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Showing posts with the label Normal Curve

z-scores or standard scores

  A z -score tells you the distance of the score from the arithmetic mean of a set of scores that are normally distributed. The z -score represents standard deviation units thus, a z -score of 1 means it is one standard deviation above the mean of the set of scores. A z -score of minus one (-1) means the score is one standard deviation below the mean of the set of scores. The z -scores are often plotted along the x -axis of  a normal distribution, which is sometimes called the bell curve. Use lower case italics when reporting z -scores in APA style. The upper case Z is a different score. You can calculate a  z -score by subtracting a raw score from the mean and dividing by the standard deviation of the set of scores. Example: A raw score on a test = 60. If the mean = 50 and the standard deviation = 10 then (60-50) = 10 and 10 divided by 10 = 1.0. The z score is 1.0, it is one standard deviation above the mean. Most z - scores fall between -3.0 and +3.0 but it is possible to have scor


 Kurtosis is a statistical concept. The value indicates whether a distribution is similar to the normal curve or different from the normal curve. Compared to the normal curve, kurtotic distributions of data appear either peaked in the middle or flat. In a normal distribution, the value of kurtosis = 0. The peaked distribution has a positive value. It's called leptokurtic (think leap). The flatter distribution has a negative value. It's called platykurtic (think of the animal, Platypus). There are different formulas for calculating kurtosis. In Excel, the function for kurtosis can be found under Formulas, More Functions. In the drop down list, choose KURT. Please check out my website    and see my books on    AMAZON         or   GOOGLE STORE Also, consider connecting with me on     FACEBOOK     Geoff W. Sutton         TWITTER    @Geoff.W.Sutton     You can read many published articles at no charge:   Academia    Geoff W Sutton       ResearchGate   

Normal Distribution or Bell Curve

  The bell curve is also known as the normal curve or normal distribution . The bell curve has mathematical  properties that allow researchers to draw conclusions about where scores (or data) are located relative to other scores (or data). Click hyperlinks for more details. The three measures of central tendency (mode, median, mean ) are at the same middle point in a normal curve. The numbers representing the middle of the bell curve divide the distribution in half. On the x -axis in the normal distribution, the mean is at zero and there are standard deviation units above and below the mean.  The height of the curve indicates the percentage of scores in that are a. You can see that a large percentage of the scores are between 1 and -1 standard deviations. About 68% of scores fall between +1 and -1 standard deviations from the mean.  Look at the illustration below to see that there are about 34% of the scores in falling one standard deviation above the mean and another 34% in one st

Skewed Distributions

  Skewed Distributions* Skewed distributions have one tail that is longer than the other tail compared to the "normal" distribution, which is perfectly symmetrical. Skew affects the location of the central values of the mean and median. Positive Skew Below is an image of positive skew, which is also called right skew. Skew is named for the "tail." If you had statistics, you may have heard a professor say, "the tail tells the tale." The tail is the extended part of the distribution close to the horizontal axis. The large "hump" area to the left represents the location of most data. In behavioural science, the high part often refers to the location of most of the scores. Thus, in positively skewed distributions, most of the participants earned low scores and few obtained high scores as you can see by the low level of the curve, or the tail, to the right. Negative Skew As you might expect, negatively skewed distributions have the long tail on the le

Measurement Error Standard Error of Measurement

In testing, measurement error usually refers to the fact that the same people can obtain different scores on the same test at different times. In a broad sense, measurement error can also refer to the degree of accuracy of a test to correctly identify a condition, which is discussed as test validity. Recall that test score reliability is a necessary but insufficient condition for test score validity. Many tests in psychology, medicine, and education are useful. The reliability of the scores will vary depending on such factors as the properties of the test itself as well as how well the user follows standard procedures in administering the test, environmental factors that can affect the scores, and factors within the person taking the test. The scores on many tests conform to the pattern called the normal curve or bell curve. In classical test theory, the scores people obtain on tests are simply called obtained scores (symbol X). Statisticians consider the variation in scores t