NORMES

Analyzing Learning Equity Research Trends (ALERT)

Font Size : ++ / --

Text Only / Default

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.

This website works best with IE 7 and Fire Fox

Contact NORMES Tech-Help

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.

1 - Represents the 90th Percentile

2 - Represents the 75th Percentile

3 - Represents the Mean

4 - Represents the 25th Percentile

5 - Represents the 10th Percentile

6 - Represents the Interquartile Spread
(25th to 75th Percentile)

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

Mobile Students

Non-Mobile Students

Performance Values:

	Mobile Students	Non-Mobile Students
1:	255	280
2:	208	233
3:	184	197
4:	160	181
5:	147	165
6:	48	47

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.

Example 1:	Fourth Grade Benchmark Exam	n = 128
	Sixth Grade Benchmark Exam	n = 138
	Eighth Grade Benchmark Exam	n = 125
	EOC Literacy Exam	n = 129
	Total	N = 520

Further, let us assume a the following values:

Mobility	N	Mean Literacy Scaled Score	Standard Deviation

Mobile	287	184	37.5
Non-Mobile	233	197	32.6

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).