Standardized Testing Basic Terminology Evaluation a judgment Measurement

Standardized Testing

Basic Terminology • Evaluation: a judgment • Measurement: a number • Assessment: procedure to gather information

Norm- and Criterion. Referenced Tests • Normreferenced – General ability – Compares people to people – Selecting top candidates • Criterionreferenced – – Mastery Basic skills Prerequisites Grouping for instruction

What Do Test Scores Mean? • • • Standardized test Norming sample Frequency distributions Central tendency Variability

Frequency Distribution Histogram

Central Tendency • Mean – The arithmetic average • Median – The middle score • Mode – The most frequently occurring score

Variability • Range • Standard deviation – Indicates how much the scores vary from the mean

Calculating the Standard Deviation • • Calculate the mean: c Subtract the mean from each score: (c-c) Square each difference: (c-c)2 Add all the squared differences: S(c-c)2 Divide by the number of scores: S(c-c)2 N Find the square root : S(c-c)2 N

Sample Problems

Calculate the mean, median, mode, range, and standard deviation for the following sets of scores • Reading – – – – – 95 90 85 80 75 70 65 60 55 • Arithmetic – – – – – 76 78 77 71 75 79 74 72 73

Calculations • Reading c c-c (c-c)2 – – – – – 95 90 85 80 75 70 65 60 55 20 15 10 5 0 -5 -10 -15 -20 400 225 100 225 400 S(c-c)2 = 1500 • Arithmetic c c-c (c-c)2 – – – – – 76 78 77 71 75 79 72 73 74 +1 +3 +2 -4 0 +4 -3 -2 -1 1 9 4 16 0 16 9 4 1 S(c-c)2 = 60

Calculations continued Reading Arithmetic S(c-c)2 N S(c-c) 2 N =166. 67 S(c-c)2 =6. 67 N =12. 91 S(c-c)2 N = 2. 58 Standard deviations

Completed Calculations – – – Reading Mean = 75 Mode = none Median = 75 Range = 40 Standard deviation = 12. 91 – – – Arithmetic Mean = 75 Mode = none Median = 75 Range = 8 Standard deviation = 2. 58

Normal Distributions • The “bell curve” • Mean, median, mode all at the center of the curve • 50% of scores above the mean • 50% of scores below the mean

Normal Distribution with Standard Deviations Percent of the population 34% 2% 34% 14% -3 SD -2 SD -1 SD 2% 14% 0 +1 SD +2 SD +3 SD Standard Deviation Units

Types of Scores • Percentile rank • Grade-equivalent • Standard scores – z scores – T scores – Stanine scores

Interpreting Test Scores • • • Reliability True score Standard error Confidence intervals Validity

Types of Standardized Tests • Achievement Tests – Measure previous learning • Diagnostic Tests – Identify strengths and weaknesses • Aptitude Tests – Measure abilities

Issues in Testing • Widespread testing • Accountability and high stakes testing