#### State Comparisons Overview

NAEP State Comparisons list states and jurisdictions according to average scale scores of students overall and average scale scores of selected student groups (e.g., male and female students, White students, Black students, Hispanic students) for a specific year. It also orders states and jurisdictions by differences between groups of students and/or years (changes), and by changes in differences. Note: Comparisons are based on numeric precision (up to eight decimal places) rather than the displayed precision and do not take statistical significance into consideration. For example, the selected value of a state appearing higher in the sort order may not be significantly different from a state appearing lower in the order. National Public is not included in the sort order.

In addition, the tool displays whether the selected results are statistically different from one another. Whether two scores are statistically different depends on the variability of the scores. It is important to consider whether apparent differences are statistically significant because the scores themselves are estimates and are variable, depending on sampling and measurement.

NAEP State Comparisons uses a t-test (the method most commonly used to evaluate the differences in means between two groups) to detect whether a difference is statistically significant or not. There are four possible outcomes when comparing the average scores of jurisdictions A and B:

- Jurisdiction A has a higher average score than jurisdiction B,
- Jurisdiction A has a lower average score than jurisdiction B,
- No difference in scores is detected between jurisdiction A and B, or
- The sample does not permit a reliable statistical test. (This may occur when the sample size for a particular group is small, often in combination with a large amount of clustering. In these cases the variability of a score estimate cannot be determined accurately.)

When comparing all jurisdictions to each other, the testing procedures are based on all pairwise combinations of the jurisdictions in a particular year or pair of years. Results will appear in three columns showing how each jurisdiction compares to all other jurisdictions in terms of the number of jurisdictions above, not different from, or below it. One column will show the comparative results for the user-specified jurisdiction. This comparison is of interest because it shows how a jurisdiction performs compared to other jurisdictions.