## Topic 1: Norms and Meaning of Test Scores {by 5/28}

Based on the text readings and lecture recording due this week consider the following two discussion points: (1) In your own words, provide a general description of the difference between criterion/domain-referenced instruments and norm-referenced instruments. Why is it important to understand this difference? (2) What are your thoughts on your understanding of the normal distribution? In other words, does it generally make sense (explain) or is it still a little confusing (that’s okay – explain)?

Your original post should be posted by 5/28. Post your two replies no later than 5/25. *Please remember to click the “reply” button when posting a reply. This makes it easier for the reader to follow the blog postings.

Haley Scola

May 24, 2020@ 16:57:44The difference between criterion/domain-referenced instruments and norm-referenced instruments is that criterion-referenced instruments are used in order to measure a whole-group performance, while a norm-differenced instrument measures the performance of the individuals in the group. Criterion-referenced instruments also measure performance on specific concepts while norm-referenced instruments measure performance based on several resources. It’s important to understand the difference because if you used a norm-differences instrument in attempt to measure the performance of a whole group you would be unable to and it would not be efficient, resulting in the wrong answers. Normal distribution is a bell-shaped curve where most of the data lies. It can show data unknown based on the probability. I understand the overall concept of normal distribution but still struggle understanding the specifics.

Althea Hermitt- Mcpherson

May 25, 2020@ 03:57:40Me too Haley I don’t understand it all and feel like a little a zoom explanation would personally help me.

Madi

May 26, 2020@ 14:25:09I thought your response to the first part of the question showed a clear understanding of the topic. It was very clean and concise. Regarding the second part of the question you are right it is a bell curve but i think it is important to note it is a bell curve because most of the data is in the center which is why it has that shape.

Yen Pham

May 24, 2020@ 19:47:581. In your own words, provide a general description of the difference between criterion/domain-referenced instruments and norm-referenced instruments. Why is it important to understand this difference?

To interpret a score on any instrument, practitioners first need to consider whether it is a norm-referenced or criterion/domain- referenced instrument.

A norm-referenced instrument is one in which an individual’s performance is compared with the performance of the other individuals who have taken the same instrument. The examples of the norm-referenced instrument are the tests include the SAT, IQ tests, and tests that are graded on a curve. Anytime a test offers a percentile rank, it is a norm-referenced test. If you score at the 90th percentile that means that you scored better than 90% of people in your group. The term norm refers to the group of individuals who took the instrument to which other’s scores are then compared. A norming group can be quiet large, such as a national sample of 2, 000 adults who have taken a personality inventory. A norm also could be your classmates, such as when an instructor “grade on the curve”. Thus, to evaluate the norming group we consider the size, the sampling, and the representation.

A criterion-referenced instrument or domain is designed to compare an individual’s performance on an instrument to an established criterion or standard. Its focus is on what test-takers can do and what they know, not on how they compare with others. Sometimes with a criterion-referenced test, there is a mastery component- a predetermined cutoff score indicates whether the person has attained an established level of mastery such as a state’s department of education may designate a certain test score on a high school graduation examination that all high school students must achieve before they can graduate, a teacher may test to find out if a student has mastered the multiplication table for the number 3 before allowing the student to learn the multiplication table for the number 4. Standard is determined as common practice, professional organizations or experts, and empirically-determined.

Difference between Norm and Criterion-referenced Instruments:

Firstly, on the performance, Norm-Referenced Instruments (NRIs) are judged based on other individuals’ performance while Criterion-Referenced Instruments (CRIs) are each individual is independently assessed. Secondly, on the comparison, NRIs are compared to an individual’s performance with other individuals while CRIs do not compare an individual’s performance with other individuals. Thirdly, on the objective, NRIs its main objective is to assess an individual’s performance with other individuals while CRIs its main objective is to help individuals learn without getting questioned about grades. Finally, on the criteria, NRIs’ criteria change with outcomes while CRIs have fixed criteria (standard) for assessment. In conclusion, the characteristics and difference between norm and criterion-referenced instruments are (1) both are suitable for different tasks, (2) both have their own criteria of judgment, (3) they follow different norms and values.

It is important to understand the characteristics and differences between norm and criterion-referenced instruments because they provide a counselor, a teacher, and an entrepreneur a capacity to apply what these instruments in a particular context or circumstances. If so, they will achieve the desired and purpose as they wish to do. For example, they should use the norm and criterion-referenced instruments if they want to compare the performance of an individual with the other individuals who have taken the same instrument. However, if they want to compare an individual’s performance with a criterion or standard, they should use the criterion-referenced instruments.

2. What are your thoughts on your understanding of the normal distribution? In other words, does it generally make sense (explain) or is it still a little confusing?

My understanding of the normal distribution or a normal curve that it is one type of frequency distributions. It the most important probability distribution in statistics, because it fits many natural phenomena such as heights, blood pressure, measurement error, points on a test, IQ scores, and salaries follow the normal distribution.

There are several properties of a normal distribution that the mean, mode and median are all equal. The mean is in the center of the standard normal distribution, and a probability of 50% equals zero standard deviations. The mean defines the location of the peak for normal distributions. Most values cluster around the mean. Changing the mean shifts the entire curve left or right on the X-axis. The curve is symmetric at the center (i.e. around the mean, μ). Exactly half of the values are to the left of center and exactly half the values are to the right. The total area under the curve is 1 i.e., the total area under a standard normal distribution curve is 100% (that’s “1” as a decimal): The left half of the curve is 50%, or 0.5. So the probability of a random variable appearing in the left half of the curve is 0.5. Similarly, a random variable appearing in the right half of the curve is 0.5

The normal curve reflects that the largest number of cases falls in the center range and that the number of cases decreases gradually in both directions. There exists an empirical rule, also known as the three-sigma rule or the 68-95-99.7 rule, which provides a quick estimate of the spread of data in a normal distribution given the mean and standard deviation. Specifically, the empirical rule states that for a normal distribution: 68% of the data will fall within one standard deviation of the mean. 95% of the data will fall within two standard deviations of the mean. Almost all (99.7%) of the data will fall within three standard deviations of the mean. The empirical rule is used as a rough gauge of normality. When some data points fall outside the three standard deviation range, it can indicate non-normal distributions.

Let’s look at a pizza delivery example. Assume that a pizza restaurant has a

mean delivery time of 30 minutes and a standard deviation of 5 minutes. Using the Empirical Rule, we can determine that 68% of the delivery times are between 25-35 minutes (30 +/- 5), 95% are between 20-40 minutes (30 +/- 2*5), and 99.7% are between 15-45 minutes (30 +/-3*5).

Note: The standard deviation controls the spread of the distribution. A smaller standard deviation indicates that the data is tightly clustered around the mean; the normal distribution will be taller. A larger standard deviation indicates that the data is spread out around the mean; the normal distribution will be flatter and wider.

Althea Hermitt- Mcpherson

May 25, 2020@ 03:59:27Yen, thanks for the pizza examples.

Althea Hermitt- Mcpherson

May 25, 2020@ 03:43:38Criterion/domain referenced instruments analyze participants’ scores on a particular assessment tool based on that individual own capacity and knowledge which hinges on some kind of benchmark or gauge. Therefore if the criteria to pass or fail a particular test is based on getting over 75% then it means that anyone who gets a score of 75 or above will pass and any one who gets a score below 75% will fail eg. LMHC exam.

Normed referenced Instruments according to the text refers to any instrument that compares the scores of a norming group/ standardized sample (individuals who were used to make the test) to an individual who is taking the test eg. ADHD instruments, Depression Instrument. Therefore these instruments compare individuals to ascertain whether you fall in the normal range or abnormal range.

It’s important to understand these differences because it will give more information on the interpretation and presentation of the data.

What are your thoughts on your understanding of the normal distribution? In other words, does it generally make sense (explain) or is it still a little confusing (that’s okay – explain)?

Normal distribution is necessary to make inferences on the distribution of data. Normal distribution takes a number of scores or data and organizes it in such a way that comparison and contrast can be made to figure out trends. Therefore average scores, middle score, most frequent score and less frequent score are all calculated and represented based on the normed group/standardized sample. Normal distribution is therefore represented by a single peak diagram due to the fact that the most frequent score, the middle score and the average score are the same and fall mainly in the center of the diagram, while the other scores lessen or tape off on either side.

Madi

May 26, 2020@ 14:20:521. The difference between criterion / domain-references instruments are instruments that compare an individual’s performance to a standard. Whereas norm-referenced instruments are instruments that compare an individual’s performance to others that have taken the same instrument. It is important to understand this difference because the first looks at an individual’s scores compared to a predetermined cut off and the second compares the scores to other individuals.

2. Normal distribution is a bell cure where the bulk of the scores are in the middle creating two tail ends. Where one standard deviation away from the mean is 34.2%, two standard deviation away from the mean is an additional 13.6%, and three standard deviations away from the mean is an additional 2.1%.