Measurement

Question 1

What is measurement?

Answer 1

“the process of assigning numbers to persons in such a way that some attributes of the persons being measured are faithfully reflected by some property of the numbers”;

Question 2

What are we measuring in psychology?

Answer 2

We measure behavior, never a psychological construct

Question 3

What are metrics?

Answer 3

metrics are tools that we use to compare people

Question 4

What are statistics?

Answer 4

statistics are tools we use to describe and evaluate how well tests perform

Question 5

Why are scores arbitrary?

Answer 5

a score locates an individual on a scale of that psychological dimension, but what is the magnitude between scores? What does it mean?

Question 6

Types of measurement scales?

Answer 6

Nominal
Ordinal
Interval
Ratio

Question 7

What is a nominal scale? Please give an example.

Answer 7

numbers take on the meaning of a verbal label, but don’t signify any particular amount of a trait (boy, girl; boy isn’t any better than girl)

Question 8

What is a ordinal scale? Please give an example.

Answer 8

numbers denote order or ranking, but not amount of a trait, and there is no consistent differences between numbers (e.g., satisfaction on a Likert scale—can’t say exactly how far apart they are)

Question 9

What is a interval scale? Please give an example.

Answer 9

numerical differences in scores represent equal differences in trait being measured (e.g., Temperature F or C)

Question 10

What is a ratio scale? Please give an example.

Answer 10

have a true zero point, with zero=total absence of the trait being measured AND can make proportional statements, with twice the score=twice the attribute (e.g., money, Temperature K, height M; depression scale where possible that person is not depressed at all, and a person with a score of 10 is twice as depressed as score of 5)

Question 11

What are the measures of central tendency? Describe each.

Answer 11

Mode: most frequently occurring;
Median: the literal middle score, the number that separates the top half from the bottom half of a score distribution, the 50th percentile;
Mean: the arithmetical average score, calculated by summing the scores, then dividing by the total number of scores. (xi)/N

Question 12

In the normal curve, what is the relationship between mean, median, and mode?

Answer 12

theoretical distribution of human traits in nature; also called the normal distribution or bell curve; mean, median, and mode are the same value in a normal distribution; same proportion of scores can always be found within the same standard deviation limits

Question 13

What is variability and why is it important to psychometrics?

Answer 13

variation among test scores is the life blood of psychometric analyses. Compare individuals, groups, understand how different individual characteristic are related and examine the effectiveness of interventions. Without variability among test scores, it would be very difficult to learn anything at all. Variance reflects the extent to which individuals differ (compared to the test mean).

Question 14

What are the two types of variability?

Answer 14

Interindividual (group) vs Intraindividual (within on person).

Question 15

What is variability determined by?

Answer 15

1. The degree to which the scores in the group actually differ
2. The metric of the scores

Question 16

How do you calculate variance?

Answer 16

Variance is standard deviation (s) squared.

It is the absolute value of the sum of (point minus mean) squared over the population (N)

Question 17

Purpose of standard deviation?

Answer 17

To return squared measure of variability to original metric

Question 18

How do you calculate standard deviation?

Answer 18

Well, it’s the square root of variance.

Or, the square root of the squared sums of (data point minus mean) all over N

Question 19

How do you interpret a variance or standard deviation score?

Answer 19

Interpreting a variance score: can never be less than zero, no simple way to interpret a variance or standard deviation score as large or small; the variance of a distribution of scores is most interpretable and meaningful when its put into some kind of use; we use these concepts to help us find other values that we can interpret more directly

Question 20

How do you interpret psychological tests? What are the two pieces of information you need?

Answer 20

many psychological tests produce “raw” scores that are (initially ambiguous). Reframe scores (that mean nothing-40 on a scale? What?). Reframe it within a useful informational context. The distribution of raw scores on a test can be useful contextual information. How far above or below the mean (of the distribution) is the score? Need two pieces of information:

1. The mean of the distribution (x̄).
2. The standard deviation of the distribution (sX)

Question 21

What is a z-score? What is the purpose and how do you calculate it?

Answer 21

translate a person’s raw score (X) into a z-score. Reflects how far above/below the mean the person’s raw score is. + z-score means the person is above the mean (- is below the mean). The size of the z score in standardized units will tell you how far away the individual is from the mean. Purpose: how many standard deviations form the mean

Formula: (score minus mean) over standard deviation

Question 22

What is a standard T-score?

Answer 22

Translate an individual’s z score (say zi=1.5) into something potentially more intuitive—a T score, or “converted standard score” (e.g., IQ test scores). While Z score is based on standard normal distribution with a mean of 0 and a SD of 1, T-scores take into account small sample sizes. It is perfectly symmetrical around 0. As the sample size increases towards infinity, the t-distribution approaches the standard normal distribution.
Two Steps:
1. Select a new mean and SD (e.g., want x̄new=50 and snew=10)
2. Ti=Zi(snew)+x̄new

T = (Z x 10) + 50

A t score is similar to a z score — it represents the number of standard deviations from the mean. While the z-score returns values from between -5 and 5 (most scores fall between -3 and 3) standard deviations from the mean, the t score has a greater value and returns results from between 0 to 100 (most scores will fall between 20 and 80). Many people prefer t scores because the lack of negative numbers means they are easier to work with and there is a larger range so decimals are almost eliminated.

Question 23

What is correlation? Why is it used?

Answer 23

reflects the degree to which a score on one measure or variable is associated with a score on another measure or variable. Range from +1 to -1, with numbers close to +/-1 indicating a strong relationship and numbers closer to zero indicating a weak relationship. Relationship can be positive, indicating scores vary in the same direction, or negative, indicating scores vary in opposite directions

Question 24

What is plotted in linear regression?

Answer 24

our predictors (Xs) and the variables that we wish to predict (Ys) are often on different scales of measurement. Linear Regression: allows for an adjustment for different scales of measurement Y=a + bX

Question 25

What are the types of norms for norm-referencing and interpreting an individual’s score?

Answer 25

Two ways of expressing norms

1. Equivalency: locating the group with which the individual’s score is most consistent (e.g., grade equivalence, age equivalence—example, standardized tests)
2. Reference group: expressing how the individual performed compared to others in the same norm group (e.g., percentile)

Question 26

What is a percentile vs a percentage? What do they tell you?

Answer 26

calculate the percentile by ranking all of the scores. Percentiles tell you where you are located within a group, whereas percent’s do not. The percentile does not tell you how many questions you got correct (that would be percentage

Question 27

What are things to be cautious of when norming test scores?

Answer 27

beware of over-interpreting equivalency scores! These are highly susceptible to developmental changes. Be sure you are using the norm group that is most appropriate for the purpose of evaluation and will yield the most representative results. Remember, you are getting relative information, not absolute information.