Week 2

Question 1

A Question From L2: A - Test Scores and Norms

What is fundamental to any test score?

Answer 1

• Knowing what that score means relative to some sort of criteria or reference group.

Question 2

A Question From L2: A - Test Scores and Norms

What is criterion referencing?

Answer 2

• Criterion referencing is a way of giving meaning to test
  score by specifying the standard that needs to be reached
  in relation to a limited set of behaviours.

Question 3

A Question From L2: A - Test Scores and Norms

What type of test is a driving test considered as and why?

Answer 3

• It is a criterion referenced test.
• This is because there are a number of componencies you have to prove, to obtain an adequate score to get your licence.
• Your performance is not measured against others; it only matters how well you do relative to the driving test criteria.

Question 4

A Question From L2: A - Test Scores and Norms

Why isn’t criterion testing for measures of personality or intelligence?

Answer 4

• Criterion testing works well when there is a known pool of behaviours you will be testing.
• For things like personality and intelligence, we do not have a sense of the full spectrum of behaviours associated with those constructs, so we can judge all behaviours against a list of criteria.
• Instead we would use norm referencing.

Question 5

A Question From L2: A - Test Scores and Norms

What is norm referencing? What is a key part of norm referencing that makes or breaks it?

Answer 5

NORM REFERENCING:
* * Norm referencing is a way of giving meaning to test score by relating it to the performance of an appropriate reference group for the test taker/person.

**KEY OF NORM REFERENCING: **
* The reference group must be meaningful to the test taker/person.
* Essentially, you are expressing the raw score total in terms of its position in the distribution of all the raw scores from a sample of individuals with whom it is sensible to compare the test taker with.

Question 6

A Question From L2: A - Test Scores and Norms

What is an item score and how is it different from a raw score total?

Answer 6

Every test comprises a number of items.
Normally, what happens is those items are scored and then
the raw score total is the score obtained by adding
all the items scores get.

Raw score by itself is meaningless - it must be transformed!

Question 7

A Question From L2: A - Test Scores and Norms

Linear transformations

Answer 7

So when you add, subtract, divide or multiply all
raw scores by a constant, you change the scores.
But you still preserve the linear relationship between the raw
school and the transform school.
The order is the same. If you add five to every school, the order and
the distance between schools is the same.
The linear transformation, um, means that the transformation can be
plotted as a line and that follows the equation Y
equals MX plus C,

Example: converting your test score out of 40 to a percentage. Doing this to everyone’s scores still keeps all the individual scores equivalent to ttheir original scores, as well as perserving the proportions between each score.

Question 8

A Question From L2: A - Test Scores and Norms

What happens when you plot a linear transformation on a graph?

Answer 8

• If we map a linear transformation onto a graph, your raw score is plotted against the transform score, which creates a straight line. AKA, you get a linear transformation.

Question 9

A Question From L2: A - Test Scores and Norms

What is a Z score?
How is a Z score a transformation?

Answer 9

THE Z SCORE:
* The z score is a linear transformation that expresses the distance of each raw score from the mean of the distribution in units of the standard deviation of that distribution.
* The z score represents a number of standard deviations above or below the mean.

HOW IS A Z SCORE A TRANSFORMATION:
* A Z score is a transformation.
* It takes a raw score and transforms it by making the mean 0 and the standard deviation 1.

THE CALCULATION:
1. You take a raw score, subtract the mean from the raw score.
2. Then divide that by the standard deviation.

Question 10

A Question From L2: A - Test Scores and Norms

What is the difference between an item, a raw score, an item score and a raw score total?

Answer 10

ITEM:
* An item refers to a single question or task in a test, survey, or assessment.
* For example, in a multiple-choice exam, each question is an item.

**RAW SCORE: **
* A raw score is the unaltered numerical value obtained from scoring an individual item or a set of items.
* For example, if a question is worth 1 point and the answer is correct, the raw score for that item is 1.

**ITEM SCORE: **
* An item score is the specific score assigned to a single item, often reflecting the correctness or quality of the response.
* For example, an item scored as 0 (incorrect) or 1 (correct) in a binary grading system.
*
A RAW SCORE TOTAL:
* A raw score total refers to the sum of all individual raw scores for a given set of data or responses.

Question 11

A Question From L2: A - Test Scores and Norms

What equation is this? What does X, M and SD mean?

Answer 11

It is a Z score!
* M = mean
* SD = standard deviation
* X = raw score
* A positive score indicates the data point is above the mean.
* A negative score indicates it is below the mean.
* A score of 0 means the data point is exactly at the mean.

Can also look like this:

Question 12

A Question From L2: A - Test Scores and Norms

What is the answer if X = 30; M = 25; SD = 5? What is meanful about this?

Answer 12

• Z score is 1
• We know that you score is a standard deviation higher then the scores of everyone in the sample.
• It tells you something about the relative position of your score.

Question 13

A Question From L2: A - Test Scores and Norms

What do we do linear transformations?

Answer 13

• A linear transformation helps you to be able
  to make comparisons between different measures and different components of a test.
• For example, it means that you can take different sub-tests and make those different scores comparable.
• When they are in their raw scores they are meaningless and you cannot make any sort of comparison.
• But once you’ve transformed them into a Z score or
  into a scaled score, then they become comparable.

Question 14

A Question From L2: A - Test Scores and Norms

Why is Z considered untidy?

Answer 14

• There are positive and negative numbers.
• Any score above the mean is positive and any score below the mean is negative.
• You work with decimal places which is messy.

Question 15

A Question From L2: A - Test Scores and Norms

What is a standardised score?

Answer 15

• A standardized score, also known as a z-score, is a statistical measure that describes how far a data point is from the mean of a dataset, measured in terms of standard deviations.
• Different people have used different variants of the
  Z score, by setting it a particular mean and standard deviation.

Question 16

A Question From L2: A - Test Scores and Norms

What is Deviation IQ, what is the equation, and how do you interpret the score?

Answer 16

DEFINITION:
* * The Deviation IQ calculation involves comparing an individual’s test performance to the performance of their age group within a standardized sample.
* This is done by converting the raw score to a z-score, and then scaling the z-score to an IQ score with a mean of 100 and a standard deviation of 15.

INTERPRETING SCORES:
* This ensures that the average IQ is 100 and that approximately 68% of the population will have an IQ between 85 and 115 (one standard deviation from the mean).

THE EQUATION:
The calculation can be either:

or:
Deviation IQ = 15z + 100

Question 17

A Question From L2: A - Test Scores and Norms

What is a T score, what is the equation and how do you interpret the score?

Answer 17

DEFINITION:
* A T score is a standardized score that indicates how many standard deviations a data point is from the mean of a distribution. It is commonly used in statistics to compare individual scores to a reference group.

INTERPRETING SCORES:
* A T score of 50 represents the mean of the reference group.
* Scores above 50 indicate performance above the mean, while scores below 50 indicate performance below the mean.
* Each 10-point difference corresponds to one standard deviation from the mean.

THE EQUATION:

It can also look like:
T-Score = 10z + 50

Question 18

A Question From L2: A - Test Scores and Norms

What is a scales score, what is the equation?

Answer 18

DEFINITION:
* A scale score is a numerical representation of a test taker’s performance, typically derived from raw scores (e.g., number of correct answers) and transformed to a standardized scale for easier interpretation and comparison.
* Scaling adjusts raw scores to account for variations in test difficulty across different versions or administrations, ensuring fairness and consistency in scoring.

THE EQUATION:
The calculation for this is:
Scale Score = 3z + 10

Question 19

A Question From L2: A - Test Scores and Norms

What is a sten score, what is the equation and how do you interpret the score?

Answer 19

THE DEFINITION
* * A sten score, or Standard Ten Score, is a method of standardizing test scores into a 10-point scale.
* It is commonly used in psychological and educational testing to simplify the interpretation of results.
* This scale provides a straightforward way to compare individuals’ performance relative to a norm group.

INTERPRETING SCORES:
* Scores range from 1 to 10, where:
* 1–4 indicates below-average performance,
* 5–6 represents average performance,
* 7–10 signifies above-average performance.

THE EQUATION:
The equation is:
Sten = 2z + 5.5

Question 20

A Question From L2: A - Test Scores and Norms

What is a non-linear transformation and how is it different from linear transformations?

Answer 20

DEFINITION:
* A non-linear transformation is a type of mathematical operation that maps a set of input values to a set of output values in a way that is not a straight line when plotted on a graph.
* A non linear transformation does not preserve the equivalence of distances between scores.

DIFFERENCE BETWEEN LINEAR AND NON-LINEAR TRANSFORMATIONS:
* Linear transformations preserve operations of addition and scalar multiplication and result in straight-line graphs.
* Non-linear transformations involve more complex relationships that can include curves, bends, or other non-linear characteristics.

Question 21

A Question From L2: A - Test Scores and Norms

What are the key characteristics of non-linear transformations?

Answer 21

1. Non-Linearity:
   * The relationship between input and output is not a straight line.
   * This means that the transformation cannot be represented by a simple linear equation of the form
   .
2. Complex Relationships:
   * Non-linear transformations can involve polynomial, exponential, logarithmic, trigonometric, or other complex functions.
3. Applications:
   * These transformations are widely used in various fields such as machine learning, computer graphics, and data analysis to model complex phenomena that cannot be captured by linear models.

Question 22

A Question From L2: A - Test Scores and Norms

What is a percentile and percentile rank?

Answer 22

DEFINITION OF PERCENTILE:
* Percentiles are the most common non linear transformation in psychological testing.
* A percentile is a measure used in statistics indicating the value below which a given percentage of observations in a group of observations falls.
* For example, the 20th percentile is the value below which 20% of the observations may be found.
* Percentiles divide a dataset into 100 equal parts.
* They are useful for comparing individual data points to the broader dataset, such as in standardized test scores or growth charts.

DEFINITION OF PERCENTILE RANK:
* A percentile rank indicates the percentage of a distributional scores that falls below a particular score.
* It’s your position relative to other people in a
particular reference group expressed as a percentage.
* Percentile ranks looks at what’s the percentage of scores that fall up to and including our score of interest?
* Using our Z score, we can work out what is the area under the curve up to that value, what are the percentage of scores that are higher than that particular Z score, as well as what is the area between two scores

HOW TO CALCULATE:
One way in which you can calculate percentile ranks is to compute the Z score, (assuming normal distribution) and then you read from the normal distribution table to identify the percentile.

Question 23

A Question From L2: A - Test Scores and Norms

What is a stanine and how do you calculate one?

Answer 23

DEFINITION:
* A stanine (short for “standard nine”) is a method of scaling test scores on a nine-point standard scale with a mean of 5 and a standard deviation of 2.
* Stanines are used to simplify the interpretation of test scores by dividing the distribution of scores into nine intervals, each representing a specific range of percentile ranks.
* It is a way of conveying percentiles in a clear manner; one way of categorising a person poisiton on a distribution.

CALCULATION:
Stanines are derived by ranking scores and assigning them to one of nine groups:
* Stanine 1: Bottom 4% of scores
* Stanine 2: Next 7% of scores
* Stanine 3: Next 12% of scores
* Stanine 4: Next 17% of scores
* Stanine 5: Middle 20% of scores
* Stanine 6: Next 17% of scores
* Stanine 7: Next 12% of scores
* Stanine 8: Next 7% of scores
* Stanine 9: Top 4% of scores

Question 24

A Question From L2: A - Test Scores and Norms

Why is it nice to have a standard normal distribution?

Answer 24

• When data is normally distributed, you have more
  information that you can use in your interpretation of someone’s test performance.
• You can calculate Z scores to make things more comparable, and then to use that to identify, the percentile.
• That’s all adds meaning to that score in terms
  of how a person has done relative to other measures
  and relative to other people in that cohort.

Question 25

# *A Question From L2: A - Test Scores and Norms* Why is sampling important?

Answer 25

* These linear and nonlinear transformations are very useful in terms of interpreting a score. But they rely on having a reliable and accurate, mean and standard deviation for the reference group, and that is a critical part of you rely on. * You need to be confident that in order to interpret test scores using, Z scores or percentiles, it might be that you're using a mean and standard deviation that is the accurate for the reference group and that is meaningful for the test taker. * Norms are created from the sample knowing that the reference group was representative of the studied population, according to those key variables.

Question 26

# *A Question From L2: A - Test Scores and Norms* What is the difference between random sampling, convenience sampling and stratified sampling?

Answer 26

**RANDOM SAMPLING:** * Random sampling is a method where every member of the population has an equal and independent chance of being selected. * This ensures the sample is representative of the population, minimizing bias. * Much more likely to be representative, and less likely to be biased. **CONVENIENCE SAMPLING:** * Convenience sampling involves selecting participants based on their availability and willingness to take part. * This method is quick and easy but often introduces bias, as the sample may not represent the broader population. **STRATIFIED SAMPLING:** * Stratified sampling divides the population into subgroups (strata) based on shared characteristics, then randomly selects samples from each stratum. * This ensures representation across key subgroups, improving accuracy for heterogeneous populations. Final Answer ## Footnote Random sampling ensures equal chance of selection, convenience sampling selects based on availability, and stratified sampling divides the population into subgroups for representative sampling.

Question 27

# *A Question From L2: A - Test Scores and Norms* What are some things to be mindful of when it comes to sampling?

Answer 27

* What type of sampling is being used: Random, convenience, or stratified? * How well does that sample represent a sample group? Is it a meaningful representation? * How big is the sample size? * The sample size on which the different normative data are based. Generally, bigger samples are much better than smaller samples as they're less likely to be biassed. But bigger samples are also expensive to collect, so there's a rule of thumb suggesting how big a sample should be. * Are there appropriate local norms for the test? But those groups then tend to be small

Question 28

# *A Question From L2: B - Finding Percentile Rank, Given Z* What is the standard normalised distribution?

Answer 28

* A standard normal distribution, also know as a Z distribution, is a special case of the normal distribution: 1. *mean = 0 2. variance = 1 3. standard deviation = 1 4. area = 1 (this means that the proportion of scores that fall somewhere underneath the curve is one). * It is a precise mathematical shape that is symmetrical ## Footnote **VARIANCE:** Variance is a statistical measure that quantifies the dispersion or spread of a set of data points around their mean. It is calculated as the average of the squared differences from the mean.

Question 29

# *A Question From L2: B - Finding Percentile Rank, Given Z* How to work out a percentile rank when given a + Z score?

Answer 29

**EXAMPLE:** Z = 0.8 1. Draw a diagram *(in this example my diagram tells me that the Z score is greater than 50% but not that close to 100%). * 2. Look at the info availble in the table? Is the answer just provided? *(in the example, no it does not)* **STRATEGY 1** 3. Blue area total = Area from 0 to Za *(score of interest)* + 0.5 *(the negative area between -3.00 and 0)* 4. Pop it into the equation: 0.2881 + 0.5 = 0.7881 X 100 = 78.81% **STRATEGY 2:** 3. Blue area total = 1 - Area beyond Za *(score of interest)* 4. Pop it into the equation: 1 - 0.2119 = 0.7881 X 100 = 78.81%

Question 30

# *A Question From L2: B - Finding Percentile Rank, Given Z* How to work out a percentile rank when given a - Z score?

Answer 30

**EXAMPLE:** Z = -1.22 1. Draw a diagram *(in this example my diagram tells me that the Z score is in the lower, negative part of the diagram)*. 2. Look at the info available in the table? Is the answer just provided? *(in the example, yes it is! But there are no negatives. That is okay as we know that the Z distribution is perfectly symmetrical)* 3. In the table I look for a Za (score of interest) of 1.2200 and then look for answer under the column 'Area beyond Za'. This is where I find, 0.1112. 4. I turn that into a percentage and I get 11.12%

Question 31

# *Definition please* Criterion Referencing

Answer 31

**Criterion Referencing** * Criterion referencing is a way of interpreting test scores by specifying a standard that needs to be achieved in relation to a defined set of behaviors or tasks. * It establishes the pass or fail criteria based on explicit performance levels rather than comparative scores.

Question 32

# *Definition please* Deviation IQ

Answer 32

**Deviation IQ** * Deviation IQ is a method that allows an individual's score on an intelligence test to be compared with the scores of same-age peers. * It is reported as the distance from the mean in standard deviation units.

Question 33

# *Definition please* Linear Transformation

Answer 33

**Linear Transformation** * Linear transformation refers to the method of changing test scores in such a way that the relationships and differences between scores are preserved. * It is typically represented by a straight-line equation.

Question 34

# *Definition please* Local Norms

Answer 34

**Local Norms** * Local norms are norms developed for specific population groups or geographical regions, allowing for more relevant comparisons in test scoring.

Question 35

# *Definition please* Norm Referencing

Answer 35

**Norm Referencing** * Norm referencing interprets a test score by comparing it to the scores of a relevant reference group. It provides context on how an individual's performance correlates with peers.

Question 36

# *Definition please* Norms

Answer 36

**Norms** * Norms are standards derived from the data of a representative sample that describe the distribution of scores on a test. * They are used for comparing an individual's score to an established benchmark.

Question 37

# *Definition please* Percentile

Answer 37

**Percentile** * A percentile indicates the position of a specific score in a distribution by dividing the ranking into 100 equal parts, showing the percentage of scores that lie below it.

Question 38

# *Definition please* Standard Score

Answer 38

**Standard Score** * A standard score is a score derived from transforming a raw score into a new score based on a specific mean and standard deviation, allowing comparison across different tests.

Question 39

# *Definition please* Sten Score

Answer 39

**Sten Score** * A sten score is a point on a scale from 1 to 10, with specific percentiles assigned to each point, used to summarize a person's performance relative to the norm group.

Question 40

# *Definition please* Stratified Sampling

Answer 40

**Stratified Sampling** * Stratified sampling is a sampling method that involves dividing a population into distinct subgroups (strata) and randomly sampling individuals from each strata to ensure representation across key characteristics.

Question 41

# *Definition please* T Score

Answer 41

**T Score** * A T score is a standardized score that has been transformed to a distribution with a mean of 50 and a standard deviation of 10.

Question 42

# *Definition please* Raw score

Answer 42

**Raw score** * A raw score refers to the total score obtained by summing individual item scores on a psychological test. * It represents a numerical value without any transformation or normalization applied to it, providing a basis for further interpretation within the context of the test's structure and content.

Question 43

# *Definition please* Nonlinear transformation

Answer 43

**Nonlinear transformation** * Nonlinear transformation, in the context of psychological test scores, refers to altering the distribution of raw scores in a way that does not preserve the equivalence of differences between scores. * This transformation is used to enhance discrimination in certain score ranges, particularly in the middle of the distribution, without maintaining a linear relationship between the original and transformed scores.

Question 44

# *Definition please* Percentile rank

Answer 44

**Percentile rank** * The term percentile rank refers to the percentage of scores in a distribution that fall below a specific score. * It provides a clear way to understand an individual's performance relative to others, indicating their standing within the distribution.

Question 45

# *Definition please* Z score

Answer 45

**Z score** * In the context of the research paper, a Z score represents a linear transformation of a raw score that reflects the distance of that score from the mean of a distribution in terms of standard deviations. * Z scores are commonly used in psychological testing to indicate an individual's position relative to the mean of a distribution, with positive values indicating scores above the mean and negative values indicating scores below the mean.

Question 46

# *Definition please* Difficulty

Answer 46

**Difficulty** * In the context of the paper, "Difficulty" refers to the level of challenge presented by individual items in cognitive ability tests. It is a key factor influencing scoring probability and is quantified through item response theory, specifically using the Rasch model's logit scale. * The transformation of item difficulty on the logit scale, such as the W scale for specific tests like the Woodcock-Johnson III, allows for consistent interpretations of scores across different reference groups.

Question 47

# *Definition please* Cluster sampling

Answer 47

**Cluster sampling** * Cluster sampling is a sampling method where the population is divided into groups or clusters, and a random selection of clusters is chosen to represent the entire population. * This method is useful when it is difficult or impractical to sample individuals individually.

Question 48

# *Definition please* Random sampling

Answer 48

**Random sampling** * Random sampling, as described in the context of the text, is a method of sampling in which individuals are selected from a population in a manner that provides each member an equal chance of being chosen. * This approach helps ensure that the sample is representative with regard to specific characteristics deemed important for the study’s objectives.

Question 49

# *Definition please* Age equivalent

Answer 49

**Age equivalent** * In the context of the summary, "Age equivalent" refers to a specific age at which a median test score is achieved by children, allowing for a comparison of an individual’s raw score to typical performance levels within a defined age group. * For example, if a raw score of 20 corresponds to the median score for 10-year-olds, that score is assigned an age equivalent of 10 years, indicating typical performance for that age.

Question 50

# *Definition please* Probability sampling

Answer 50

**Probability sampling** * Probability sampling is a method of sampling in which the sample is drawn from the population in such a way that it matches it with respect to certain characteristics considered important for the study. * This sampling method aims to provide a representative subset of the population where each member has a known, non-zero probability of being selected.

Question 51

Non-probability sampling

Answer 51

** Non-probability sampling** * Non-probability sampling refers to a sampling method where samples are selected from a population based on non-random criteria, meaning that not every individual has a known or equal chance of being included. * In the context of the paper, it is characterized as stratified or quota sampling, which ensures that the sample reflects certain important characteristics of the population relevant to the study's objectives.