Introduction This presentation presents results from a number of examinations covering students’ verbal skills. On each examination, a student would take a pre test and at a later point time a post test covering the same information, although using what is called a “parallel form” of the test. Using the same test for pre and post testing would bias results because of what are called “Memory Effects” or, simply stated, students would remember large amounts of information from the previous test. The fact that they would have time to discuss the pre test afterwards would further bias results. That error was not made in this study. Presenting Numeric Information Many find the science of statistics intimidating and horrifying. This is understandable considering terms like multicollinearity, coefficients of skewness and kurtosis, autocorrelation and others tend to glaze the eyes. This presentation
will avoid use of intimidating terms and data are presented in terms of the students’ first test scores (Called Pretest hereafter), and last test score (Called Post Test hereafter). Note that each student has two scores from the pre test and post test. It would bias the study to pair a pre test score from Susie Smith with a post test score from Kevin Simms. Performance is judged on the basis of mean scores. “Mean” is another name for “Average.” To compute one, add up scores and divide by the number of scores. One problem area is how to determine what is called “Statistical Significance.” This is an arbitrary construct although on an intuitive basis easily understood. If a teacher’s salary is increased by ten cents per day, she would be earning more although hardly impressed. For this presentation’s purposes, it will use the word “Significant” interchangeable with “Huge,” “Tremendous,” and “Exceptional.” Real-world examples would include a student improving from 500 to 700 on the SAT or a golfer whose average for 18 holes was usually 110 suddenly starting to consistently shoot in the high 60’s. Space considerations do not permit providing visuals so the presentation will focus on the mean and what is called the t statistic. The t test for paired scores (it is incorrect to simply say one used a t test) is used as parametric data (data with decimal places) are used at what is called the .05 level of significance. In other words researchers acknowledge that regardless of the size of the t value they admit possibilities of their information being incorrect 5% of the time. This is the industry standard. Pre vs Post Word Reading Gr. Equiv 2007-2008
t-Test: Paired Two Sample for Means
t Critical two-tail
The means of the two tests (pre vs post) are 4.403 (pre) and 5.557 (post). Although there seems to be some distance between the two means, the paired t test must be used to determine if the distance is “Significant” or not. Although the computation is not a difficult one, the formulas used are sufficiently appalling that most people avoid them religiously. Those curious may refer to any statistics test for Paired (Related) T Test. Although it will only be done for this set of scores, showing an Excel printout will help.
t Critical two-tail
Reading the table is easily done. The t stat was derived from computations based upon the scores. The t critical is the dividing line between what is declared significant and not significant. In other words if the t critical is larger than the t stat, nothing significant happened or, in layman’s terms, there was not enough improvement noted to state that the treatment applied (a reading program, new text etc) worked any better than what had been done in the past. With all of that said, we can state that on this particular test that students improved tremendously as the computed t stat of 2.49 is greater than the critical value of 2.059. We end the process with a plain English statement that students in this study improved substantially. From our information, luck was not a factor.Pre vs Post Sentence Comp Gr. Equiv 2007-2008 Students were administered this test under the same conditions of the others. We are dealing with paired scores as two scores were obtained from the same student at different points in time using parallel form tests defined earlier. Students’ performances improved significantly (tremendously) as the computed t statistic of 2.957 exceeded the critical value of 2.055. Pre vs PostSpelling Gr. Equiv. 2007-2008Comparing the t statistic of 5.668 with the t critical value of 1.996 indicates improvement that not only is significant but staggering bringing to mind a weekend golfer who suddenly qualifies for the PGA Tour and becomes a consistent money winner. Pre vs Post Word Reading Gr. Equiv 2006-2007Given the computed t statistic of8.31592 when compared to the t critical value of 1.9949, we must conclude students made tremendous gains well outside the realms of chance. Pre vs Post Sentence Comp Gr. Equiv 2006-2007Given the computed t statistics of 6.88763 when compared to the t critical value of 1.994945, students made tremendous gains over this study gains which cannot be attributed to chance. Pre vs PostSpelling Gr. Equiv. 2006-2007The computed t statistic of 8.315 when compared to a t critical value of 1.99 indicates improvement on a level which can only be considered staggering.