Answered: A local school district would like to…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A local school district would like to implement a reading intervention to help students who are struggling with their reading skills. The school gives all of their 2nd grade students a reading test. They split the students into a high-performing and low-performing group based on the scores. The high-performing group is taught via the traditional method. The low-performing group is taught with the special intervention method. The two groups are re-tested after eight weeks. The school found that the low-performing group improved drastically, while the high-performing group did worse. The school district concludes the intervention works.

Based on the story above, address the following:

Does the school district have definitive evidence that the reading intervention works?
How might the results be related to the concept of regression towards the mean?
What suggestions would you make to the school district if they wanted to mitigate the regression towards the mean effect?

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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