Basic Concepts in Measurement

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. 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.

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

8. 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 being 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

9. 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

10. 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.

11. 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

12. 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!

13. 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

14. 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.

15. 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 the test 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.

16. 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

17. 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.

18. 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.

19. 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 • typically about 2/3 of data values lie within one standard deviation of the mean.

20. Example – using individual data values 2 3 4 5 6 7 8 9 10 1 weight kg Answer: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. = 7 kg Variance is the average square distance from the mean

21. Example – using individual data values 2 3 4 5 6 7 8 9 10 1 weight kg Answer: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. = 7 kg Method 1 Variance Variance is the average square distance from the mean

22. 2 3 4 5 6 7 8 9 10 1 weight kg Answer: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. = 7 kg Method 1 Variance Variance is the average square distance from the mean = 4 kg2

23. 2 3 4 5 6 7 8 9 10 1 weight kg Answer: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. = 7 kg Method 1 Variance = 4 kg2 standard deviation  = = 2 kg

24. 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.

25. 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

26. Relational/Correlational Research • Relational 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.

27. Use and Meaning of Correlation Coefficients • Value can range from -1.00 to +1.00 • An r = 0.00 indicates the absence of a linearrelationship. • An r = +1.00 or an r = - 1.00 indicates a “perfect” relationship between the variables. • A positive correlation means that highscores on one variable tend to go with highscores on the other variable, and that lowscores on one variable tend to go with low scores on the other variable. • A negative correlation means that highscores on one variable tend to go with lowscores 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.

28. 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)

29. 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. It is accomplished by a series of mathematical calculations, designed to extract patterns of intercorrelations among a set of variables.

30. 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

31. Prediction/Linear Regression • The method was first used to examine the relationship between the heights of fathers and sons. The two were related, of course, but the slope is less than 1.0. A tall father tended to have sons shorter than himself; a short father tended to have sons taller than himself. The height of sons regressed to the mean. The term "regression" is now used for many sorts of curve fitting. • Linear regression analyzes the relationship between two variables, X and Y. For each subject (or experimental unit), you know both X and Y and you want to find the best straight line through the data.