1.Statistics are often used to describe and interpret the results of intelligence testing. They often contain the three measures of central tendency.(mean, median, mode) The mean, which is used to describe an entire set of observations with a single value representing the center of the data, is used as a standard reference point. For example, five people are waiting in line for the roller coaster. The waiting time(in minutes) of the five waiting are 3, 2, 4, 1, and 2. The mean waiting time is 3+2+4+1+2/5 = 12/5 = 2.4 minutes/ The mean is 2.4 minutes. The median is a little different. The median is used to describe an entire set of observations with a single value representing the center of the data. The median is the middle number. It is determined by ranking the data and finding observation number [N+1] / 2. If there is an even number of observations, the median is the value midway between that of the observation numbers N / 2 AND [N / 2] +1. For example, the median in this set of observations is 13. For this ordered data the median is 13.
That is, 50% of the values are less than or equal to 13, and 50% of the values are greater than or equal to 13. (Ordered data- 7 9 10 12 13 14 17 18 19.) The mode is the value that occurs most frequently in a set of observations. The mode may be used with mean and median to give an overall characterization of your data distribution. While the mean and the median require a calculation, the model is found simply by counting the number of times each value occurs in a data set. Usually, it’s easier to understand the distribution after the mode is identified. There are also cases when there is more than one mode. This simply indicates that you’ve actually sampled from a mixed population.
The three central tendencies can be used to describe skewed distributions, which are always shown on graphs. A distribution is said to be skewed when the data points cluster more toward one side of the scale than the other, creating a curve that isn’t symmetrical. In other words, the right and the left side of the distribution are shaped differently from each other.
There are normally two types of skewed distribution, positive and negative distribution. A distribution is positively skewed if the scores fall toward the lower side of the scale and there are very few higher scores. Positively skewed data is also referred to as skewed to the right because that is the direction of the long tail end of the chart. A distribution that is negatively skewed is the exact opposite. A distribution that is negatively skewed is when the scores fall toward the higher side of the scale and there are very few low scores. Negatively skewed data is also referred to as skewed to the left because that’s the direction that the long tail endpoints. There is also a normally distributed sample. When you have a normally distributed sample, you can legitimately use both the mean or the median as your measure of central tendency. The mean, median, and mode are usually equal during asymmetrical (normal) distribution.
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In this situation, however, the mean is highly preferred as the best measure of central tendency because it includes all the values in the data set for its calculation, and any changes in the scores will affect the mean. This doesn’t apply to the median or the mode. The median is sometimes considered the best representative of the central location of the data. An intelligence test for which the scores are normally distributed has a mean of 100 in the general population and a standard deviation of 15. Half the scores will be greater than 100 and a half will be less than 100. A score of 115 is one standard deviation above the mean, and a score of 85 is one standard deviation below the mean. Approximately two-thirds of the scores will fall between 85 and 115. Approximately one-sixth will be below 85 and one-sixth above 115. A score of 130 is two standard deviations above the mean and a score of 70 is two standard deviations below the mean. Approximately 95% of the scores fall between 70 and 130. About 2.3% are less than 70 and 2.5% are greater than 130.
2.Norms are periodically updated in order to make sure that the scores are being standardized to the most recent cohort group. Research has actually shown that IQs appear to be increasing (they don’t know the reason: more education, better nutrition, and medical care, etc), so the “average” keeps changing. They update them in order to re-standardize them. The bias question is more complex than you would think. Certain ethnic groups tend to do more poorly/better on certain IQ tests, however, this information in and of itself is not proof of bias. The other way that has been suggested is to examine the items of the test to determine whether bias is shown at an item-level. Most of your well-known standardized IQ tests have been revised a number of times and have not been shown to have a bias (Wechsler Adult Intelligence Scale; Standford-Binet). This is also why having updated norms that included various ethnic groups is so important.
Sometimes, however, tests can be biased. Educational tests are considered biased if a test design, or the way results are interpreted and used, systematically disadvantages certain groups of students over others, such as students of color, students from lower-income backgrounds, students who are not proficient in the English language, or students who are not fluent in certain cultural customs and traditions. Identifying test bias requires that test developers and educators determine why one group of students tends to do better or worse than another group on a particular test. For example, is it because of the characteristics of the group members, the environment in which they are tested, or the characteristics of the test design and questions? As student populations in public schools become more diverse, and tests assume more central roles in determining individual success or access to opportunities, the question of bias—and how to eliminate it—has grown in importance. There are a few general categories of test bias:
Construct-validity bias refers to whether a test accurately measures what it was designed to measure. On an intelligence test, for example, students who are learning English will likely encounter words they haven’t learned, and consequently, test results may reflect their relatively weak English-language skills rather than their academic or intellectual abilities. Content-validity bias occurs when the content of a test is comparatively more difficult for one group of students than for others. It can occur when members of a student subgroup, such as various minority groups, have not been given the same opportunity to learn the material being tested, when scoring is unfair to a group (for example, the answers that would make sense in one group’s culture are deemed incorrect), or when questions are worded in ways that are unfamiliar to certain students because of linguistic or cultural differences.
Item-selection bias, a subcategory of this bias, refers to the use of individual test items that are more suited to one group’s language and cultural experiences. Predictive-validity bias (or bias in criterion-related validity) refers to a test’s accuracy in predicting how well a certain student group will perform in the future. For example, a test would be considered “unbiased” if it predicted future academic and test performance equally well for all groups of students. Test bias is closely related to the issue of test fairness—i.e., do the social applications of test results have consequences that unfairly advantage or disadvantage certain groups of students? College-admissions exams often raise concerns about both test bias and test fairness, given their significant role in determining access to institutions of higher education, especially elite colleges and universities.
For example, female students tend to score lower than males (possibly because of gender bias in test design), even though female students tend to earn higher grades in college on average (which possibly suggests evidence of predictive-validity bias).To cite another example, there is evidence of a consistent connection between family income and scores on college-admissions exams, with higher-income students, on average, outscoring lower-income students. The fact that students can boost their scores considerably with tutoring or test coaching adds to the perception of socioeconomic unfairness, given that test preparation classes and services may be prohibitively expensive for many students. (Concerns about bias and unfairness are one contributing factor in a trend toward “test-optional” or “test-flexible” collegiate admissions policies.)
The following are several representative examples of other factors that can give rise to test bias: If the staff developing a test is not demographically or culturally representative of the students who will take the test, test items may reflect inadvertent bias. For example, if test developers are predominantly white, upper-middle-class males, the resulting test could, due to cultural oversights, advantage demographically similar test takers and disadvantage others. Norm-referenced tests (or tests designed to compare and rank test takers in relation to one another) may be biased if the “norming process” does not include representative samples of all the tested subgroups. For example, if test developers do not include linguistically, culturally, and socioeconomically diverse students in the initial comparison groups (which are used to determine the norms used in the test), the resulting test could potentially disadvantage excluded groups.
Certain test formats may have an inherent bias toward some groups of students, at the expense of others. For example, evidence suggests that timed, multiple-choice tests may favor certain styles of thinking more characteristic of males than females, such as a willingness to risk guessing the right answer or questions that reflect black-and-white logic rather than nuanced logic. The choice of language in test questions can introduce bias, for example, if idiomatic cultural expressions—such as “an old flame” or “an apples-and-oranges comparison”—are used that may be unfamiliar to recently arrived immigrant students who may not yet be proficient in the English language or in American cultural references. Tests may be considered biased if they include references to cultural details that are not familiar to particular student groups. For example, a student who recently immigrated from the Caribbean may never have experienced winter, snow, or snow-related school cancellation, and may therefore be thrown off by an essay question asking him or her to describe a snow-day experience.
Another aspect of culturally biased testing is implicated in the overrepresentation of black students, especially black males, in special-education programs. For example, the concern is that the tests used to identify students with disabilities, including intelligence tests, are misidentifying black students as learning disabled because of inherent racial and cultural biases. As for reform, with measurement error, some degree of bias and unfairness in testing may be unavoidable. The inevitability of test bias and unfairness are among the reasons that many test developers and testing experts caution against making important educational decisions based on a single test result. The Standards for Educational and Psychological Testing—a set of proposed guidelines jointly developed by the American Educational Research Association, American Psychological Association, and the National Council on Measurement in Education—include a recommendation that “in elementary or secondary education, a decision or characterization that will have a major impact on a test taker should not automatically be made on the basis of a single score.”
Given the fact that test results continue to be widely used when making important decisions about students, test developers and experts have identified a number of strategies that can reduce, if not eliminate, test bias and unfairness. A few representative examples include: Striving for diversity in test-development staffing, and training test developers and scorers to be aware of the potential for cultural, linguistic, and socioeconomic bias. Having test materials reviewed by experts trained in identifying cultural bias and by representatives of culturally and linguistically diverse subgroups. Ensuring that norming processes and sample sizes used to develop norm-referenced tests are inclusive of diverse student subgroups and large enough to constitute a representative sample.
Eliminating items that produce the largest racial and cultural performance gaps, and selecting items that produce the smallest gaps—a technique is known as “the golden rule.” (This particular strategy may be logistically difficult to achieve, however, given the number of racial, ethnic, and cultural groups that may be represented in any given testing population). Screening for and eliminating items, references, and terms that are more likely to be offensive to certain groups. Translating tests into a test taker’s native language or using interpreters to translate test items. Including more “performance-based” items to limit the role, that language and word-choice plays in test performance. Using multiple assessment measures to determine academic achievement and progress, and avoiding the use of test scores, in exclusion of other information, to make important decisions about students.