educational statistics and spss

Practice Exercise 24: Determining the Appropriate Analysis For each of the following scenarios, identify the appropriate analysis.

1. The question is whether verbal reinforcement affects response rates. Subjects in Group 1 were verbally reinforced every time they respond to the instructor’s questions. Subjects in Group 2 were not. After 2 weeks, the two groups were compared by gauging the number of students who raised their hand when questions were asked. The following data were collected.

Group 1: 13, 15, 12, 17, 14, 14, Group 2: 10, 12, 12, 11, 13, 9

2. A guidance counselor at a high school wants to be best informed about the universities and colleges that students prefer most frequently. He glances at the institutions attended by last year’s graduates and notes that the three closet colleges appear to have about equal appeal. To test this assumption, he begins asking students who are planning on postsecondary schooling where they will apply. His data are as follows:

The technical institute: 22 The community college: 18 The comprehensive university: 12

3. A biology instructor wishes to know if there is a difference between performance on a state developed benchmark test and her comprehensive final examination. To maintain consistency, both test included the same number of questions (100), and the instructor used the number of items correct as the grade. The following data were collected from a sample of 10 students.

Student State exam Biology

final Student State exam Biology

final 1 2 3 4 5

56 73 61 85 43

63 74 73 81 57

6 7 8 9 10

60 45 86 79 92

65 51 84 86 94

4. Assume that an educator wants to know how closely time spent doing homework

is related to student grades. Data was collected from 8 students. Time spent on homework is reported in the number of hours completed per night, and grades are reported on a 4-point scale. The following data were collected.

Student Homework Grades Student Homework Grades

1 2

.25

.50 2.00 1.75

5 6

1.00 1.25

2.00 2.25

3 4

.75 1.00

2.00 2.50

7 8

1.50 2.00

2.00 3.60

5. Three groups of students involved in the same curriculum are obliged to study for 15 minutes, 30 minutes, or 90 minutes a night for 8 weeks before taking a mathematics test. Scores from 5 students in each group were randomly selected to determine if there was a difference among the three time groups. Their scores are as follows:

15 minutes: 43, 39, 55, 56, 73 30 minutes: 55, 58, 66, 79, 82 90 minutes: 61, 66, 85, 86, 91

6. An administrator is interested in determining if the type of reading curriculum students receive is related to whether they meet reading standards for their grade. The following data were collected.

Curriculum A Curriculum B Curriculum C Met Standard 8 5 3 Did Not Meet Standard 7 13 13

7. Suppose the National Transportation Safety Board (NTSB) wants to examine the

safety of compact cars, midsize cars, and full-size cars. It collects a sample of three for each of the treatments (cars types). The hypothetical data provided below from 10 trials report the mean pressure applied to the driver’s head during a crash test for each type of car.

Compact: 635, 671, 648, 685, 648, 651, 654, 682, 687, 627 Midsize: 482, 529, 541, 518, 497, 526, 507, 492, 499, 451 Full-size: 451, 483, 464, 447, 456, 499, 484, 492, 449, 449

8. To determine whether students represent five selected counties in roughly equal proportions, a university official randomly selects a group of 95 university students and finds that 60 of them came from the 5-county area. The distribution of the students across the five counties is given below.

Card County Mountain View

County Stirling County Garden County Welling County

15 8 12 10 15

9. Seventh-grade students have just completed a battery of tests, and administrators are interested in determining if there is a relationship between math and spelling scores. Twelve students were randomly selected and their scores were recorded.

Student Math Spelling Student Math Spelling 1 2 3 4 5 6

15 5 16 10 11 3

10 4 11 8 13 4

7 8 9 10 11 12

12 11 10 14 8 9

10 8 7 9 6 9

10. An instructor teaching algebra 1 to ninth-grade students wishes to analyze the

difference between student achievement before and after the implementation of an online help resource. For 6 weeks, students worked with conventional, in-class and homework resources, and then for the next 6 weeks, an online help desk was made available to them. The scores for 6 students on a district benchmark test before and after the implementation of the online help resource are listed below.

Before: 22, 18, 33, 20, 23, 27 After: 28, 21, 32, 25, 33, 28

11. In a certain town, there are about one million eligible voters. A simple random sample of 10,000 eligible voters was chosen to study the relationship between sex and participation in the last election. The results are summarized in the following table:

Male Female Voted 2792 3591 Didn’t Vote 1486 2131

12. A college counselor wonders whether second semester students take fewer units than first semester students. From the population of each group (first semester and second semester), she selects 10 students at random. The following data were collected:

First semester students: 10, 12, 14, 14, 15, 15, 15, 16, 16, 18 Second semester students: 6, 9, 9, 10, 12, 12, 13, 14

Practice Exercise 25: Using Existing Data Files

A district administrator was interested in assessing the culture and climate at schools within the district. The Revised School Culture Elements Questionnaire (RSCEQ) was distributed to all teachers in the district. A unique feature of the RSCEQ is that is assesses three dimensions of culture and climate (Leadership and Vision, Teacher Collegiality, and Teacher Professionalism) using Actual and Preferred scales. The Actual scale assesses how respondents perceive the culture and climate actually is within their schools. The Preferred scale assesses how respondents would like the culture and climate to be within their schools. A total of 765 teachers responded. Use the datafile, rsceq_pe25_data.sav, to answer each of the following questions. The following table explains the data that was collected through the survey and is contained in the file. Variable name Label Values degree Highest degree earned 1 -- Associates/Bachelors

2 -- Masters or higher yrs_exp Total Years of Experience 1 -- 1-3 years

2 -- 4-7 years 3 -- 8-15 years 4 -- 16 or more years

grade_level Grade Level Taught 1 -- Elementary/Middle 2 -- High School

admin_a Actual Leadership and vision These variables represent the scores for each of the three dimensions on the Acutal and Preferred scales. The range of possible scores is 1 to 4 with higher scores representing more positive perceptions.

collegial_a Actual Teacher collegiality professional_a Actual Teacher professionalism admin_p Preferred Leadership and vison collegial_p Preferred Teacher collegiality professional_p Preferred Teacher professionalism The administrator is interested in the following questions. For each question, conduct the specified analysis and report the results as they would appear in an article.

1. Is there a statistically significant difference between elementary/middle and high school teachers with respect to scores on the actual leadership and vision scale? (Independent Samples t-test)

2. Is there a statistically significant difference between scores on the actual and

preferred teacher collegiality scales? (Dependent Samples t-test)

3. Is there a statistically significant difference in scores on the preferred leadership and vision scale based on years of experience? (Oneway ANOVA with Tukey post hoc)

4. Is there a statistically significant correlation between scores on the actual teacher

collegiality and actual teacher professionalism scales? (Correlation)

5. The administrator believes that the teachers within the district are equally distributed across the four years of experience categories. Therefore, is there a statistically significant difference in the distribution of teachers? (One Sample Chi-Square)

6. The administrator believes that there is a relationship between grade level (e.g.,

elementary/middle and high school) and burnout. Because the survey did not measure the degree of burnout among teachers, the administrator uses years of experience as a substitute for burnout (believing that burnout would lead to lower years of experience). Therefore, is there a statistically significant relationship between the grade level taught and the number of years of experience? (Chi- Square test of independence)