CH 24-Measurement and Analysis for Student Assessment

4 Qualities of Good Assessments

A good assessment is supposed to show what we have truly learned. There are four qualities of good assessments. Educators should ensure these qualities are met before assessing students. They are: Reliability Standardization Validity Practicality

Which of the following patterns of scores lies mostly in the mid-range?

A normal distribution is a pattern of educational characteristics or scores in which most scores lie in the middle range and only a few lie at either extreme.

A parent is confused by her child's score on two exams testing knowledge of musical terminology. On the first test, the child scored a 90. On the second test, the score was 30. What aspect of the test is the parent questioning?

An assessment is considered reliable if the same results are yielded each time the test is administered. In the example above, the musical terminology assessment did not yield similar results; therefore, it was not a reliable form of measurement.?

Cumulative Percentage and Percentile Rank

Another method to convert a raw score into a meaningful comparison is through percentile ranks and cumulative percentages. Percentile rank scores indicate the percentage of peers in the norm group with raw scores less than or equal to a specific student's raw score. In this lesson, 'norm group' is defined as a reference group that is used to compare one score against similar others' scores.

Standard Deviation & Bell Curves | Overview & Examples

Descriptive statistics are used to measure the essential properties of statistical data sets, including in particular the central tendency and dispersion (or variation) of the data. One measure of central tendency is the mean, often known as the average value. The standard deviation measures dispersion by identifying the typical difference between a data point and the central mean. The standard deviation is calculated as the square root of the variance, another measure of dispersion. Bell curves, or more specifically, bell-shaped normal distributions can be best understood by referring to their means and standard deviations, which determine the exact location and shape of the distribution. For example, a higher standard deviation will make the curve wider and shallower, while a lower deviation makes it taller and narrower. For a bell curve, the standard deviation can be considered as approximately measuring the width of the central bell. If the distribution is normal, about 68% of values will fall within a range of one deviation from the central mean value. According to the central limit theorem, normal distributions are commonly encountered in situations involving sample data. Symmetrical bell curves can be compared in positively-skewed and negatively-skewed distributions, where values are more dispersed on one side of the mean than the other. Some common properties of all normal distributions are summarized by the empirical rule which relates percentiles to a count of standard deviations. All normal distributions can be converted to the standard normal distribution, which is represented using a �-score. By assigning grades based on �-scores rather than raw scores, a test can be graded on a curve, meaning students are assessed more fairly based on their performance relative to others.

How does one grade a curve in a normal distribution?

Grading on a curve is done by assuming grades in a class follow a normal distribution. The actual grade can be determined based on a student's z-score, measuring their performance in terms of standard deviations relative to the class average.

Grading on a Curve and Standard Deviation

Grading on a curve refers to the process of assigning grades on an academic test based on the assumption that grades in a class will be normally distributed. A student's grade is determined not only by their personal score on the test but by their position on the curve, relative to the scores of the other students. For example, a student scoring 85% has done much better, relatively speaking, if the class average was 65% rather than if the average was 90%. By grading on a curve, grades from different years, different teachers, or different versions of a test can be compared on a more equal basis. A simple method to grade on a curve is to assign grades based on students' �-scores, rather than raw test scores. The �-score will indicate how many standard deviations a student scored on the test above or below the class average. Using the empirical rule as a guide, thresholds can be set for assigning different letter grades. For example, scores of �>1 could receive As, and scores 0≤�≤1 could receive Bs. Under this scheme, the top 15% of students would get an A, and the next 34% would get a B.

Qualities of Good Assessments: Standardization, Practicality, Reliability & Validity

Hey! The qualities of good assessments make up the acronym 'RSVP.' That's easy to remember! It's also important to note that of the four qualities, validity is the most important. That is because the assessment must measure what it is intended to measure above all else. Grades, graduation, honors, and awards are determined based on classroom assessment scores. Reliability is important because it ensures we can depend on the assessment results. Standardization is important because it enhances reliability. And practicality is considered last, when the other qualities have been accounted for.

According to the 68-95-99.7 rule _____.

In statistics, there is a rule called the 68-95-99.7 rule. This rule states that for a normal distribution, almost all values lie within one, two or three standard deviations from the mean. Specifically, approximately 68% of all values lie within one standard deviation of the mean. Approximately 95% of all values lie within two standard deviations of the mean and approximately 99.7% of all values lie within three standard deviations of the mean.

Using Mean, Median, and Mode for Assessment

In summary, classroom teachers often want to know how well an assessment went by summarizing the general trend in how well students did. We covered three different types of summary statistics. The mean is the arithmetic average score, or the number you get when you add up all the individual scores, then divide by the number of students. The median is simply the score in the middle, where half of the students did better than this score and half did worse. We use the median when there are outliers, or extreme scores that might affect the mean. Finally, the mode is simply the most common score or category. Modes are usually used when the data aren't in numerical form, which means that the mean or median are impossible to use. No matter which of these statistics you use, any of them are great ways to summarize a classroom assessment with a single, simple answer.

What is the best reason to use a median summary score instead of a mean summary score?

In the case of outliers, it's better to use the median.

Three raters compared their individual scores in order to assess _____ reliability.

Inter-rater reliability is used to assess the degree to which different observers or scorers give consistent estimates or scores.

A teacher includes three test items that assess the same concept. This teacher is attempting to assess _____ reliability of the instrument.

Internal consistency reliability is used to assess the consistency of scores across items within a single test. For example, if our science teacher wants to test the internal consistency reliability of her test questions on the scientific method, she would include multiple questions on the same concept.

Test-Retest Reliability

It is used to assess the consistency of scores of an assessment from one time to another. The construct to be measured does not change - only the time at which the assessment is administered changes. For example, if we are given a test in science today and then given the same test next week, we could use those scores to determine test-retest reliability. Test-retest reliability is best used to assess things that are stable over time, such as intelligence. Reliability is typically higher when little time has passed between administrations of assessments.

Norm-Referenced Scores

Norm-Referenced Scores Now let's discuss the type of score that compares one student's performance on an assessment with the average performance of other peers. This is referred to as norm-referenced scores. Norm-referenced scores are useful when educators want to make comparisons across large numbers of students or when making decisions on student placement (in K-12 schools or college) and grade advancement. Some familiar examples of norm-referenced assessments are the SAT, ACT and GRE.

Summarizing Assessment Results: Comparing Test Scores to a Larger Population

So you can see there are a few ways to understand and summarize assessment results. Let's recap what we discussed, and hopefully you will be able to apply these concepts to your classrooms. Test scores fall along a normal distribution, which we learned about in a previous lesson. A normal distribution shows that the majority of scores fall in the middle of the curve, with a few falling along the upper or lower range. This distribution shows us the spread of scores and the average of a set of scores. The normal distribution enables us to find the standard deviation of test scores, which measures the average deviation from the mean in standard units. Standard scores indicate how far a student's performance is from the mean with respect to standard deviation, and there are a few types of standard scores used in education, including stanines and Z-scores. Finally, we also discussed ways to represent scores by percentile and cumulative percentage rankings, which indicate the percentage of peers in the comparison group with raw scores less than or equal to the specified top score.

What is standard deviation on a bell curve?

Standard deviation is a measure of dispersion or spread within a distribution. For a bell curve, the standard deviation can be considered as approximately measuring the width of the central bell. If the distribution is normal, about 68% of values will fall within a range of one deviation from the central mean value.

How does standard deviation affect a bell curve?

Standard deviation is a measure of dispersion or spread within a distribution. In the case of a bell curve, a higher standard deviation will make the curve wider and shallower, while a lower deviation makes it taller and narrower.

Knowledge of basic statistics is helpful when interpreting _____ scores.

Standard score indicates how far a student's performance is from the mean with respect to the normal distribution of scores (also referred to as standard deviation units).

When an assessment has similar administration procedures, instructions and questions, it is considered to be a _____ assessment.

Standardization refers to the extent to which the assessment and procedures of administering the assessment are similar, and the assessment is scored similarly for each student.

Stanines

Stanines are used to represent standardized test results by ranking student performance based on an equal interval scale of 1-9. A ranking of 5 is average, 6 is slightly above average and 4 is slightly below average. Stanines have a mean of 5 and a standard deviation of 2.

Which of the following statistical tools is used to represent standardized test results by ranking student performance on an equal interval scale of 1-9?

Stanines are used to represent standardized test results by ranking student performance based on an equal interval scale of 1-9. A ranking of 5 is average, 6 is slightly above average and 4 is slightly below average. Stanines have a mean of 5 and a standard deviation of 2.

Statistics of Summary: the Mode

Statistics of Summary: the Mode The third and final statistic of summary is called the mode, which is simply the score obtained by the most people in the group. Let's go back to our original example of scores on the history test for the Revolutionary War. When you look at the test scores again, what is the most common score? The answer here is the score of 10. Five students got that score, so the mode in our example is the score of 10. Again, in this particular example, the mode is similar to both the mean and the median. So why would you use the mode instead of the mean or median? Usually the mode is used for examples when scores are not in numerical form. Remember, the mode is telling you what the most common answer is. So modes are good when the data involved are categorical instead of numerical. The most common score among the group represents the mode. Think about baseball teams. Who won the World Series last year? Do you know the team that's won the World Series the most often ever since it began? The answer is the New York Yankees. So it's accurate to say that the mode team for winning the World Series is the Yankees, because it's the most common answer. Let's go over one more example. When you get a new car, your car insurance price is based on a lot of things, like your gender and age, but it's also based on the color of your car. You have to pay more for insurance if you drive a red car. Why is that? It's because the mode color of car that gets into accidents is red. In other words, red cars get in more accidents than any other car - so red is the mode car accident color. It wouldn't make sense to try to use a mean or a median when talking about colors of cars, because there aren't any numbers involved. So for categories like colors or baseball teams, you have to use the mode if you want to create a statist

Using Assessments

Teacher: Thank you for coming in today to meet with me regarding your child's progress in school. I want to provide you information on the multiple types of assessments we take in the classroom and explain how we score and use the results for various purposes. We take multiple types of assessments in our class, and there are many ways I summarize the results of these assessments. These summaries provide feedback regarding your child's level of mastery and understanding. These assessments also give me a way to address any areas of weakness for individual students or in the class as a whole.

A school wants to determine if an assessment has reliability over time. They administer the same assessment at the beginning of a school year and at the end. The school is assessing _____ reliability.

Test-retest reliability is used to assess the consistency of scores of an assessment from one time to another.

standard score.

The final type of norm-referenced scoring is standard score. These scores indicate how far a student's performance is from the mean with respect to the normal distribution of scores (also referred to as standard deviation units). While these scores are useful when describing a student's performance compared to a larger group, they might be confusing to understand without a basic knowledge of statistics - which is covered in another lesson. We see here from your son's score that he falls about one standard deviation away from the mean (the average scores of the population that took the same assessment). This information tells us that his score is slightly above the scores of the other students.

Practicality

The fourth quality of a good assessment is practicality. Practicality refers to the extent to which an assessment or assessment procedure is easy to administer and score. Things to consider here are: How long will it take to develop and administer the assessment? How expensive are the assessment materials? How much time will the assessment take away from instruction?

Scores that compare one student's performance to the average performance of other students are referred to as _____.

The type of score that compares one student's performance on an assessment with the average performance of other peers is referred to as norm-referenced scores.

The normal distribution shows two things:

The variability or spread of the scores. The midpoint of the normal distribution. This midpoint is found by calculating a mean of all of the scores, or, in other words, the mathematical average of a set of scores. For example, if we had the following raw scores from your classroom - 57, 76, 89, 92, and 95 - the variability would range from 57 being the low score to 95 being the high score. Plotting these scores along a normal distribution would show us the variability. The midpoint of the distribution is also illustrated.

Which of the following is a method to obtain a reliability coefficient?

There are different way to get a reliability coefficient. There is inter-rater reliability, test-retest reliability, parallel-forms reliability, and internal consistency reliability.

Types of Validity

There are three main types of validity: content, predictive, and construct validity.

Study the examples below, and choose which one is the most appropriate for use of the mode, instead of the mean or median.

Usually the mode is used for examples when scores are not in numerical form.

A student complains that only 10 questions on a 100-question test were taken from the material assigned to study for the test. The student is questioning the test's _____.

Validity addresses whether or not an assessment accurately measures what it is intended to measure. In the example above, the assessment only tested 10 questions taken from the assigned study material; therefore, the student is questioning the test's validity.

The Relationship Between Validity and Reliability

Validity and reliability in the assessment are two concepts necessary in evaluating the quality of the research. They show how well a technique or test works when measuring a variable. Reliability is the consistency of any measure, meaning that it looks into how often the same result appears using the same technique. While a reliable measurement may not always be valid, the results must be reproducible even if they are incorrect. The validity, however, proves the reliability of the technique by producing accurate results. The importance of validity and reliability in assessment is that they help obtain valuable results that are both accurate and reproducible.

Validity is defined as _____.

Validity generally refers to how accurately a conclusion, measurement, or concept corresponds to what is being tested. Validity is defined as the extent to which an assessment accurately measures what it is intended to measure.

Measurement of Validity in Assessment

Validity in assessment is measured using coefficients. Correlation coefficients determine the relationship between two or more variables, in addition to their agreeability. The measurement involves two scores from two different assessments or measures calculated to get a figure between 0 and 1. The closer the coefficient is to 1, the higher the validity.

How do you determine the validity of an assessment?

Validity is determined using a coefficient. Basically, two different assessments are used to get two sets of scores which need to be between 0 and 1.

Validity in Assessment | Factors, Measurement & Types

Validity is the accurate conclusion of measurement or concept corresponding to the test conducted. It is how an assessment accurately depicts what needs to be measured. There are three types of validity, content, construct, and predictive. Content validity refers to how an assessment represents all areas addressed by a test. It identifies whether an assessment is representative of the content that needs evaluation. Construct validity looks into immeasurable traits that cannot be measured except through specific indicators. These traits include self-esteem, happiness, and motivation. On the other hand, predictive validity refers to the extent to which a score on an assessment predicts future performance. High predictive validity is represented by a coefficient of anything between 0 to 1. Companies or colleges will administer a test to a group to determine the predictive validity of an assessment and then measure the group's success in the behavior being predicted after a few weeks or months. The higher the validity coefficient, the higher the predictive validity.

What is an example of validity in assessment?

Validity requires reliability. For example, if the weighing scale is off by 10 pounds, then the weight of the individual using it should be off by the same amount.

A group of ten students take a test and they all get an F. What type of distribution would result considering the full possible range on the test was anywhere from an F to an A?

When a distribution is not normal and is instead weighted heavily on either side like this (all students got an F), it's called a skewed distribution.

When most people in a group have test scores in a certain range, but a single person has an extreme score that's very different, the single, different score is called a(n) _____.

When a score is extremely different from the rest of the scores in a distribution, that score is called an outlier.

When the shape of a distribution has a large rounded peak tapering away at each end, it is called a _____.

When the graph of a group of scores makes a bell curve, we see a large rounded peak tapering away at each end.

The reliability coefficient

is a numerical index of reliability, typically ranging from 0 to 1. A number closer to 1 indicates high reliability. A low reliability coefficient indicates more error in the assessment results, usually due to temporary factors that we previously discussed. Reliability is considered good or acceptable if the reliability coefficient is .80 or above.

A normal distribution is

is a pattern of educational characteristics or scores in which most scores lie in the middle range and only a few lie at either extreme. To put it simply, some scores will be low and some will be high, but most scores will be moderate.

bell curve

A pattern common to many data sets is to see values clustered symmetrically around a single central value, with decreasing numbers of data points further and further away from the mean. The resulting frequency distribution has a characteristic shape known as a bell curve: highest in the middle, and tapering off on either side. Measurements of physical characteristics, such as height and weight, often exhibit this pattern, with most people being relatively average, and smaller numbers being unusually short or tall, for example. The value of the standard deviation will be related to the width of the central body of the bell curve, where most values are concentrated. A larger standard deviation will correspond to a wider and flatter curve, spread over a wider range of values, though the exact value of the deviation cannot be exactly identified simply from the graph of a bell curve.

A raw score represents the _____.

A raw score is the score based solely on the number of correctly answered items on an assessment.

All of the following are ways to compare one test-taker score to a population of test-taker scores, EXCEPT:

A raw score is the score based solely on the number of correctly answered items on the assessment. This raw score will tell you how many questions the student got right, but just the score itself won't tell you much more.

Of the following standard deviations listed, which one indicates the most variance among test scores?

A small standard deviation tells us that the scores are close together, while a larger number tells us that they are spread apart more, indicating more variance among the scores.

The score that indicates how far a student's performance is from the mean with respect to standard deviation units is called the _____.

A standard score is the score that indicates how far a student's performance is from the mean with respect to standard deviation units. A specific type of standard score called the Z-score tells how many standard deviations a score is above or below the mean.

Standardization

Another quality of a good assessment is standardization. We take many standardized tests in school that are for state or national assessments, but standardization is a good quality to have in classroom assessments as well. Standardization refers to the extent to which the assessment and procedures of administering the assessment are similar, and the assessment is scored similarly for each student. Standardized assessments have several qualities that make them unique and standard. First, all students taking the particular assessment are given the same instructions and time limit. Second, the assessments contain the same or very similar questions. And third, the assessments are scored, or evaluated, with the same criteria. Standardization in classroom assessments is beneficial for several reasons. First, standardization reduces the error in scoring, especially when the error is due to subjectivity by the scorer. Second, the more attempts to make the assessment standardized, the higher the reliability will be for that assessment. And finally, the assessment is more equitable as students are assessed under similar conditions.

Mr. Yaki gives his students a test where scores can range from 0 to 10. The scores result in a normal distribution. Given this information, what was probably the most common score on the test?

Because Mr. Yaki's scores resulted in a normal distribution, we know that a lot of the scores fell in the middle. This might be like a letter grade of a C, but based on the data we have, it would be a score of 5.

A group of ten students take a test and they all get an A. Which of the following statistical results would be true for this group?

Because the scores are all close together (everyone got an A), the standard deviation is going to be very small.

A test with high _____ validity references the material actually taught to the students.

Content validity refers to the extent to which an assessment represents all facets of tasks within the domain being assessed. Content validity answers the question: Does the assessment cover a representative sample of the content that should be assessed?

Scores that indicate the level of knowledge or skills a student possesses in a specific area are referred to as _____.

Criterion-referenced scoring refers to a score on an assessment that specifically indicates what a student is capable of or what knowledge they possess. Criterion-referenced scores are most appropriate when an educator wants to assess the specific concepts or skills a student has learned through classroom instruction.

What are validity and reliability in assessment?

Reliability and validity are two concepts used in research. Reliability ascertains the consistency of a measure while validity looks to explore the accuracy.

Criterion-Referenced Scores

I want to discuss another method of scoring: criterion-referenced scoring. This refers to a score on an assessment that specifically indicates what a student is capable of or what knowledge they possess. Student scores can be tied to an equivalent age or grade level. Criterion-referenced scores are most appropriate when an educator wants to assess the specific concepts or skills a student has learned through classroom instruction. Most criterion-referenced assessments have a cut score, which determines success or failure based on an established percentage correct. For example, in my class, in order for a student to successfully demonstrate their knowledge of the math concepts we discuss, they must answer at least 80% of the test questions correctly. Your child earned an 85% on his last fractions test; therefore, he demonstrated knowledge of the subject area and passed. It's important to remember that criterion-referenced scores tell us how well a student performs against an objective or standard, as opposed to against another student. For example, a learning objective in my class is 'students should be able to correctly divide fractions.' The criterion-referenced score tells me if that student meets the objective successfully. The potential drawback for criterion-referenced scores is that the assessment of complex skills is difficult to determine through the use of one score on an assessment.

Positively and Negatively Skewed

If a distribution is not symmetrical then it is skewed, with more values falling on either the left or right side versus the other. A distribution is negatively skewed if values are dispersed over a wide range on the left side of the mean, and positively skewed if they are more dispersed on the right side. Visually speaking, negatively-skewed distributions often show a peak on the right (positive) side, while positively-skewed distributions peak on the left (negative) side. Positively- and negatively-skewed distributions. The name refers to the location of the long tail of the curve and not the high peak. While normal distributions may often be observed when measuring physical parameters, skewed distributions are more likely in financial data. For example, the distribution of employment incomes is positively skewed, since the majority of people have a low or moderate-income, with none below zero, but there is a small number of high-income individuals scattered over a very large range of values.

If a teacher wants to assess predictive validity of a test, a common way to achieve this is by _____.

In order to determine the predictive ability of an assessment, companies, such as the College Board, often administer a test to a group of people, and then a few years or months later, will measure the same group's success or competence in the behavior being predicted. A validity coefficient is then calculated, and higher coefficients indicate greater predictive validity.

Inter-Rater Reliability

In other words, do different people score students' performances similarly? This type of reliability is used to assess the degree to which different observers or scorers give consistent estimates or scores. For example, we performed in front of three teachers who scored us individually. High inter-rater reliability would indicate each teacher rated us similarly.

A _____ is an attribute (such as self-esteem, motivation and language proficiency) that is inferred from consistent behavior.

In psychology, a construct refers to an internal trait that cannot be directly observed but must be inferred from consistent behavior observed in people. Self-esteem, intelligence, and motivation are all examples of a construct. Construct validity, then, refers to the extent to which an assessment accurately measures the construct. This answers the question of: are we actually measuring what we think we are measuring?

Summarizing Assessment Results: Understanding Basic Statistics of Score Distribution

Now you can see a few ways to understand and summarize assessment results. First, we convert the raw score, which is the score based on the number of correctly answered items. We can then compare the results of one student to a larger population of students. We must understand the basic statistics of test score distribution. Test scores fall along a normal distribution, which shows that the majority of scores fall in the middle of the curve, with a few falling along the upper or lower range. This distribution shows us the spread of scores and the average of a set of scores. The normal distribution enables us to find the standard deviation of test scores, which measures the average deviation from the mean in standard units. Finally, according to the 68-95-99.7% rule, approximately all scores will fall within one, two or three standard deviations away from the mean.

Standard Deviation and Bell Curve

Numerical data sets can be summarized and analyzed using descriptive statistics, meaning measurements of certain essential features of the data set. Two key properties of any data set are central tendency, measured using an average value like the mean, and dispersion or variation, which measures how far values are scattered away from the central average.

The most important quality of a good assessment is _____.

Of the four qualities of a good assessment, validity is the most important. That is because the assessment must measure what it is intended to measure above all else.

Norm- vs. Criterion-Referenced Scoring: Advantages & Disadvantages

Okay, so let's recap what we have discussed in our meeting. First, there are multiple ways to score assessments. The scores tell us different things about a student's progress. Raw scores are simply the number of items correct on an assessment. Criterion-referenced scores tell us what a student is capable of because the score is reflective of successful demonstration of knowledge or failure to demonstrate knowledge in a specific area. Norm-referenced scores are a bit more complicated. These scores compare one student's score to other students across large groups. Scores can be compared by age and grade, referred to as age or grade equivalent scores. Scores can also represent a percentile ranking, which indicates the percentage of peers in the norm group scoring equal or lower to a specific student's score, referred to as percentile scores. Finally, scores can be compared to a mean, referred to as standard scores.

Standard Score, Stanines and Z-Score

Okay, you explained how to use a normal distribution to understand test scores. Now I still need to compare individual test scores to a larger population. Can you help me understand how to do that? A common method to transform raw scores (the score based solely on the number of correctly answered items on an assessment) in order to make them more comparable to a larger population is to use a standard score. A standard score is the score that indicates how far a student's performance is from the mean with respect to standard deviation units. In another lesson, we learned that standard deviation measures the average deviation from the mean in standard units. Deviation is defined as the amount an assessment score differs from a fixed value. The standard score is calculated by subtracting the mean from the raw score and dividing by standard deviation. Example of a standard deviation graph In education, we frequently use two types of standard scores: stanine and Z-score.

standard deviation,

One of the most important measures of dispersion is the standard deviation, which measures the typical difference that can be expected between individual values and the mean value. Most values will be scattered within one deviation above or below the mean. A small standard deviation indicates that values in the data set are mostly clustered together, while a large standard deviation indicates dispersion across a wider range. The standard deviation, denoted by � is defined to be the square root of the variance, the average squared deviation between individual values ��, and the mean value �:

Which of the following is NOT considered a statistic of summary?

Outliers are not a statistic of summary.

A percentile rank of 60 indicates that _____.

Percentile rank indicate the percentage of peers in the norm group with raw scores less than or equal to a specific student's raw score.

A student's score at the 85% percentile indicates that the student _____.

Percentile rank scores indicate the percentage of peers in the norm group with raw scores less than or equal to a specific student's raw score. In this lesson, 'norm group' is defined as a reference group that is used to compare one score against similar others' scores.

A school principal wants to know the cost and length of time needed to administer an exam. This refers to the _____ of the exam.

Practicality refers to the extent to which an assessment or assessment procedure is easy to administer and score, including how expensive the materials are and how long it will take to develop and administer.

A test is more valid if:

Predictive validity refers to the extent to which a score on an assessment predicts future performance.

The Reliability Coefficient and the Reliability of Assessments

Reliability ensures the consistency of scores or observations of student performance. External and internal temporary factors may impact reliability, such as day-to-day changes in the student, physical environment factors, and subjectivity of the scorer. Reliability is measured through the reliability coefficient with a numerical index range from 0 to 1. 1 indicates high reliability, while 0 would indicate lower. The different types of reliability - inter-rater, test-retest, parallel-forms, and internal consistency - measure different aspects, but all use the standard reliability coefficient range. Generally, a reliability of .80 or above indicates good or acceptable reliability.

Which of the following is most likely an acceptable reliability coefficient for a standardized assessment?

Reliability is considered good or acceptable if the reliability coefficient is .80 or above.

Standard deviations are used as a measure of variability

The mean and standard deviation can be used to divide the normal distribution into several parts. The vertical line at the middle of the curve shows the mean, and the lines to either side reflect the standard deviation. A small standard deviation tells us that the scores are close together, and a large number tells us that they are spread apart more. For example, a set of classroom tests with a standard deviation of 10 tells us that the individual scores were more similar than a set of classroom tests with a standard deviation of 35. In statistics, there is a rule called the 68-95-99.7 rule. This rule states that for a normal distribution, almost all values lie within one, two or three standard deviations from the mean. Specifically, approximately 68% of all values lie within one standard deviation of the mean. Approximately 95% of all values lie within two standard deviations of the mean and approximately 99.7% of all values lie within three standard deviations of the mean.

Examine this list of numbers: 3, 5, 5, 7, 7, 7, 7, 10, 18. What is the mode?

The mode is simply the score obtained by the most people in the group. In this case, it is 7.

Raw Scores

The most basic way to summarize an assessment is through a raw score. A raw score is the score based solely on the number of correctly answered items on an assessment. For example, this is your child's most recent math test. His raw score was a 96 because he got 96 items correct on the assessment. Raw scores are often used in teacher-constructed assessments. The potential drawback to the use of raw scores is that they may be difficult to interpret without knowledge of how one raw score compares to a norm group, which is a reference group used to compare one test taker's score to similar other test takers. We'll talk about using norm-referenced scores in a moment. Raw scores may also be difficult to understand without comparing them to specific criteria, which we will discuss now.

Standard Deviation

The normal distribution curve helps us find the standard deviation of the scores. Standard deviation is a useful measure of variability. It measures the average deviation from the mean in standard units. Deviation, in this case, is defined as the amount an assessment score differs from a fixed value, such as the mean.

The normal distribution shows the _____ and _____ of scores.

The normal distribution shows two things: The variability or spread of the scores. The midpoint of the normal distribution. This midpoint is found by calculating a mean of all of the scores, or, in other words, the mathematical average of a set of scores.

percentile rank.

The second type of norm-referenced scoring is percentile rank. These scores indicate the percentage of peers in the norm group with raw scores less than or equal to a specific student's raw score. Percentile rank scores can sometimes overestimate differences of students with scores that fall near the mean of the normed group and underestimate differences of students with scores that fall in the extreme lower or upper range of the scores. For example, let's look at your child's percentile score on a recent math standardized assessment. The percentile indicates he scored a 55. This means that he scored better than 55% of other students taking the same assessment.

A measurement that indicates how much a group of scores vary from the average called _____.

The standard deviation is a measurement that indicates how much a group of scores vary from the average.

Normal Distribution

The term "bell curve" is often used to specifically refer to the normal distribution. This is a continuous probability distribution that is symmetrical and bell-shaped, with a central peak occurring at the mean value (which coincides with the median and mode, two other measures of central tendency). The distribution tapers rapidly above and below the central value, decreasing asymptotically to zero. The equation that defines the curve of the normal distribution is �(�)=1�2��−12(�−��)2 The parameters � and � determine the mean and standard deviation of the distribution. There are thus many different normal distributions, with different means and standard deviations, but all having the characteristic bell shape. The normal distribution is particularly important in statistics because, according to the central limit theorem, it describes the sampling distribution of the mean. The sampling distribution covers the possible outcomes when an average value is calculated based on a random sample, which is a basic method of scientific data collection.

Validity

The third quality of a good assessment is validity. Validity refers to the accuracy of the assessment. Specifically, validity addresses the question of: Does the assessment accurately measure what it is intended to measure? An assessment can be reliable but not valid. For example, if you weigh yourself on a scale, the scale should give you an accurate measurement of your weight. If the scale tells you that you weigh 150 pounds every time you step on it, it is reliable. However, if you actually weigh 135 pounds, then the scale is not valid. Similar to reliability, there are factors that impact the validity of an assessment, including students' reading ability, student self-efficacy, and student test anxiety level.

Age/Grade Equivalent, Percentile, Standard

There are three types of norm-referenced scores. The first is age or grade equivalent. These scores compare students by age or grade. Breaking this type down, we can see that age equivalent scores indicate the approximate age level of students to whom an individual student's performance is most similar, and grade equivalent scores indicate the approximate grade level of students to whom an individual student's performance is most similar. These scores are useful when explaining assessment results to parents or people unfamiliar with standard scores. For example, let's look at your child's raw score on a recent math standardized assessment. Looking at the chart, we see that your child's raw score of 56 places him at an 8th grade level and an approximate age of 13. The potential disadvantage of using age or grade equivalent scores is that parents and some educators misinterpret the scores, especially when scores indicate the student is below expected age or grade level.

Internal Consistency Reliability

This form of reliability is used to assess the consistency of scores across items within a single test. For example, if our science teacher wants to test the internal consistency reliability of her test questions on the scientific method, she would include multiple questions on the same concept. High internal consistency would result in all of the scientific method questions being answered similarly. However, if students' answers to those questions were inconsistent, then internal consistency reliability is low.

Parallel-Forms Reliability

This type of reliability is determined by comparing two different assessments that were constructed using the same content domain. For example, if our science teacher created an assessment with 100 questions that measure the same science content, she would divide the test up into two versions with 50 questions each and then give two versions of the test to her students. She would use a score from version 1 and a score from version 2 to assess parallel-forms reliability.

How to Read a Bell Curve

While there are many different normal distributions, they all have certain underlying features in common. Remember that standard deviation measures the distance from the mean which will contain "most" data points. For normal bell curves it can now be more specific: "most" means approximately 68%, no matter what the precise value of the standard deviation may be. Expanding to a range of two deviations above and below the mean will contain about 95% of the data, and a range of three deviations includes more than 99%. This property of all normal distributions is known as the empirical rule. A fixed proportion of normally-distributed values will fall within a given number of standard deviations from the mean. According to the empirical rule, all normal bell curves are, in a way, proportional. Take advantage of this by converting any normal distribution to the standard normal distribution, which has mean �=0 and standard deviation �=1. The formula for converting to a a standardized �-score is �=�−�� Converting raw measurements to �-scores make it easier to read and interpret normal distributions. All values can be expressed on a common scale, which represents a count of standard deviations. Any measurement with a score of �=0 is exactly average within its distribution. Positive scores indicate a measurement that is above average, while negative scores are below average. More specifically, any value with a score of �=1 falls one deviation above the mean, while scores of �=2 and higher cover the small proportion of values that are two deviations or more above average, meaning they are relatively large.

Which of the following statistical tools has a standard deviation of 1 and a mean of 0?

Z-scores are used frequently by statisticians and have a mean of 0 and a standard deviation of 1. A Z-score tells us how many standard deviations someone is above or below the mean.

Z-scores

Z-scores are used frequently by statisticians and have a mean of 0 and a standard deviation of 1. A Z-score tells us how many standard deviations someone is above or below the mean. To calculate a Z-score, subtract the mean from the raw score and divide by the standard deviation. For example, if we have a raw score of 85, a mean of 50 and a standard deviation of 10, we will calculate a Z-score of 3.5.

Calculate the z-score using the following data: Raw score is 75, mean is 50, and standard deviation is 10

Z-scores are used frequently by statisticians and have a mean of 0 and a standard deviation of 1. A Z-score tells us how many standard deviations someone is above or below the mean. To calculate a Z-score, subtract the mean from the raw score and divide by the standard deviation.

Predictive or

criterion validity is essential in evaluating the correspondence of results concerning each other, such as how closely the test results of one student correspond to a different student's test. A criterion is the external measurement of two similar things and is favored when evaluating validity. For example, a teacher creates a test to measure the ability of the students to develop a good story. However, the teacher also uses a different test that is the standard for measuring the ability to create a good account. Therefore, the teacher will use the results of the standard test as the grading criteria and compare the results of both tests to assess the students' abilities. They may also examine and measure the success a few weeks or months later to determine validity. High predictive ability is therefore realized when the results of both tests are similar.

Cumulative percentages

determine placement among a group of scores. Cumulative percentages do not determine how much greater one score is than another or how much less it is than another. Cumulative percentages are ranked on an ordinal scale and are used to determine order or rank only. Specifically, this means that the highest scores in the group will be the top score no matter what that score is. For example, let's take a test score of 85, the raw score. If 85 were the highest grade on this test, the cumulative percentage would be 100%. Since the student scored at the 100th percentile, she did better than or the same as everyone else in the class. That would mean that everyone else made either an 85 or lower on the test. Graph illustrating cumulative percentages Cumulative percentages and percentiles are ranked on a scale of 0%-100%. Changing raw scores to cumulative percentages is one way to standardize raw scores within a certain population.

Reliability

is defined as the extent to which an assessment yields consistent information about the knowledge, skills, or abilities being assessed. An assessment is considered reliable if the same results are yielded each time the test is administered. For example, if we took a test in History today to assess our understanding of World War I and then took another test on World War I next week, we would expect to see similar scores on both tests. This would indicate the assessment was reliable. Reliability in an assessment is important because assessments provide information about student achievement and progress. There are many conditions that may impact reliability. They include: day-to-day changes in the student, such as energy level, motivation, emotional stress, and even hunger; the physical environment, which includes classroom temperature, outside noises, and distractions; administration of the assessment, which includes changes in test instructions and differences in how the teacher responds to questions about the test; and subjectivity of the test scorer.

Content validity

is necessary to evaluate whether a test is representative of the various aspects of a specific subject. To get valid results, it is crucial for the content of the test to cover all the relevant areas that the subject needs to measure. If there are any missing areas in the measurement, the validity is compromised. For example, assume a mobile company needs to conduct a survey on customer satisfaction on a phone model they are launching. The survey needs to include questions like the quality, features, design, price, and other features to cover the study.

A raw score

is the score based solely on the number of correctly answered items on the assessment. This raw score will tell you how many questions the student got right, but just the score itself won't tell you much more. Let's now move onto how scores can be used to compare one student's results to the results of other students.

Construct validity

is the type that aids in evaluating various measurement tools with ease and providing an actual representation of what needs measuring. It is vital in signifying the overall validity of the method used. A construct is defined as a feature or concept that one cannot directly observe but can be measured by observing the indicators that relate to the characteristic. These features to monitor may include happiness, depression, motivation, and fitness. Since construct validity measures things that do not have units, such as emotions, the most helpful way is to collect indicators of these concepts. For example, happiness is measured through indicators such as positivity, smiling, energy levels, and laughing. On the other hand, an emotion like anxiety is measured by noting restlessness, distraction or difficulty concentrating.