Analysing Learning Equity Research Trends (ALERT)
Technical Information on the Development of Boxplots and Effect Sizes
The use of boxplots was first advocated by Tukey (1978) as a method to graphically represent differences in performance. The boxplot provides information on the distribution of the data, the interquartile spread of scores (25th percentile to 75th Percentile) and the mean. The graphical nature allows most people to readily identify differences in performance between two groups represented on the boxplot.
ALERT Boxplots and Effect Sizes
|
||
| The software package PHP used to generate the boxplots does not allow for the reporting of the mean and the median. However, to aide in interpretation, we have elected to use the mean to represent the middle bar. | ||
|
||
| The goal of the boxplots is to represent many facets of the scores in the subject area, while also allowing you to make comparisons between the specific group. For example |
|
|||||||||||||||||||||
| Performance Values: | |||||||||||||||||||||
|
|||||||||||||||||||||
Practical Example and Development of Boxplots |
|||||||||||||||||||||
| The boxplots used in the ALERT series was developed following the models provided by Tukey (1978), with a few minor variations. | |||||||||||||||||||||
| Calculation of Mean Literacy Scaled Scores | |||||||||||||||||||||
| All the Literacy scaled scores from the Arkansas Benchmark 4th, 6th, and 8th grade exams are combined with the End-of-Course (EOC) Literacy Exam results to produce a composite score for the district. |
|||||||||||||||||||||
|
|||||||||||||||||||||
| Further, let us assume a the following values: | |||||||||||||||||||||
|
|||||||||||||||||||||
| All computations for the Mobile/non-Mobile comparison would be generated from this pool of 520 literacy scaled scores. First, a mean scores, then standard deviation scores are generated. Next, a pooled variance score is computed using: | |||||||||||||||||||||
|
|||||||||||||||||||||
| Next, the effects sizes (?) are computed using: |
|||||||||||||||||||||
|
|||||||||||||||||||||
| Interpretation Thus, the achievement gap between Mobile and Non-Mobile student is .367 or representative of a moderate effect size according to Cohen (1995). |
|||||||||||||||||||||
