week3-1_testing.ppt

Basic Concepts in Measurement & Statistics 01/18/24 1 Defining Measurement Psychological measurement is the process of assigning numbers (that is, test scores) to people. Scales of measurement; Nominal scales Ordinal scales Interval scales Ratio scales 01/18/24 2 Scales of Measurement...

Basic Concepts in Measurement & Statistics 01/18/24 1 Defining Measurement Psychological measurement is the process of assigning numbers (that is, test scores) to people. Scales of measurement; Nominal scales Ordinal scales Interval scales Ratio scales 01/18/24 2 Scales of Measurement Nominal scales (in name only)  (e.g., eye color, gender, ethnicity) Ordinal scales (ordering)  (e.g., ranking according to height) Interval scales (equal distances)  (e.g., calendar years) Ratio scales (absolute zero)  01/18/24 (e.g., weight in pounds, age 3 Scales of Measurement 01/18/24 4 Scales of Measurement 01/18/24 5 Distribution A distribution is a set of scores Normal distribution: A theoretical distribution with a symmetrical shape and the highest frequency concentrated in the middle. 01/18/24 6 Distribution 01/18/24 7 Distribution A distribution is a set of scores 01/18/24 8 Distribution Negatively Skewed. 01/18/24 Positively Skewed. 9 Distribution 01/18/24 10 Distribution Positively Skewed. 01/18/24 11 Evaluating Psychological Tests Reliability: A reliable test yields consistent scores when a examinee takes two alternate forms of the test or when s/he takes the same test on two or more different occasions. 01/18/24 12 Evaluating Psychological Tests Validity Validity of measurement Whether the test adequately measures what it purports to measure.  If this is the case, an intelligent person should receive higher scores than do less intelligent people.  Validity of decisions  01/18/24 A valid test is useful for making accurate decisions about individuals. 13 Statistical concepts 3 major concepts: Variability Allows us to measure and describe the extent to which test scores differ.  Computing the difference between each person’s score and the mean.   01/18/24 A large variance indicates that individual scores often differ from the mean. 14 Variability 01/18/24 15 Statistical concepts Variability  One application of the standard deviation is to form standard scores, z scores.  A (+) z score means that you are above the mean. score frequency 4 4 3 6 2 8 1 2 01/18/24 Z scores mean=2.6 sd=.94 16 Statistical concepts Correlation  are often illustrated by using scatterplot. Aptitude scores and grades Correlation coefficient describes the strength and direction of a relationship between variables.  a[ 01/18/24 17 Correlation 01/18/24 18 Correlation 01/18/24 19 Statistical concepts r = .90 r = - .85 r = .21 r = -.10 Strong, positive correlation Strong, negative correlation Weak, positive correlation Weak, negative correlation  Pearson Product-Moment Correlation Coefficient  When variables are on an interval or ratio scale.  Spearman Rank Correlation Coefficient  When the variables are on an ordinal scale  Point-Biserial Correlation Coefficient  One variable dichotomous; one on an interval or ratio scale 01/18/24 20 Statistical concepts Prediction  01/18/24 We can predict one’s behavior from test scores. 21 Prediction Linear Regression allows you to predict values on one variable given information on another variable. Note: Y = a + bX when a = 10 and b = 0.5. For example, if X is 30, then Y = 10 + (0.5)30 = 25. 01/18/24 22 Prediction Percentile The point below which a specified percentage of the observations fall. If a student’s IQ score (130, z= 2) is at 98 th percentile, 98% of the IQ scores are below this score. Student’s score is better than 98% of the all students. 01/18/24 24 Percentile 01/18/24 25 Percentile 01/18/24 26 Scales & Transformations Comparing scales A score of 4 on a 5-point scale. What is the equivalent score of it on a 7-point scale? 01/18/24 27 Scales & Transformations Raw scores do not tell whether the subject did well.  Need more interpretable scores Characteristics of transformations: Doesn’t change a person’s score, just expresses it in a different way.  Takes into account information not contained in the raw scores itself.  Expresses the scores in more interpretable units.  01/18/24 28 Linear Transformations Changing number(s) by adding (+), substracting (-), multiplying (x) or dividing (/) Transformed score= constant + (weight x raw score) Most familiar linear transformation is z score Z=(X-M)/SD  Easy to interpret (- and + scores), can be easily converted to percentiles.  Negative scores, have fractional values (at least 2 decimal points).  01/18/24 29 Linear Transformations z score A z score of 0? 84.1%? 01/18/24 30 Linear Transformations 01/18/24 31 Linear Transformations t score=(z score x 10)+50 01/18/24 score frequency z scores 4 4 1.49 3 6 .43 2 8 -.64 1 2 -1.70 t scores 32 Area Transformations express a person's score in terms of where it falls on the normal curve, rather than simply providing a new unit of measurement (like linear one did). 01/18/24 33 Area Transformations Percentile Scores 1.Cum Fm= (0.5 x f) + Cum F below 2.Percentile scores= Cum Fm x (100 / n) scor e fre q Cum f Cum Fm Percentile scores 4 4 20 .5 x 4 + 16 = 18 18x(100/20) = 90 3 6 16 .5 x 6 + 10 = 13 13x 5 = 65 2 8 10 .5 x 8 + 2 = 6 6x5 = 30 1 2 2 .5 x 2 + 0 =1 1x5 = 5 01/18/24 34 Area Transformations 01/18/24 35