Practice Exercises

1. Write a directional, non-directional, null hypothesis for the following sets of variables:

1. IV = Group (teachers, staff, administrators), DV = attitude toward a new school policy (measured from 1 = strong dislike to 10 = strongly favor)
2. IV = Age, DV = verbal acuity (treat this as a quantitative variable)

1. This question consists of two parts.

1. Provide a literal interpretation for the following regression coefficients (i.e., explain exactly what b0 and b1 represent—and indicate how many units of change is expected for each dependent variable in the literal interpretation). Note that for each dependent variable explained below, higher scores on that variable represent more of that variable. (2.) Provide predicted values for each dependent variable as directed.

(a) The independent variable is years of work experience and the dependent variable is number of job promotions experienced. The estimate is: b0 = 0 and b1 = .20.

(b) Someone with 10 years of experience is predicted to have how many promotions? Someone with 5 years of experience is predicted to have how many promotions?

(c) The independent variable is test anxiety (higher scores indicate more test anxiety and the range is 0 to 10) and the dependent variable is achievement test scores. The estimate is: b0 = 93.5 and b1 = -3.5.

(d) Someone with an anxiety level of 10 (which is very high) is likely to score what on the achievement test? Someone with anxiety of 0 is likely to score what on the achievement test?

3. Below are several research scenarios. For each, indicate whether the researcher committee a Type 1 error, a Type 2 error, or no error in hypothesis testing .

(a) Assume there is a strong, positive relationship between variable X (number of 6th grade students in a teacher’s classroom) and variable Y (amount of stress that 6th grade teachers experience during the school day) in the population of 6th grade teachers in the United States. That is, the more 6th grade students in the classroom, the more stress the teacher experiences. As with any educational study, researchers investigating the relationship between X and Y are not aware of the true relationship in the population, so researchers must conduct studies with samples and then use inferential statistics to make decisions whether to reject the null hypothesis (Ho: There is no relationship between X and Y) or fail to reject the null hypothesis. A local researcher wishes to study the relationship between X and Y and he samples 6th grade teachers from local counties. After collecting relevant data, the researcher finds a strong, positive relationship between X and Y and therefore rejects the null hypothesis. The local researcher infers there is a positive relationship between X and Y in the population of 6th grade teachers in the United States.

(b) Assume there is a strong, positive relationship between variable X (number of hours per week a child reads for pleasure) and variable Y (language arts scores in the classroom) in the population of 3rd grade students in the United States. As with any educational study, researchers investigating the relationship between X and Y are not aware of the true relationship in the population, so researchers must conduct studies with samples and then use inferential statistics to make decisions whether to reject the null hypothesis (Ho: There is no relationship between X and Y) or fail to reject the null hypothesis. A local researcher wishes to study the relationship between X and Y and he samples 3rd grade students from Bulloch County. After collecting relevant data, the researcher finds no relationship between X and Y and therefore fails to rejects the null hypothesis. The local researcher infers there is no relationship between X and Y in the population of 3rd grade students in the United States.

(c) Assume there is no relationship between variable X (number of 6th grade students in a teacher’s classroom) and variable Y (amount of stress that 6th grade teachers experience during the school day) in the population of 6th grade teachers in the United States. That is, the number of 6th grade students in the classroom does not influence the level of stress a teacher experiences. As with any educational study, researchers investigating the relationship between X and Y are not aware of the true relationship in the population, so researchers must conduct studies with samples and then use inferential statistics to make decisions whether to reject the null hypothesis (Ho: There is no relationship between X and Y) or fail to reject the null hypothesis. A local researcher wishes to study the relationship between X and Y and he samples 6th grade teachers from local counties. After collecting relevant data, the researcher finds no relationship between X and Y and therefore fails to reject the null hypothesis (i.e., the researcher states that he believes the null hypothesis is correct). The local researcher infers that X and Y are unrelated in the population of 6th grade teachers in the United States.

(d) A researcher found a statistically significant difference between group means. If the researcher committed an error in hypothesis testing, which error is possible?

4. In regression (as well as in other statistical procedures, such as t-test and ANOVA, although not often discussed), model fit is an important consideration. Answer the following questions about model fit:

(a) What is model fit; what does the term indicate?

(b) How is model fit assessed; what statistics discussed in this course are used to assess model fit?

(c) What information is used to calculate these statistics? Don’t discuss formula; rather focus your response on the actual data/variables/information used to calculate these statistics.

5. Assume you obtained the following results for each test below. What do these results mean?

(a) r = -0.05 (correlation)

(b) F = 0.00 (ANOVA F ratio)

(c) b1 = -2.50 (regression slope)

(d) χ2 = 0.00 (chi-square)

6. Below are several research scenarios. Indicate which set of statistical analyses (e.g., ANOVA, independent samples t test, correlated samples t test, correlation, chi-square) should be used to analyze the data collected in study, and explain why that statistical test should be used .

(a) Teachers at a local middle school were interested in exploring the effects of a collaborative peer tutor teaching program on the motivation levels seventh-grade students. Four of eight classes of seventh grade students were randomly selected at Bulloch Middle School to serve as subjects in this study. Students within each class were then randomly assigned to one of three groups: a collaborative peer tutor teaching program, group learning activities, or individual learning activities. Each class was taught by a different teacher. The Middleman motivation scale was used to measure motivation in the subjects, and this scale produces scores that range from 1 to 25 with higher scores indicating greater motivation. Validity for the Middleman scale was previously ascertained by examining how scores from the Middleman motivation scale corresponded to scores from variables that are theoretically related to motivation, such as effort to achieve, persistence, intelligence, and self-efficacy. Internal consistency for scores from the Middleman scale typically range between .81 and .86. Data for the current study were collected at the end of a 16 week program. Analysis of these data revealed that students in the individual learning activities demonstrated a statistically higher level of motivation compared with students in the two other, traditional groups (collaborative peer tutor teaching program, and group learning activities).

(b) Two researchers hypothesized that students who spend less time reading at home will have lower standardized reading scores. The researchers asked all students in each fifth grade classroom within the local school district to participate in the study. These students kept daily home reading logs over a four month period. Based on this information, the researchers calculated the average number of minutes read daily for each student. The amount of reading time and the corresponding reading test score for each student were analyzed to determine the type of association between these two variables.

(c) A researcher developed a video designed to enhance creative writing. Fifty high school students were asked to participate in the study. Twenty-five were randomly assigned to group A and the other twenty-five were assigned to group B. The video was shown to group A, and group B read a short story by Mark Twain. Both groups knew they were participating in an experiment, and both groups also knew that group A was the experimental group. After receiving their treatments, both groups were asked to write an essay on anything they chose. The next day three English teachers were asked to read each and every essay and provide a creativity score for the essay ranging from a low of one to a high of ten.

(d) Dr. Einstein is interested in determining whether an association exists between teacher experience with sexual harassment and satisfaction with their job. Einstein anticipates that teachers sexually harassed by their administrators will show less satisfaction with their jobs than teachers sexually harassed by other teachers. In addition, he also thinks that those who are sexually harassed, by anyone on the job, will be less satisfied with their jobs than those who are not sexually harassed. Einstein created a list of all public and private schools in the states of Texas, California, and New York, randomly selected thirty schools and mailed his sexual harassment and satisfaction instrument to each teacher within the thirty schools selected. Once the data from the surveys were received, Einstein analyzed the data to learn if satisfaction differed by harassment group. Satisfaction was measured on a scale that ranges from 15 to 75 with higher scores indicating greater satisfaction.

7. Over the past few years 225 students enrolled in sections of class I’ve taught have completed the final test of three tests administered in that course. The overall mean is 83.9 with a standard deviation of 10.8. These data are nearly normal in distribution; given this answer the following questions:

(a) What percentage of students will score 83.9 or higher on this test?

(b) What percentage of students will score better than 73.1?

(c) What percentage of students will score lower than 78.5?

(d) What is the percentile rank for a student with a score of 83.9?

(e) What is the percentile rank for a student with a score of 73.1?

(f) What is the percentile rank for a student with a score of 78.5?

(g) What is the raw test 3 score for a student with a z score of 1.5?

(h) What is the raw test 3 score for a student with a z score of –0.75?

(i) What is the raw test 3 score for a student with a z score of 0.00?

8. Describe two benefits of adding covariates ANOVA models .

9. Two high school biology classes were selected for an experiment on instructional strategies. Class 1 received Method 1 and class 2 received Method 2. Before the experiment commenced, students’ IQ scores were collected so IQ could be used as a covariate in the statistical analysis to follow the experiment. After students were exposed to instructional methods for one

semester, a posttest to measure biology achievement was administer to all students. Below is a table of results from this experiment. Method 1

ANCOVA will be used to analyze these data. In which direction will posttest mean scores for Method 1 be adjusted if an adjustment occurs? In which direction will posttest mean scores for Method 2 be adjusted if an adjustment occurs?

Note : For the remaining items you are to create an APA styled results presentation. This will include a table of results, and written inference and interpretation. If you are unclear about APA styled tables, review carefully the examples provided in the linked Word document on the Course Index. Each item is worth 8 points (unless specified otherwise) and will be graded according to the following rubric:

10. Foos and Clark (1982) studied the influence of expectations on test performance. They found that the kind of test that a student expected to take would affect the way in which they studied the material. Below are scores from an experiment designed to replicate Foos and Clark's research. A total of 20 undergraduate students were given a 3000-word passage to read and were told that they would be tested over the material. They were then assigned to one of four treatment groups. In the first group, the students were told to expect a multiple-choice test, in the second group, they were told to expect an essay; in the third group, they were told to expect a memory test; and in the fourth group they were not told what to expect. After studying the passage, all students were give exactly the same test, which had a combination of multiple-choice and short-answer items. Given below are scores from their test. Is there any evidence that expectation influences performance?

11. The hypothesis is that instructor reputation is related to student ratings of the instructor and therefore presents a bias in student ratings. Students were asked what they heard about an instructor before enrolling in a class taught by the instructor. Their comments were classified into two categories:

Positive Reputation for students who heard positive information about the instructor,

Negative Reputation for students who heard negative information about the instructor.

12. Below is one individual's record on 23 swimming sessions. Time represents the minutes (and fractions thereof) in the pool, and pulse represents pulse rate (in beats per minute) immediately after exiting the pool. Are these variables related? If yes, does this relationship make sense? Explain why it is or is not sensible should a relation be found.

13. It is December, 2000 and the following question was of concern in the US. Is political party affiliation related to opinion about whether Algore should concede?

Note. y = yes, n = no

14. The following research excerpts were extracted from Samuel Peng and Jay Jaffe's study (1979, Women who enter male-dominated fields of study in higher education, American Educational Research Journal, 16 , 285-293). Based upon the information and data given, what conclusions would you, acting as Peng and Jaffe, draw?

Using data drawn from the National Longitudinal Study of the High School Class of 1972, this study examined 16 variables classified into categories of family background, high school experience, academic ability, life-goal orientations, and extent of education planned that might influence women's entry into male-dominated fields of study in higher education. (p. 285)

This study was, therefore, designed to examine ... factors that may influence the entry of women into male-dominated fields as they move from high school into college. ... The results will help to answer such questions as: What types of women defy strong sex-role stereotypes by entering male-dominated fields? ... (p. 286).

One variable presented is the academic ability of women sampled (with a scale ranging from a low of 15 to a high of 75). The field selected by each woman was classified on a scale ranging from 0 (almost exclusively a female-dominated field of employment) to a high of 5 (field strongly dominated by males).

(a) Is there any evidence that women of greater academic ability tend to select fields dominated more by men?

(b) Does knowing a women’s academic ability reduce error in predicting whether a women will select a male-dominated field, and if yes, by how much?

(c) A woman with an academic ability of 30 is predicted to seek what level of male-dominated field? A woman with an academic ability of 60 is predicted to seek what level of male-dominated field?

15. Recently I collect data from 920 students asking them to evaluate instruction in their classes at FSU. Many questions were asked including one that asked students to rate their instructor. The specific wording and response options for this question are listed below:

30. Overall, how would you rate this instructor?

Two other variables measure were intrinsic motivation (internal interest in learning material for the given course) and instructor autonomy support for students (providing students with some degree of decision making within the course). To measure intrinsic motivation, responses to the following three items were averaged:

Strongly Disagree Strongly Agree

20. The most satisfying thing for you in this course is trying 1 2 3 4 5

to understand the content as thoroughly as possible.

21. In a class like this, you prefer course material that really 1 2 3 4 5

challenges you so you can learn new things.

22. In a class like this, you prefer course material that arouses 1 2 3 4 5

your curiosity, even if it is difficult to learn.

To measure autonomy support, responses to these items were averaged:

Strongly Disagree Strongly Agree

24. The instructor was willing to negotiate course requirements 1 2 3 4 5

with students.

25. Students had some choice in course requirements or activities 1 2 3 4 5

that would affect their grade.

26. The instructor made changes to course requirements or 1 2 3 4 5

activities as a result of student comments or concerns.

Of interest to researchers of student ratings is whether autonomy support and intrinsic motivation predict overall student ratings of the instructor. Below are 30 randomly selected cases from the data of 920 student responses. Use these data to learn whether autonomy support and intrinsic motivation are related, or predict, overall ratings of the instructor.

16. Is there a relationship between student performance on the mathematics section of the SAT, and the student-teacher ratio found across states and average teacher salary within a state? The data for this study are real ; the three variables of interest are:

math_sat -- Average mathematics SAT scores in each state.

pupil_teacher_ratio -- Average ratio of students to teacher in each state; a higher number indicates more students per teacher

average_teacher_salary -- Average salary per teacher in each state in thousands of dollars, thus a figure of 25.000 means the average salary per teacher is $25,000 per year

(a) Write hypotheses for these two predictors and the one outcome; what do you expect to find regarding the relationship between student performance on the mathematics SAT and the two predictors? The hypotheses you write should indicate what you expect to find before you analyze these data.

(b) Analyze these data statistically and present results (both written and tabular) in APA format. Do not present SPSS output; present only APA formatted results.

17. Studies of student evaluations have shown that the grade one expects in a class correlates positively to overall ratings of the instructor. Thus, students who expect lower grades tend to evaluate the instructor lower, and students who expect higher grades tend to evaluate the instructor higher. Some have argued, however, that the association between grades and ratings is spurious, to some extent, and may be moderated somewhat by the level of intrinsic motivation a student has to learn course content. The more motivated the student, the less low or high expected grades influence or predict ratings. However, for students with low intrinsic motivation, extrinsic factors such as grades may play a more important role in how that student evaluates instruction. Is there any evidence that expected course grade and level of intrinsic motivation are associated with overall ratings of the instructor? Data appear below. For data analysis purposes, treat "Level of Intrinsic Motivation" as a nominal/categorical variable despite its appearance as an ordinal variable.

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