Test Interpretation and Norms

• Test interpretation involves placing measurement data in a context to make sense of test scores
• It relies on the validity of prior steps like test construction, administration, and scoring
• Interpretation needs statements about the test's limitations and potential sources of error
• Without proper accounting for limitations, test scores can be misinterpreted
• Test interpretation focused on norms, comparing a test score to a group of scores
• Norm-referenced interpretations contrast with criterion-referenced interpretations which compare to a standard

Norms

• Norms consist of data about a distribution of scores for a particular test
• Testing aims to compare individual scores and detect differences
• Developers of norm-referenced tests look for items with the greatest possible variability
• Achievement tests retain items of average difficulty, discarding items everyone passes or fails
• Aggregating such items increases valid distinctions among individuals
• Norm-referenced testing is common in selection testing due to its lower cost
• It's useful when selecting a portion of a group, rather than those who can perform a function
• Norm-referenced tests are useful in selection when resources are scarce

Measurement-Related Statistics

• Statistics facilitate the interpretation of test scores
• Understanding statistical indices is important
• Test developers examine the frequency distribution of all test scores to check for normal distribution

Mean or Average

• Mean or average measures central tendency in a group of scores
• It's found by summing scores and dividing by the number of scores
• Median and mode are other measures of central tendency
• Useful for comparing different groups taking same test

Standard Deviation

• Standard deviation is a measure of how dispersed scores are
• It refers to the average deviation of scores from the mean
• A larger standard deviation signifies a wider spread of scores
• It quantifies the amount of variation or dispersion in a set of values
• Low standard deviation = data points close to mean
• High standard deviation = data points spread out over a wider range
• Standard deviation calculated by finding data set mean, subtracting the original mean from each data point, squaring the result, finding the mean of the squared differences, then taking the square root to get the standard deviation
• Formula for population: σ = √(Σ (Χί - μ)² / Ν)
• σ = Population standard deviation
• N = Number of observations in the population
• Xi = ith observation in the population
• μ = Population mean
• Formula for sample: s = √(Σ (xi - x)² / (n - 1))
• s = Sample standard deviation
• n = Number of observations in the sample
• xi = ith observation in the sample
• x = Sample mean

Z Scores

• Z scores (or standard scores) transform raw scores into deviations from the mean
• z = (Raw score – mean) / Standard deviation
• Z scores indicate how high or low a person scored in the distribution
• Positive z scores = above the mean
• Negative z scores = below the mean

T-Score

• Converts test scores to a standardized scale
• It has a mean of 50
• It has a standard deviation of 10
• T-Scores are a type of scaled score presented in a meaningful way

Sten Score

• Converts scores on a test to a standardized scale
• Has a mean of 50
• Has a standard deviation of 10
• Like T-Scores, Sten scores present scores meaningfully

Stanine

• Stanine scores scale test scores on a nine-point standard scale
• Test scores are converted from the original to a number between 1 and 9
• The two-step process scales test scores to stanine scores.
• Stanines 1, 2, 3 are below average
• Stanines 4, 5, 6 are average
• Stanines 7, 8, 9 are above average

Percentile

• Percentile tells the percentage of all scores that given test score lies above
• A test score higher than 90% of all other test scores is at the 90th percentile
• A test score exactly in the middle of all test scores is the 50th percentile

Test interpretation involves placing measurement data in a context to make sense of test scores. It relies on validity and requires statements about the test's limitations and potential errors. Norms consist of data about a distribution of scores for a particular test.