Iowa
State Staff Development
Practitioner Research Reports
1997-1998
THE ACCURACY OF GED PRACTICE TEST SCORES AS PREDICTORS OF GED TEST SCORES
A Practitioner Research Project
Barbara A. Herr
Adair Co. Adult Basic Education/GED Instructor
Southwestern Community College
and
Ronald J. Herr
Instructor
Buena Vista University - Creston Center
Special thanks to Dr. Frances Antonovitz, Ph.D., Iowa State University for her assistance on this research project.
Introduction
General Educational Development (GED) instructors need a good measure of a student's preparedness to take the GED tests. Students need realistic expectations of their GED test performance. Practice test standard scores supposedly give good estimates of a student's future GED test scores. Do they? There is a difference of opinion among Southwestern Community College (SWCC) GED instructors as to whether or not the practice test standard scores truly predict GED test performance. This debate inspired this research.
Questions Addressed
- Is the GED Practice Test standard score truly a good predictor of the GED test score?
- What is the actual relationship between practice test scores and their corresponding GED test scores? Is it the "one- to-one" relationship as commonly assumed, or is it something else?
- Could the prediction of GED test scores be improved by consideration of other factors?
- What factors may cause the GED test score to vary significantly from the practice test standard score in individual cases?
The first three questions can be answered using elementary statistical methods and analysis. The last question can be best answered by the students themselves through researcher interviews.
The Sample Data
There are two types of practice test sets commonly used by SWCC GED instructors: tests published by the Steck-Vaughn Company and tests published by Contemporary Books. Both the practice test sets and the GED test set consist of five tests by subject area: writing skills, social studies, science, literature and arts, and mathematics. From the records at SWCC, pairs of practice test scores and corresponding GED test scores from SWCC area GED students over the two past years were collected. Also collected were each student's age, highest grade achieved in school, and the number of days between the practice test and the GED test. (If the days between tests were greater than 90 days, the pair of scores was removed from the sample, as the time difference was judged to be too great for meaningful comparisons of the scores.)
The edition form of the practice tests was not considered. Data on days between tests were available only for the Steck- Vaughn practice tests. The Contemporary practice test records usually gave the standard score as a five point range, rather than an single number. In these cases, the midpoint was used as the score. (For example, if the range was 45-50, 47.5 was used as the practice test standard score.)
Ten samples were formed by subject and by practice test publisher. The majority of SWCC GED instructors use the SteckVaughn practice tests, hence the five Steck-Vaughn samples had sample sizes ranging from 50 to 57 sets of observations. The Contemporary practice tests are used regularly at only one GED center, hence the five Contemporary samples ranged from 10 to 19 sets of observations.
Process
A. Statistical analysis.
A student's practice test standard score and that same student's actual GED score for a given subject form a ordered pair of bivariate data. The practice test score can be considered as an independent variable (X), while the GED score can be considered as the dependent variable (Y). It is reasonable to assume that, if a relationship does exist, the relationship would be a positive one [ie. as the practice test score (X) increases, the GED test score (Y) increases]. It is also assumed that the relationship would be a linear or straight-line relationship. Indeed, if the practice scores were perfect predictors of the GED scores, the prediction equation would be a simple Y = X (ie. GED score equals practice test score). On a graph, such perfectly related ordered pairs (or paired scores) would form a 45 straight line.
Hypothetical Graph of GED Scores and Practice Scores if the Practice Scores Were Perfect Predictors
Of course, the practice test standard scores are not perfect predictors, as shown by the scatter graphs of the paired scores given in the Appendix.
Given the samples of ordered pairs of practice test scores (X) and GED scores (Y) for each of the five subject areas, the first question can be addressed by linear correlation and the second question can be addressed by linear regression together with appropriate tests for statistical significance at the 0.05 level. Given the samples of ordered sets of practice test scores (X), days between tests (X2), age (X3), grade achieved (X4) and GED scores (Y), the third question can be addressed by multiple linear regression together with appropriate tests for statistical significance at the 0.05 level.
B. Interviews.
The last question as to why some students have large differences between practice scores and GED scores can best be answered by those students themselves. Students who had a GED test score more than one-and-a-half standard errors of the Y estimate from their practice test score were interviewed as to the reasons in their minds that account for this variation.
Results of the Statistical Analysis
Are the commonly used practice tests useful predictors of a student's performance on the GED test? The first step was to determine if a relationship does exist between the practice test scores and the GED test scores and, if a relationship, how strong that relationship is. A linear correlation coefficient measures the strength of the linear relationship between two variables. The linear correlation coefficient (Pearson's product moment correlation coefficient) between the GED scores and the practice test scores was calculated for each sample. The results are given in TABLE ONE.
| TABLE ONE: Linear Correlation Coefficients of the Relationship Between Practice Test Scores and GED Test Scores | ||
|---|---|---|
| Subject | Steck-Vaughn | Contemporary |
| Writing Skills | +0.796 | +0.557 |
| Social Studies | +0.709 | +0.327* |
| Science | +0.697 | +0.895 |
| Literature | +0.527 | +0.614 |
| Mathematics | +0.656 | +0.716 |
| * Not significantly different from zero at the 0.05 level of significance. | ||
A linear correlation coefficient can range from -l to +1. A coefficient of zero means that there is absolutely no linear relationship between the variables; a "+1" means a perfect positive linear relationship and a coefficient of "-1" means a perfect negative relationship.
These coefficients were all positive, showing that, for each sample, the relationship is positive, as hypothesized. All SteckVaughn coefficients were statistically significant, and all Contemporary coefficients were statistically significant except social studies. The Contemporary social studies sample was excluded from further analysis. (The Contemporary tests had small samples; the Contemporary social studies sample may have been nonrepresentative of the true population of paired scores and the cause of this low correlation.) All of the significant correlation coefficients were greater than +0.5, indicating that relatively strong positive relationships exist between the practice test standard scores and their corresponding GED test scores.
The linear correlation coefficient has now shown that a relationship exists between the practice test scores and the GED scores, but what is the nature of the relationship? A simple linear regression of GED scores (Y) on practice test scores (X) was computed for each sample. A linear equation was given by each regression. The regression equation is often referred to as the equation of the "line of best fit." The regression equation is that equation that "best fits" or "best describes" the scatter of paired scores. It can be used to calculate a predicted value of a student's GED score (Y. said "Y HAT") from the student's practice test score (X). These regression equations are given in TABLE TWO. The regression lines are shown graphically superimposed over the scatter of paired scores on the graphs in the Appendix.
The X coefficients (slopes of the lines) were tested for statistical significance and all were found significant. Note that the X coefficients are all positive, but less than one, except the Contemporary writing skills test. Each equation also has a constant term greater than zero. These results suggest that the relationship between the practice test standard scores and the GED scores is not a one-to-one relationship. The regression equations are different that a simple Y = X. Therefore, the practice test standard score by itself is not a good predictor of a GED test score, but when a student's practice test score is "plugged into" the regression equation, a reasonably good prediction of the GED test score can be expected.
| TABLE TWO: Linear Regression Equations of GED Scores (Y) on Practice Test Scores (X) | |||
|---|---|---|---|
| Regression Equations | Standard Error of Y Estimate | ||
| Writing Skills: | Steck-Vaughn | Y = 0.671X +14.240 | 3.847 |
| Contemporary | Y = 1.076X + 2.571 | 5.293 | |
| Social Studies: | Steck-Vaughn | Y = 0.526X + 23.256 | 4.508 |
| Science: | Steck-Vaughn | Y = 0.721X + 14.827 | 5.184 |
| Contemporary | Y = 0.801X + 13.221 | 2.600 | |
| Literature & Arts: | Steck-Vaughn | Y = 0.449X + 28.840 | 6.173 |
| Contemporary | Y = 0.851X + 11.537 | 5.701 | |
| Mathematics: | Steck-Vaughn | Y = 0.714X + 15.619 | 4.719 |
| Contemporary | Y = 0.724X + 19.119 | 5.594 | |
The utilization of the regression equation for predictions is quite straightforward. For example, a student obtained a standard score of 45 on a Steck-Vaughn science test. The predicted GED science test score would be: predicted GED score (Y) = 0.721(45) + 14.827 = 47.272, rounded to 47. The predicted GED score of 47 is a point estimate. There will often be some difference between a predicted GED score and the actual GED score. The standard error of the Y estimate is a measurement of how much a student's actual GED score can be expected to vary from the predicted GED score. About 68 percent of all students will have actual GED scores within one standard error of their predicted GED score, and about 95 percent of all students will have actual GED scores within two standard errors of their predicted GED score. In the Steck- Vaughn science test example, the standard error is 5.184. A range estimate can be formed: 47.272 + 5.184 or 42.088 to 52.456, rounded to 42 to 52. The interpretation for this range is that 68 percent of the time, a student with a Steck-Vaughn science practice test standard score of 45 will obtain a GED science test score between 42 and 52.
These results also suggest that students with "low" practice scores tend to earn GED scores higher than their corresponding practice scores, while students with "high" practice scores tend to obtain GED scores lower than their practice scores. The approximate breakpoint practice scores between "low" and "high" scores are given in TABLE THREE.
| TABLE THREE: Approximate Breakpoint Values Of Practice Test Scores | ||
|---|---|---|
| Steck-Vaughn | Contemporary | |
| Writing Skills | 43 | NA |
| Social Studies | 49 | NA |
| Science | 53 | 66 |
| Literature & Arts | 52 | 77 |
| Mathematics | 54 | 69 |
These relationships can be seen in the graphs of the paired scores with the linear regression equation and the "Y equals X" line superimposed. (See Appendix) Note that the Contemporary tests have high breakpoints. In the Contemporary samples, most students had GED scores higher than their practice test scores.
Could consideration of other factors further improve the prediction of GED test performance? Three other factors were considered: time between the practice test and GED test, student age and student grade level achievement. It was hypothesized that the longer the time between practice and GED tests, the greater the difference between scores, because students study or fail to study on the days between tests. Student age could be a factor because age is associated with years since attending school. Younger students may be more familiar with test taking and more relaxed when taking tests, hence more consistent scores. The grade achieved before dropping out was considered because one would expect a higher grade level to mean higher GED scores.
Multiple linear regressions of GED scores on all four variables (practice test scores, days between tests, age and grade level) were calculated for the Steck-Vaughn samples. The Contemporary samples did not have data on days between tests, so a multiple linear regression of GED scores on three variables (practice test score, age and grade level) was calculated. The multiple regressions gave a coefficient for each variable. These coefficients were then tested for significance at the 0.05 level.
For each sample, only the practice test score coefficients were significant. The other variables were found to be not statistically significant. Further, the multiple linear regression equations were only slightly better predictors than the regression equations with practice scores alone. This researcher judged the improvements to be too small to warrant further consideration.
As a further check, the difference between the practice scores and the GED scores were calculated for each sample. Correlations and regressions of the differences in scores on the days between tests were calculated. Correlations and single regressions of GED scores on age, GED scores on grade level, practice scores on age, and practice scores on grade level were also conducted. In every case, the correlation coefficients and the regression coefficients were not statistically significant. These results suggest that age, grade achieved and days between tests have no significant relationship with practice test and GED test performance.
How do these results compare with the results of other research? In 1979, Walter J. Musgrove and Glenn J. Musgrove conducted a similar study considering the General Education Performance Index test score, age and sex in the prediction of a GED score. They found no significant difference in GED scores on the basis of sex or age, but they found the practice test (GEPI) scores were significantly correlated to GED scores. Their regression equations were also similar to these results. The equations had practice score coefficients less than one and positive constant terms, like the equations of this study. In conclusion, they also found a strong relationship between practice test scores and GED scores, but not a one-to-one GED score equals practice test score relationship.
The Steck-Vaughn Company presents its practice tests' standard scores as direct predictors of the GED test scores, but they also give standard errors of measurement similar to the standard errors of the Y estimate for the regression equations given in Table Two. How do the Steck-Vaughn standard errors of measurement compare with the standard errors of the Y estimate of these results? Table Five gives the comparison.
| TABLE FIVE: COMPARISON OF STANDARD ERRORS | ||
|---|---|---|
| Standard Error of Y Estimate | Steck-Vaughn Standard Error of Measurement | |
| Writing Skills | 3.85 | 3.16 |
| Social Studies | 4.51 | 3.16 |
| Science | 5.18 | 3.32 |
| Literature & Arts | 6.17 | 3.87 |
| Mathematics | 4.72 | 3.32 |
For each test, the Steck-Vaughn standard errors are less that the standard errors from the regression equations. If the regression equation is a better estimator than the practice test standard score alone, why are the standard errors greater for the regression equations? The Steck-Vaughn standard errors were derived from a controlled experimental testing where high school seniors, not GED students, took a practice test and then immediately took the corresponding GED test. GED students do not take practice tests and GED tests back-to-back in a controlled experimental environment. A large number of physical and psychological factors come into play as GED students take the practice tests and the GED tests. One would expect the standard errors to be larger using real world data. An examination of factors that cause large differences between practice test standard scores and actual GED scores is the next part of this report.
Results of the Interviews
A total of 38 students with GED scores that were one and a half standard errors or more from their corresponding practice test scores were selected for interviews. The researcher found that former GED students are difficult to contact. Only 12 students, or 32 percent, could be contacted for interviews. Of there 12 students, seven had GED scores lower than their practice scores, three had GED scores higher than their practice scores, and two had some scores higher and some scores lower than their practice scores. All interviewees were asked two specific questions.
The first question was "Did you study during the days between taking the practice test and taking the GED test? Two students answered "yes," while the other ten answered "no."
The second question was "Why do you think your GED score was so different from your practice test score?"
Here are the responses given by those with GED scores higher than the practice test scores:
- I knew I had to do better on the GED test as it was "final." I really buckled down to it.
- I have no clue.
- The practice test didn't matter. If I failed it, I could just take the test again. I spent a little more time on the GED test.
- I don't know: I didn't study at all.
- I remembered the formulas for math once I took the math practice test, then it all came back to me. I never studied for the GED test.
Here are the responses given by those with GED scores lower than the practice test scores:
- I was in too much of a hurry.
- I have no clue.
- Social studies was the last test taken in two days of testing. The practice tests didn't seem as hard as the GED tests.
- During the practice test, I didn't worry about the time limit. There was no stress on the practice test. The atmosphere was more casual in the classroom during the practice test.
- I don't know. I didn't study at all.
- I wasn't working. I had straight A's in high school, but I had emotional problems at the time of the GED test. I was tired and stressed.
- I felt a lot of pressure and was worried because my Grandma was in the hospital. She wanted to see me earn my GED, but she died before I completed the GED. I walked across the stage three weeks ago, but Grandma wasn't there to see it.
- I was not nervous, but it was the second test I took that day.
- I was nervous.
These student observations can be summarized in four words:
Attitude. If students do not take the practice tests seriously, their practice test scores will be below their true ability. The difference between practice test score and GED test score will be greater. Remember how the regression equations showed that students with "low" practice test scores tended to have GED scores higher than their practice test scores. Lack of seriousness and intensity of effort on practice tests may explain much of this condition.
Anxiety. Unlike the test publishers experimental norm groups, real GED students have an important stake in their GED test performance. Anxiety while taking the GED tests works against achieving one true potential.
Overload. Taking two or more GED tests in a day may work against good GED test performance.
Life. Students bring the problems and stresses of their work and personal lives with them to the GED test. These problems and stresses may well have a greater effect when taking the "real" test in unfamiliar surroundings.
The survey regarding studying between the tests was inconclusive. The two students who did study had mixed results, as did those who did not study. It is probably best for GED instructors to assume that their students will not study between the tests.
Conclusions
Based on the statistical analysis of the sample data, the practice test standard score by itself is not a good predictor of the GED test score. A better prediction of GED test performance can be achieved by use of the regression equations in this report.
Numerous real world factors can cause significant variation between predicted GED scores and actual GED scores. The variation between predicted GED scores and actual GED scores, given by the statistical analysis of the sample data, is greater than the variation suggested by the practice test publishers. Students can improve test performance consistency by controlling test anxiety, by adopting a serious attitude toward testing, and by spreading out testing through time.-
Age, school grade level achievement, and the days between the practice test and GED test have no consistent relationship with either practice test or GED test performance. A student does not necessarily have an advantage or disadvantage due to age or school grade level, and any initial disadvantage can be overcome by the Adult Basic Education/GED program.
BIBLIOGRAPHY
American Council on Education. Teacher's Manual For The Official Half-Length GED Practice Tests, Fourth Edition. Austin, Texas: Steck-Vaughn Company, 1995.
Contemporary's Scoring Guide for the GED Assessment Program. Chicago, Illinois: Contemporary Books, Inc., 1989
Johnson, Robert. Elementary Statistics, Seventh Edition. Belmont, California: Wadsworth Publishing Company, 1996.
Musgrove, Walter J., and Musgrove, Glenn J. "A Validity and Multiple Regression Study of Performance in the GEPI as a Predictor for Performance on the GED." Journal of Employment Counseling, June 1979, 120-127.
Snedecor, George W., and Cochran, William G. Statistical Methods. Sixth Edition. Ames, Iowa: Iowa State University Press, 1967.
APPENDIX
GRAPHS OF PAIRED SCORES WITH "Y EQUALS X" LINE and REGRESSION LINE
Note that the scaling is not the same on the Y axis as the X axis of these graphs. The graphs of the Steck-Vaughn data are not labeled as such, the graphs of the Contemporary data are so labeled.
These graphs are available here in pdf format. If you do not already have it, Adobe Acrobat Reader is available free from adobe.com.
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posted February 15, 1999