S-08: STATISTICS SELECTION CHART
Steps to choose the appropriate statistical method for the data and situation.
1. Identify whether a given research problem raises the question of describe, relate, or compare.
2. Identify whether the numbers in a given research problem
name (nominal or class C data),
rank (ordinal or class B data), or
equally space (interval or class A data).
The best procedure would seem to be to treat ordinal measurements as though they were intervals measurements, but to be constantly alert to the possibility of gross inequality of intervals (Kerlinger, 1986, p. 403).
3. Identify the number of groups, variables, or samples being described, related, or compared in a given research problem.
4. Identify whether comparison samples are related (matched on some relevant characteristic or multiple measures on the same individuals) or independent (randomly assigned).
5. Choose the appropriate statistical tool for the data and situation using the following table.
______
You say you want to COMPARE! How many samples?
______
You say you want to RELATE! How many variables?
______
You say you want to DESCRIBE! Just one question.
______
1. A pilot experiment, designed to test the effectiveness of a new approach to spelling proficiency, has been conducted over a semester-long period in a junior high school. Two different classes of 29 seventh grade pupils participated in the study. Students in Group X received their formal spelling instruction from Mr. Jordan, an experienced teacher. Mr. Jordan employed conventional methods of spelling instruction such as are commonly used in upper elementary grades. While he met with Group X five times each week for a period of one hour, only one hour per week was devoted to spelling instruction. Group Y also met with Mr. Jordan daily, but while they devoted an hour per week to spelling instruction, all formal spelling teaching was carried out through the use of newly developed programmed spelling lessons that were presented to the student through the use of self-instruction "teaching machines." Since all of the students involved in the pilot study had been pre-selected for purposes of the research, subjects in the two groups had been matched in pairs with respect to intellectual ability and pre-experimental performance on an orally administered spelling quiz of 150 words. At the conclusion of the semester’s experiment, the spelling quiz was readministered to both groups. Which statistical procedures should be selected to test whether there is a significant difference between Mr. Jordan’s conventional instruction techniques and the programmed method of teaching spelling as determined by post-experiment performance on the spelling quiz?
Question ______Measurement Level ______
Number of Samples ______Related or Independent ______
Statistic ______
2. A vocational instructor wishes to arrive at a representative performance for his class on an assigned task. In addition to the representative performance he also wishes to know the variability of the performance of the individuals in the class. The performance was assessed by a 100 point objective test and the scores were spread fairly evenly. What statistics should be used to analyze this data?
Question ______Measurement Level ______
Number of Samples ______Related or Independent ______
Statistic ______
3. Three new methods of teaching spelling are being contrasted with a conventional method by only one instructor. Four groups of fifteen pupils, randomly drawn from a large number of potential subjects, have been equated with respect to pre-experiment spelling scores, intelligence test scores, and previous scholastic performance in school. If one wished to determine significant differences in the scores of the four groups (three experimental, one control) on a post-experiment spelling test, which of the statistical procedures would be most appropriate?
Question ______Measurement Level ______
Number of Samples ______Related or Independent ______
Statistic ______
4. A high school guidance counselor wants to determine the association between number of extracurricular activities participated in by students and their scholastic achievement. This counselor tallied the number of activities each student participated in and then calculated their grade point averages. What statistics should the counselor use to analyze this data?
Question ______Measurement Level ______
Number of Samples ______Related or Independent ______
Statistic ______
5. An educational experimenter has studied the influence of a number of instructional variables on certain aspects of students’ attitudes toward school and study activities. Using a newly developed attitude inventory, the researcher has sampled a large number of pupils, attempting to establish norms for the inventory. From these early studies, he is convinced that the attitude scores yielded by the inventory are not normally distributed in the student population. Rather, samples of the numerical scores acquired through use of the inventory are always negatively skewed. The experimenter thus reasons that analyses of such data should not be conducted with those parametric techniques which require relatively normal population distributions.
He is currently conducting an experiment in which two groups of six pupils have been exposed to different instructional procedures. All twelve pupils were randomly selected an randomly assigned to one of the two groups. At the conclusion of the instructional period, both groups were given the attitude inventory. Which of the statistical techniques should be used to test whether the attitude scores of the two groups are significantly different?
Question ______Measurement Level ______
Number of Samples ______Related or Independent ______
Statistic ______
6. A school administrator studies the results of a year’s tryout of team teaching. Though achievement standards have been as high as in previous years, he is puzzled by results from a post-course questionnaire which was administered to the 95 pupils who took part in the team teaching project. In particular, he is perplexed by responses to question seven:
(7) Which type of teaching situation do you prefer? Number Checking
Team teaching with more students per group 12
Team teaching with fewer students per group 57
Conventional teaching with one teacher per 25-35 pupils 26
Of the 26 students who chose conventional teaching, all but 5 were boys. The administrator wonders whether the fact that all 3 teachers constituting the teaching team were women might be important. Specifically, he speculates that there may be a significant difference between the responses to question seven of the 55 boys and 40 girls in the group. Which of the statistics should be used?
Question ______Measurement Level ______
Number of Samples ______Related or Independent ______
Statistic ______
7. A welding instructor rated his students’ practice pads on a scale of one to ten with one representing a very poor set of beads and ten representing an excellent set. He rated one hundred of these pads and would now like to know what a representative rating would be. What statistic should he use?
Question ______Measurement Level ______
Number of Samples ______Related or Independent ______
Statistic ______
8. A teacher wished to demonstrate that two forms of an achievement test she has developed are "parallel," or relatively equivalent. If so, she can administer one form as a pre-test and the second as a post-test in a study of certain new instructional procedures she wishes to introduce to her class. The actual experiment she wishes to conduct involves a comparison of the achievement of three matched groups of pupils who have been taught a series of concepts by three relatively distinct instructional procedures. The results of the experiment will assist the teacher in deciding which of the instructional procedures to use with future classes.
Anticipating this project, the teacher prepared a large number of test items during the preceding semester and randomly divided them into two sets of items which represented two forms of the test. Having instructed her class by using combination of the three new instructional procedures, she administered the two forms to 110 pupils in four sections (classes) of the same course at the close of the instructional period. She notes with pleasure that the means for the two test forms are practically identical. Which techniques can the teacher use to test the statistical significance?
Question ______Measurement Level ______
Number of Samples ______Related or Independent ______
Statistic ______
9. Consider the case of an educational investigator who wished to test whether there are any significant differences between the achievement scores of three samples of students taught by three rather distinctive varieties of lecture instruction. The first lecture approach features a multitude of rhetorical but unanswered questions designed to stimulate the students to think about the content of the lecture. The second lecture approach embodies many rhetorical questions, which the lecturer himself quickly answers. The final lecture technique has few, if any, rhetorical questions.
The investigator also wishes to see if the student’s level of intelligence interacts in any significant fashion with the performance under the three varieties of lecture techniques. He gathers post-test achievement scores for three sets of subjects who have been exposed to the different lecture methods. Intelligence test data are also secured for each subject so that the total sample of 300 students (100 taught by each method) can be classified as "above average intelligence," "average intelligence," or "below average intelligence."
In order to test the null hypotheses (1) that there are no significant achievement differences between students taught by the three lecture methods and (2) that there is no significant interaction of intelligence level and lecture method on achievement, which of the statistical techniques should the researcher select?
Question ______Measurement Level ______
Number of Samples ______Related or Independent ______
Statistic ______
10. A high school counselor is faced with the task of setting up a systematic procedure for predicting the likely success of his school’s seniors at a nearby private university. In previous years, students with a grade point average lower than B+, regardless of intelligence or any other factors, have been advised not to enroll in the University on the grounds that they would probably fail to maintain university grade standards. Both the admission officials at the University and the administrators at the school have requested that the counseling office develop a more precise scheme for predicting potential University success. Certain of the high school’s graduates, each with C averages throughout high school, have entered the University (against advisement) and maintained excellent scholastic records.
The counselor is given complete access to records at the University, as well as the high school, for all the students who were graduated from the high school and entered the University. Records were quite complete for the past twelve years. Included in the University records were college grades and entrance examination scores. The high-school records have high-school grades, scores on a standardized intelligence test administered during the ninth grade, and certain personal data such as sex, church affiliation, etc. Which of the statistical devices should the counselor use to develop the prediction scheme which will permit more precise advisement of his high school’s university aspirants?
Question ______Measurement Level ______
Number of Samples ______Related or Independent ______
Statistic ______