The application of the 95% Confidence interval with ISAT and IMAGE

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1 Confidence intervals are commonly applied in many fields using statistical analyses. The most commonly seen usage of confidence intervals is within political polls. In the case of a political poll, an organization like Gaullup attempts to estimate the of adults of voting age who support a particular Candidate, Barak Obama or Hillary Clinton. It would be far to expensive and time consuming to poll all adults of voting age, so the polling organization might contact 1000 people, typically at random (but often not the subject for a different discussion). Based on the sample, the organization might report that the supporting a particular candidate is some, plus or minus some other points. For example, imagine that 415 of 1000 voters reported that they would vote for Obama if the election were held tomorrow. This is 41.5% of voters polled. The purpose of polling voters is to predict the results of an election, but because only 1000 people were polled, how likely is it that based on this poll that Obama will win the election? Enter the confidence interval; because of the work of statisticians we know how likely it is that a different sample of potential voters would yield a similar result. Here is how it works, the more people who are polled, the more likely the results will be similar to what would happen if the election were held today. In addition, the closer the obtained is to the extremes (i.e., 1 or 99%) the greater the confidence. The formula to calculate the confidence interval is straightforward, except for the Z index which is obtained from statistical tables representing the area under a normal curve. Specifically the formula is: Obtained Percent minus the Z-value times the square root of the Obtained Percent times 1 minus the Obtained Percent divided by the number of people polled p * (p*1-p) / N 46.5% 1.96 * (46.5%* 100%- 46.5%) / % 1.96 * (.248) / 1000 =3.09% The solution is roughly equivalent to the polling organization reporting, we are 95 percent confident that the actual of people who would vote as the poll indicated lies between 43.4 percent and 49.6 percent. Confidence intervals "automatically" account for proficiency rates based smaller samples of students being less precise than rates based on a larger numbers of students. While the computation of confidence intervals is well-established in statistical literature, most educators would prefer not to have to compute the confidence intervals for each subgroup. In the state of Illinois the 95% confidence interval is calculated based on one side of the normal curve (i.e., a one tail test), the difference in this case is that the resulting Z-value is approximately 1.64 (rather than the 2 tail version 1.96). This is based on the idea that schools are not interested in potentially how low a might be, rather, schools want to know if they made it over the bar. The tables that follow are estimates of the required number (and of students) to meet the expectations for the NCLB ladder from the requirement of 47.5% to 92% required in This file is intended as an explanation and not a planning guide. If you have questions feel free to me (below). Thank you, Ben Ditkowsky, Ph.D.

2 (i.e., the number and required to meet standards for 47.5%). Sub % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %

3 (i.e., the number and required to meet standards for 55%). Sub % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %

4 (i.e., the number and required to meet standards for 62.5%). Sub % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %

5 (i.e., the number and required to meet standards for 70%). Sub % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %

6 (i.e., the number and required to meet standards for 77.5%). Sub % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %

7 (i.e., the number and required to meet standards for 85%). Sub % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %

8 (i.e., the number and required to meet standards for 92.5%). Sub % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %