The Difference Between Standard Scores & Z-scores

Students are subject to all kinds of State and national test now to determine how much they have learned in relation to other students in the same State or country. Educators and politicians, need some way to compare the scores to know how well students are doing. How well students score determines the education funds for State, school district and individual schools. Standard scores and z-scores are used to determine how these funds are distributed.

Standard Scores Explained

Standardized tests have all their own scoring systems. The SAT is scored on a scale of 800 points for each section, while ACT scored 36 points on a scale for each test section. When a student receives his scores back from testing agencies, she will only know how well she scored for this test. This score is the raw, or standard score. The students will not know how her score is compared to other national or Statewide without having any other information available to her.

Standard Distribution

When all standard scores are picked and plotted on a histogram of the number of times that particular score occurred, a bell shape tend to show up on the graph. This time the form is called the default distribution. All results can be plotted and found on this bell curve. The upper part of the curve, where the average, median and mode of scores is usually. It’s average, the median score, and the score, there occurred the most, respectively.

A standard normal distribution corresponds to the standard distribution described above. But in the case of a standard normal distribution, mean, median and mode are all zero (0). The standard normal distribution will have a standard deviation, which is the average distance from the mean, 1. . This means that most of the scores will be found within a deviation from the mean. In fact, 68 percent of all scores on the distribution be within 1 standard deviation of the mean, 95 percent within 2 standard deviations and 99.7 percent within 3 standard deviations.

Z-Scores Explained

Z-score is a score that is located somewhere in the standard normal distribution. His counterpart on the standard distribution is the standard score. The standard normal distribution and z-score give all standardized scores must be weighed straight through a few calculations. Z-score can then be used to determine what percentile rank score falling by finding z-score on a z distribution chart.

Standard Scores to Z-scores

As noted above, a simple calculation transform standard score to a z-score. Z-score can be found by subtracting the mean of standard scores from standard score being evaluated, and then divide this difference with the standard deviation of the standard distribution. The formula is: z = (XM)/sd

This z-score is, how many standard deviations from the mean, the standard score falls. If the z-score is positive, so is the standard score is above average. If the z-score is negative, then the default score is below average.

Other Standard Scores

Standard scores used any time there is any kind of testing or evaluation involves a kind of point system. Standard and z-scores are also used to test claims that manufacturers make their products with regard to durability, strength, or other measurable function.