an independent random sample. Also we must assume that all expected cell counts are greater than four. Because of first test using all 5 frequency categories failed to produce expected cell counts of greater than 5, we grouped these frequencies into two categories-Everyday & A Few Times a Week (category A) and Once Every Few Months, Never, & Not Sure (category B). Below is a table of new expected cell counts:

  A B Total
No 9 9 18
Yes 34 22 56
Total 43 31 74

 

5.)   

6.) 

Pearson Chi-Square = 0.642, DF = 1, P-Value = 0.423

Likelihood Ratio Chi-Square = 0.637, DF = 1, P-Value = 0.425

X2 = 0.642 with 1 df

7.)  P-value = 0.423

8.)  We fail to reject the null hypothesis at the 0.05 level of significance because the p-value is greater than alpha. Therefore, we have insufficient evidence to say that there is an association between whether or not a student has a personal relationship with someone with an intellectual disability and how frequent they use the r-word.

 

1.)  H0: There is no association between whether or not a student uses the word as a medical term and how frequent they use the r-word.

2.)  Ha: There is an association.

3.)    α = 0.10

4.)  Assumptions: The cell count was based on an independent random sample. Also we must assume that all expected cell counts are greater than four. Because of first test using all 5 frequency categories failed to produce expected cell counts of greater than 5, we grouped these frequencies into two categories-Everyday & A Few Times a Week (category A) and Once Every Few Months, Never, & Not Sure (category B). Below is a table of new expected cell counts:

  A B Total
No 38 22 60
Yes 5 9 14
Total 43 31 74

5.)   

6.) 

Pearson Chi-Square = 3.557, DF = 1, P-Value = 0.059

Likelihood Ratio Chi-Square = 3.523, DF = 1, P-Value = 0.061

X2 = 0.3577 with 1 df

7.)  P-value = 0.423

8.)  We reject the null hypothesis at the 0.05 level of significance because the p-value is greater than alpha. Therefore, we have sufficient evidence to say that there is an association between whether or not a student uses the r-word as a medical term and how frequent they use the r-word.

 

1.)  H0: There is no association between whether the responder is a teacher or a student and how frequent the responder uses the r-word.

2.)  Ha: There is an association.

3.)    α = 0.05

4.)  Assumptions: The cell count was based on an independent random sample. Also we must assume that all expected cell counts are greater than four. Because of first test using all 5 frequency categories failed to produce expected cell counts of greater than 5, we grouped these frequencies into two categories-Everyday & A Few Times a Week (category A) and Once Every Few Months, Never, & Not Sure (category B). However, this too yielded expected cell counts that were less than 5.

  A B Total
Student 43 31 74
Teacher 0 9 9
Total 43 40 83

5.)   

 

6.) 

Pearson Chi-Square = 10.852, DF = 1, P-Value = 0.001

Likelihood Ratio Chi-Square = 14.323, DF = 1, P-Value = 0.000

 X2 = 10.852 with 1 df

7.)  P-value = 0.001

8.)  We reject the null hypothesis at the any reasonable level of significance because the p-value is less than alpha. Therefore, we have sufficient evidence to say that there is an association between whether the responder is a teacher or a student and how frequent the responder uses the r-word.