1. Basic Concepts in Measurement

2. Can Psychological Properties Be Measured?
A common complaint: Psychological variables can’t be measured.
We regularly make judgments about who is shy and who isn’t; who is attractive and who isn’t; who is smart and who is not.

3. Quantitative
Implicit in these statements is the notion that some people are more shy, for example, than others
This kind of statement is inherently quantitative.
Quantitative: It is subject to numerical qualification.
If it can be numerically qualified, it can be measured.

4. Measurement
• The process of assigning numbers to objects in such a way that specific properties of the objects are faithfully represented by specific properties of the numbers.
Psychological tests do not attempt to measure the total person, but only a specific set of attributes.

5. Measurement (cont.) •Measurement is used to capture some “construct”
For example, if research is needed on the construct of “depression”, it is likely that some systematic measurement tool will be needed to assess depression.

6. Measurement
Measurement--defined as application of rules to assign numbers to objects (or attributes).
Measurement rules--the procedures used to transform the qualities of attributes into numbers (e.g., type of scale used).

7. Why bother assigning numbers?
quantifying something that is expected to vary.
individual differences -- premise that people will vary (get different scores) on the attribute

8. Individual Differences
The cornerstone of psychological measurement - that there are real, relatively stable differences between people.
This means that people differ in measurable ways in their behavior and that the differences persist over a sufficiently long time.
Researchers are interested in assigning individuals numbers that will reflect their differences.
Psychological tests are designed to measure specific attributes, not the whole person.
These differences may be large or small.

9. Scales of measurement Three important properties:
Magnitude--property of “moreness”. Higher score refers to more of something.
Equal intervals--is the difference between any two adjacent numbers referring to the same amount of difference on the attribute?
Absolute zero--does the scale have a zero point that refers to having none of that attribute?

10. Types of Measurement Scales
1. Nominal
2. Ordinal
3. Interval
4. Ratio

11. Types of Measurement Scales
Nominal Scales - there must be distinct classes but these classes have no quantitative properties. Therefore, no comparison can be made in terms of one category being higher than the other.
For example - there are two classes for the variable gender -- males and females. There are no quantitative properties for this variable or these classes and, therefore, gender is a nominal variable.
Other Examples:
country of origin
biological sex (male or female)
animal or non-animal
married vs. single

12. Nominal Scale
Sometimes numbers are used to designate category membership
Example:
Country of Origin
1 = United States 3 = Canada
2 = Mexico 4 = Other
However, in this case, it is important to keep in mind that the numbers do not have intrinsic meaning

13. Types of Measurement Scales
Ordinal Scales - there are distinct classes but these classes have a natural ordering or ranking. The differences can be ordered on the basis of magnitude.
For example - final position of horses in a thoroughbred race is an ordinal variable. The horses finish first, second, third, fourth, and so on. The difference between first and second is not necessarily equivalent to the difference between second and third, or between third and fourth.

14. Ordinal Scales
Does not assume that the intervals between numbers are equal
Example:
finishing place in a race (first place, second place)
1st place
2nd place
3rd place
4th place
1 hour 2 hours 3 hours 4 hours 5 hours 6 hours 7 hours 8 hours

15. Types of Measurement Scales (cont.)
Interval Scales - it is possible to compare differences in magnitude, but importantly the zero point does not have a natural meaning. It captures the properties of nominal and ordinal scales -- used by most psychological tests.
Designates an equal-interval ordering - The distance between, for example, a 1 and a 2 is the same as the distance between a 4 and a 5
Example - Celsius temperature is an interval variable. It is meaningful to say that 25 degrees Celsius is 3 degrees hotter than 22 degrees Celsius, and that 17 degrees Celsius is the same amount hotter (3 degrees) than 14 degrees Celsius. Notice, however, that 0 degrees Celsius does not have a natural meaning. That is, 0 degrees Celsius does not mean the absence of heat!

16. Types of Measurement Scales (cont.)
Ratio Scales - captures the properties of the other types of scales, but also contains a true zero, which represents the absence of the quality being measured.
For example - heart beats per minute has a very natural zero point. Zero means no heart beats. Weight (in grams) is also a ratio variable. Again, the zero value is meaningful, zero grams means the absence of weight.
Example:
the number of intimate relationships a person has had
0 quite literally means none
a person who has had 4 relationships has had twice as many as someone who has had 2

17. Types of Measurement Scales (cont.)
• Each of these scales have different properties (i.e., difference, magnitude, equal intervals, or a true zero point) and allows for different interpretations.
• The scales are listed in hierarchical order. Nominal scales have the fewest measurement properties and ratio having the most properties including the properties of all the scales beneath it on the hierarchy.
• The goal is to be able to identify the type of measurement scale, and to understand proper use and interpretation of the scale.

18. Types of scales
Nominal scales--qualitative, not quantitative distinction (no absolute zero, not equal intervals, not magnitude)
Ordinal scales--ranking individuals (magnitude, but not equal intervals or absolute zero)
Interval scales--scales that have magnitude and equal intervals but not absolute zero
Ratio scales--have magnitude, equal intervals, and absolute zero (so can compute ratios)

19. Nominal b) Ordinal c) Interval d) Ratio
Test Your Knowledge:
A professor is interested in the relationship between the number of times students are absent from class and the letter grade that students receive on the final exam. He records the number of absences for each student, as well as the letter grade (A,B,C,D,F) each student earns on the final exam. In this example, what is the measurement scale for number of absences?
Nominal b) Ordinal c) Interval d) Ratio

20. a) Nominal b) Ordinal c) Interval d) Ratio
In the previous example, what is the measurement scale of letter grade on the final exam?
a) Nominal b) Ordinal c) Interval d) Ratio

21. a) Nominal b) Ordinal c) Interval d)Ratio
A researcher is interested in studying the effect of room temperature in degrees Fahrenheit on productivity of automobile assembly workers. She controls the temperature of the three manufacturing facilities, such that employees in one facility work in a room temperature of 60 degrees, employees in another facility work in a room temperature of 65 degrees, and the last group works in a room temperature of 70 degrees. The productivity of each group is indicated by the number of automobiles produced each day. In this example, what is the measurement scale of room temperature?
a) Nominal b) Ordinal c) Interval d)Ratio

22. In the previous example, what is the measurement scale of productivity?
a) Nominal b) Ordinal c) Interval d) Ratio

23. Select the highest appropriate level of measurement:
Bicycle models:
1= Road
2 = Touring
3 = Mountain
4 = Hybrid
5 = Comfort
6 = Cruiser
a) Nominal b) Ordinal c) Interval d) Ratio

24. a) Nominal b) Ordinal c) Interval d) Ratio
Select the highest appropriate level of measurement:
Educational Level:
1 = Some High school
2 =High school Diploma
3 = Undergraduate Degree
4 = Masters Degree
5 = Doctorate Degree
a) Nominal b) Ordinal c) Interval d) Ratio

25. a) Nominal b) Ordinal c) Interval d) Ratio
Select the highest appropriate level of measurement:
Number of questions asked during a class lecture
a) Nominal b) Ordinal c) Interval d) Ratio

26. Select the highest level of measurement:
Categories on a Likert-type scale measuring attitudes:
1 = Strongly Disagree
2 = Disagree
3 = Neutral
4 = Agree
5 = Strongly Agree
a) Nominal b) Ordinal c) Interval d) Ratio

27. Evaluating Psychological Tests
The evaluation of psychological tests centers on the test’s:
Reliability - has to do with the consistency of the instrument. A reliable test is one that yields consistent scores when a person takes two alternate forms of the test or when an individual takes the same test on two or more different occasions.
Validity - has to do with the ability to measure what it is supposed to measure and the extent to which it predicts outcomes.

28. Why Statistics?
Statistics are important because they give us a method for answering questions about meaning of those numbers.
Three statistical concepts are central to psychological measurement:
Variability - measure of the extent to which test scores differ.
Correlation - relationship between scores.
Prediction - forecast relationships .

29. Why we need statistics
Statistics for the purposes of description--numbers as summaries.
Statistics for making inferences--logical deductions about events that can’t be observed directly (e.g., opinion polls).

30. Three basic statistical concepts
Variability--extent to which individuals differ on the attribute
not simply the range of scores
determine how far from the mean each individual’s score is--square each value--then sum these values and divide by the number of people

31. Variability
There are four major measures of variability:
1. Range - difference between the highest and lowest scores
For Example: If the highest score was 60 & lowest was 40 = range of 20
2. Interquartile Range - difference between the 75th and 25th percentile.
3. Variance - the degree of spread within the distribution (the larger the spread, the larger the variance). It is the sum of the squared differences from the mean of each score, divided by the number of scores
4. Standard Deviation - a measure of how the average score deviates or spreads away from the mean.

32. Variability (continued)
square root of that value is the standard deviation
standard scores (z-scores) -- calculated using the mean (average score) and the standard deviation
positive values are above the mean, negative values are below the mean

33. Standard Deviation Standard deviation is a measure of spread
affected by the size of each data value
a commonly calculated and used statistic
equal to square root of variance
typically about 2/3 of data values lie within one standard deviation of the mean.

34. Example – using individual data values
Question: Six masses were weighed as 4, 6, 6, 7, 9 and 10 kg Find the mean, variance and standard deviation of these weights.
Answer: mean
= 7 kg
Variance is the average square distance from the mean 1 2 4 5 6 7 8 9 10
weight kg 3

35. Example – using individual data values
Question: Six masses were weighed as 4, 6, 6, 7, 9 and 10 kg Find the mean, variance and standard deviation of these weights.
Answer: mean
= 7 kg
Method 1 Variance
Variance is the average square distance from the mean 1 2 4 5 6 7 8 9 10
weight kg 3

36. Variance is the average square distance from the mean
Question: Six masses were weighed as 4, 6, 6, 7, 9 and 10 kg Find the mean, variance and standard deviation of these weights.
Answer: mean
= 7 kg
Method 1 Variance
Variance is the average square distance from the mean
= 4 kg2 1 2 4 5 6 7 8 9 10
weight kg 3

37. Question: Six masses were weighed as 4, 6, 6, 7, 9 and 10 kg
Question: Six masses were weighed as 4, 6, 6, 7, 9 and 10 kg Find the mean, variance and standard deviation of these weights.
Answer: mean
= 7 kg
Method 1 Variance
= 4 kg2
standard deviation  =
= 2 kg

38. Variability
Variability is the foundation of psychological testing.
Variability refers to the spread of the scores within a distribution.
Tests depends on variability across individuals --- if there was no variability then we could not make decisions about people.
The greater the amount of variability there is among individuals, the more accurately we can make the distinctions among them.

39. Normal Distribution Curve
Many human variables fall on a normal or close to normal curve including IQ, height, weight, lifespan, and shoe size.
Theoretically, the normal curve is bell shaped with the highest point at its center. The curve is perfectly symmetrical, with no skewness (i.e., where symmetry is absent). If you fold it in half at the mean, both sides are exactly the same.
From the center, the curve tapers on both sides approaching the X axis. However, it never touches the X axis. In theory, the distribution of the normal curve ranges from negative infinity to positive infinity.
Because of this, we can estimate how many people will compare on specific variables. This is done by knowing the mean and standard deviation.

40. Relational/Correlational Research
Attempts to determine how two or more variables are related to each other.
Is used in situations where a researcher is interested in determining whether the values of one variable increase (or decrease) as values of another variable increase. Correlation does NOT imply causation!
For example, a researcher might be wondering whether there is a relationship between number of hours studied and exam grades. The interest is in whether exam grades increase as number of study hours increase.

41. Use and Meaning of Correlation Coefficients
Value can range from to +1.00
An r = 0.00 indicates the absence of a linear relationship.
An r = or an r = indicates a “perfect” relationship between the variables.
A positive correlation means that high scores on one variable tend to go with high scores on the other variable, and that low scores on one variable tend to go with low scores on the other variable.
A negative correlation means that high scores on one variable tend to go with low scores on the other variable.
The further the value of r is away from 0 and the closer to +1 or -1, the stronger the relationship between the variables.

42. Correlation used to determine the relationship between two variables
scatterplots involve plotting the scores on each of two variables (one along the x-axis and one along the y-axis)

43. Scatter Plots
An easy way to examine the data given is by scatter plot. When we plot the points from the given set of data onto a rectangular coordinate system, we have a scatter plot.
Is often employed to identify potential associations between two variables, where one may be considered to be an explanatory variable (such as years of education) and another may be considered a response variable

44. Prediction Correlations used in prediction
Relation between test score (predictor) and the thing to be predicted (criterion)
E.g., GREs used to predict likely success in graduate school

45. Prediction/Linear Regression
Linear regression attempts to model the relationship between two variables by fitting a linear equation to observed data. One variable is considered to be an explanatory variable, and the other is considered to be a dependent variable.
Formula : Y = a + bX Where X is the independent variable, Y is the dependent variable, a is the intercept and b is the slope of the line.
Before attempting to fit a linear model to observed data, a modeler should first determine whether or not there is a relationship between the variables of interest

46. Coefficients of Determination
By squaring the correlation coefficient, you get the amount of variance accounted for between the two data sets. This is called the coefficient of determination.
A correlation of .90 would represent 81% of the variance between the two sets of data (.90 X .90 = .81)
A perfect correlation of 1.00 represents 100% of the variance. If you know one variable, you can predict the other variable 100% of the time (1.00 X 1.00 = 1.00)
A correlation of .30 represents only 9% of the variance, strongly suggesting that other factors are involved (.30 X .30 = .09)
The coefficient of determination, r 2, is useful because it gives the proportion of       the variance (fluctuation) of one variable that is predictable from the other
Variable.      It is a measure that allows us to determine how certain one can
be in making     predictions from a certain model/graph
The coefficient of determination represents the percent of the data that is the closest       to the line of best fit.  For example, if r = 0.922, then r 2 = 0.850, which means that       85% of the total variation in y can be explained by the linear relationship between x       and y (as described by the regression equation).  The other 15% of the total variation       in y remains unexplained.    The coefficient of determination is a measure of how well the regression line       represents the data.  If the regression line passes exactly through every point on the       scatter plot, it would be able to explain all of the variation. The further the line is       away from the points, the less it is able to explain.

47. Factor Analysis
Is a statistical technique used to analyze patterns of correlations among different measures.
The principal goal of factor analysis is to reduce the numbers of dimensions needed to describe data derived from a large number of data.
e.g. many of the mental disorders specified in the DSM share qualities and
Attributes. Could imagine correlating all of the disorders and determining the
Relationships (correlation) between the disorders. Would result in far too many
Correlations – can reduce this through factor analysis which will describe
The pattern of relationships among the disorders by extracting the primary
Factors associated with the correlations. Doing so may find that only two
Underlying factors are needed to account for the intercorrelations – in case of
DSM disorders – two broad factors identified as internalizing vs. externalizing
Have been identified as accounting for interrelationships between many of the
Disorders.
FA – identifies basic underlying factors that account for the correlations
Between test scores
It is accomplished by a series of mathematical calculations, designed to extract patterns of intercorrelations among a set of variables.