What are the 3 characteristics needed for a standardized sample? 

1.   Mean, median, and mode are equal to one another               

2. Perfectly symmetrical about the mea

 3. Tails are asymptotic

Understanding requires:

·      Observing

·      Measuring

·      Describing

·      Distinguishing 

 We do so for:

·      Research purposes

·      Evaluative purposes

What questions might I ask understand the 

 unit of measure?

. What if there is a new test with different levels?

(e.g. % SS vs. %SW)

·      Is this the only way to measure this variable?

·      What does it mean?

·      How does it compare to published/refereed data?

·      And does this data come from a reliable source?

·      How can this be determined?

·      How close is this to “normal”?

o   Central tendency

o   Dispersion

§  e.g., GRE scores

 “normal” curve.

o   (a.k.a. the Bell-Shaped Curve)

Visual representation of a distribution of scores

 must have knowledge of the entire field, including:

·      norms and testing techniques

·      observational techniques

·      ability to interact effectively

·      intuition

·      differentiate among or btwn:

- types of communication problems

- subtypes of particular disorders   

- between delay and disorder

- between treatment options

o   (and whether treatment will help).

This might mean…….

·      using descriptive or qualitative measures, or

·      using experimental/standardized measures.

What must the Test users  consider when selecting tests? 

-meet the intended purpose

 -appropriate for the test takers. 

1)  Define the purpose for testing, the content and skills to be tested, and the intended test takers. Select and use the most appropriate test based on a thorough review of available information.

2)  Review and select tests based on the appropriateness of test content, skills tested, and content coverage for the intended purpose of testing.

3) Review materials provided by test developers and select tests for which clear, accurate, and complete information is provided.

4) Select tests through a process that includes persons with appropriate knowledge, skills, and training.

5) Evaluate evidence of the technical quality of the test provided by the test developer and any independent reviewers.

6) Evaluate representative samples of test questions or practice tests, directions, answer sheets, manuals, and score reports before selecting a test.

7) Evaluate procedures and materials used by test developers, as well as the resulting test, to ensure that potentially offensive content or language is avoided

8) Select tests with appropriately modified forms or administration procedures for test takers with disabilities who need special accommodations.

9) Evaluate the available evidence on the performance of test takers of diverse subgroups.

Determine to the extent feasible which performance differences may have been caused by factors unrelated to the skills being assessed. 

What must be considered when Administering and scoring tests?

1) Give the test in a standardized way by following the instructions provided. 

2) Provide and document appropriate procedures for Indiv with disabilities, need special accommodations or those with diverse linguistic backgrounds.

3) Test takers: Opportunity to become familiar with test formats and materials or equipment used during testing.

4) Protect the security of test materials,

includes: copyrights and eliminating opportunities for TT to obtain scores.

5) Provide adequate training to scorers

        ensure and monitor the accuracy of  scoring 

6) Correct errors that affect the interpretation

and communicate the corrected results

promptly.

7) Develop and implement procedures to esnure confidentiality of scores. 

Describe how to Report and Interpret the Test Results

1) Interpret the meaning of the test results:

• taking into account the nature of the conten
• norms or comparison groups
• other technical evidence,
• benefits 
• limitations of test results

2) Interpret test results from modified test or test administration procedures

•  impact those modifications may have had on test results.

3) Avoid using tests for purposes other than those recommended by the test developer

• unless there is evidence to support the intended use or interpretation.

4) Review the procedures for setting performance standards or passing scores.

• Avoid using stigmatizing labels.

5) Avoid using a single test score as the sole determinant.

• Interpret scores with other information 

6) State the intended interpretation and use of  results

for groups of test takers.

• Avoid grouping test results for purposes not  recommended by the developers
•  unless evidence is obtained to support the intended use. 
• Report procedures used in determining who were and who were not included in the groups 
• being compared and describe factors may influence the interpretation 

7) Communicate test results in a timely fashion and easily understood by the TT

8) Develop and implement procedures for monitoring test use

• including consistency with the intended purposes of the test. 

What is Descriptive Statistics?

·      Used to organize and describe the characteristics of a particular data set

·      Example: the average age of everyone in this class!

What is Inferential Statistics?

·      Used to make inferences from your “sample” to the “population”

·      Example: comparing the mean age of students taking this course to average age of all students in an introductory statistics course

Basic Concepts of Research and Testing

·      The ultimate reason for research is to answer a question.

Measures of Central Tendency

·      The AVERAGE is a single score that best represents a set of scores

·      Averages are also known as “Measure of Central Tendency”

What are the 3 ways to describe the distribution of a set of scores?

·      Mean – typical average score

·      Median – middle score

·      Mode – most common score

Sample mean

•  measure of central tendency 
•  best represents the population mean

• Mean is VERY sensitive to extreme scores that can “skew” or distort findings

=

Computing the Median

Median = point/score at which 50% of remaining scores fall above and 50% fall above.

NO standard formula

Rank order scores from highest to lowest or lowest to highest

Find the “middle” score

BUT…

What if there are two middle scores?

What if the two middle scores are the same?

Answer

You take their average.

With an odd number of values, there's no problem, say you have 7 values and you've ranked them lowest to highest. The fourth value is your median.

If you had 8 values, add 

Use the Mode when the data are nominal

Use the Median 

when you have extreme scores or the data is ordinal

Use the Mean 

hen you have data that do not include extreme scores and are not categorical (interval or ratio)

Variability

How different scores are from one particular score.   

•  measures of Spread or Dispersion.                
• how each score in a group of scores differs from the mean 

Measures of Variability

What are the Three types of variability?  

the amount of spread or dispersion in a group of scores…

1. Range

2. Standard Deviation

3. Variance

Typically report the measure of central tendency and the measure of dispersion together to describe a distribution. 

Computing the Range

Range is the most “general” estimate of variability…

R = h – l

(Note: R is the range, h is the highest score, l is the lowest score)

Ages of students in this class:

21,23,22,22,24,53,22

R = 53 -21

Standard Deviation

 (SD) is the most frequently reported measure of variability

SD = average amount of variability in a set of scores

What do these symbols represent?

Why n – 1?

• an estimate of the POPULATION 
•  “unbiased estimate”

Things to Remember…

• SD computed as the avg distance from the mean
• larger the SD the greater the variability
• SD is sensitive to extreme scores
• If s = 0, no variability among scores
• they must all be the same value.