Norms

Norm-referenced testing and assessment

method of evaluation and a way of deriving meaning from test scores by evaluating an individual testtaker’s score and comparing it to scores of a group of testtakers

In this approach, the meaning of an individual test score is understood relative to other test scores on the same test

norms

the test performance data of a particular group of testtakers that are designed for use as a reference for evaluating or interpreting individual test scores

nromative sample

• a group of people whose performance on a particular test is analyzed for reference in evaluating the performance of individual testtakers

• Members of the normative sample should be typical with respect to some characteristic(s) of the people for whom the particular test was designed

• A test administration to this representative sample of testtakers yields a distribution (or distributions) of scores

• These data constitute the norms for the test and typically are used as a reference source for evaluating and placing into context test scores obtained by individual testtakers

Standardization

The process of administering a test to a representative sample of testtakers for the purpose of establishing norms is referred to as standardization • A test is said to be standardized when it has clearly specified procedures for administration and scoring, including normative data

Sampling

• The test developer can obtain a distribution of test responses by administering the test to a sample of the population − a portion of the universe of people deemed to be representative of the whole population • The process of selecting the portion of the universe deemed to be representative of the whole population is referred to as sampling

Population

• In the process of developing a test, a test developer has targeted some defined group as the population for which the test is designed

• This population is the complete universe or set of individuals with at least one common, observable characteristic

• Testig entire population is too much

stratified sampling

Subgroups within a defined population may differ with respect to some characteristics, and it is sometimes essential to have these differences proportionately represented in the sample

Such sampling termed stratified sampling, would help prevent sampling bias and ultimately aid in the interpretation of the findings

stratified-random sampling

If such sampling were random (that is, if every member of the population had the same chance of being included in the sample), then the process would be termed stratified-random sampling

purposive sampling

If we arbitrarily select some sample because we believe it to be representative of the population, the sample we have selected is referred to as purposive

Manufacturers of products frequently use purposive sampling when they test the appeal of a new product in one city or market and then make assumptions about how that product would sell nationally

incidental sampling

An incidental sample or convenience sample is one that it is convenient or available for use

It is not that the students in such subject pools are necessarily the most appropriate subjects for the experiments, it is just that they are the most available

Percentiles

The median is the numerical value that separates the higher half of a distribution from the lower half • Alternatively, the distribution can be divided into 100 equal parts − 100 percentiles • In such a distribution, the xth percentile is equal to the score below which x% of scores fall • Thus, the 15th percentile is the score below which 15% of the scores in the distribution fall

Additionally, percentiles are very adaptable to a wide range of tests

Percentile Formula

Raw scores may be converted to percentiles with the use of the following formula

P = nLαπο κατω /N * 100

P = percentile

nL = the number of scores lower than the score being converted to a percentile

N = the total number of scores

Type of Norms – Percentile Norms

Percentile norms are the raw data from a test’s standardization sample converted to percentile form

Type of Norms – Age Norms

Age norms indicate the average performance of different samples of testtakers who were at various ages at the time the test was administered

If the measurement under consideration is height in inches, for example, we know that scores (heights) for children will gradually increase at various rates as a function of age up to the middle to late teens

Type of Norms – Grade Norms

Designed to indicate the average test performance of testtakers in a given school grade, grade norms are developed by administering the test to representative samples of children over a range of consecutive grade levels

• Next, the mean or median score for children at each grade level is computed

Type of Norms – National Norms

National norms are derived from a normative sample that was nationally representative of the population at the time the norming study was conducted • In the fields of psychology and education, for example, national norms may be obtained by testing large numbers of people representative of different variables of interest such as age, gender, racial/ethnic background and socioeconomic status

Type of Norms – National Anchor Norms

Type of Norms – Subgroup Norms

A normative sample can be segmented by any of the criteria initially used in selecting subjects for the sample

What results from such segmentation are more narrowly defined subgroup norms.

For example, suppose criteria used in selecting children for inclusion in the XYZ Reading Test normative sample were age, educational level, socioeconomic level, geographic region, community type, and handedness • The test manual or a supplement to it might report normative information by each of these subgroups

Type of Norms – Local Norms

Typically developed by test users themselves, local norms provide normative information with respect to the local population’s performance on some test • For example, a school guidance center may find that locally derived norms for a particular test–say, a survey of personal values–are more useful in counseling students than the national norms printed in the manual