1. Psych 230 Psychological Measurement and Statistics
Pedro Wolf
August 26, 2009

2. Today
(Brief) Math review
What are statistics?
Chapter 1
Chapter 2

3. Today the logic of research descriptive and inferential statistics
samples, populations, and variables
descriptive and inferential statistics
statistics and parameters
understanding experiments
experimental and correlational studies
independent and dependent variables

4. Math Review

5. Math Review Basic operations: + , - , x , / , 2 , √
Positive and negative numbers
Order of operations (see page 28)
Work from left to right in the equation
Perform what is inside parentheses comes first
Some mathematical operations are performed before others
Exponentation and square root
Negation
Multiplication and division
Addition and Subtraction
Rounding
< 5, round down
>= 5, round up
=5, round up if last digit is even, drop the remainder if last digit is odd
use 2 decimal places
==> 4.57
==>
==>
-- only round final answer

6. Math Review Sum: ∑ ∑(1,2,3,4,5) = 1+2+3+4+5=15 ∑X where X is 1 to 5
sigma
∑(1,2,3,4,5) = =15 ∑X
where X is 1 to 5
= 15
∑X, where X is the age of people in this class
……… + 23 = 3986

7. Math Review Proportions and Percentages
A proportion is a number between 0 and 1, that indicates a fraction of an amount
A percentage is a proportion multiplied by 100
0.12 = 12%
0.5 = 50%

8. Math Review
What proportion is 5 out of 15? 5/15 = What proportion of 50 is 10? 10/50 = 0.2 One in a thousand equals what proportion? 1/1000 = Transform each answer above into a percent 33.33% 20% 0.10 %

9. Graphs

10. Graphs The horizontal line across the bottom of a graph is the X axis
The vertical line at the left-hand side is the Y axis

11. Graphs - plotting

12. Statistics and Data

13. Statistics and Data
Statistical methods are tools to make sense of data.
Data are simply the pieces of information (or scores) that we collect to answer our question of interest
These data can be in the form of:
Numbers: “what is the average age of UofA students?”
Categorical: “do more males than females major in psychology?”

14. Statistics and Data
What data would we collect to answer the following questions?
Do friendly waiters and waitresses get more tips?
Are attractive people rated as more competent in their job?
If a basketball player makes their first free throw, are they more likely to make their next one?
You are developing a new drug for treatment of schizophrenia. How do you know if it is more effective than existing treatment?

15. Statistics Statistical methods are used to: Organize data
Summarize data
Interpret data

16. The Logic of Research

17. The Logic of Research
The goal of psychological research is to understand the “laws of nature” that govern behavior
We assume that behavior is not random; that there are systematic laws that govern behavior
How do we discover what these laws are?
we generate a hypothesis or a set of hypotheses
we conduct an experiment or study
based on the data, we assess the validity of our hypothesis/hypotheses

18. The Logic of Research Hypothesis: males channel surf more than females
Experiment: monitor use of the tv remote from a sample of males and females
what data will be collected?
Assess validity: use statistical methods to answer our question

19. Populations and Samples
A population is all possible members of the group of interest
Hypothesis: males can jump higher than females
Population: all males (3,115,803,286) and females (3,375,453,559) in the world
Hypothesis: U of A seniors attend more sports events than juniors
Population: all U of A seniors and juniors

20. Populations and Samples
Hypothesis: the majority of people in this class are taking this course because it is required
Population?
Data?
Hypothesis: Irish drinkers consume more Guinness than Danish drinkers

21. Populations and Samples
Measuring the entire population of interest is almost always impossible
We usually measure a sample from the population
a small, representative subset of the population
The individuals measured are called participants or subjects

22. Populations and Samples
Though we will only measure a sample, we want to generalize back to the population
it is not very interesting to just talk about our small group of subjects
To do this it is very important that the sample be representative of the population at large
Most psychology experiments are conducted on students in Psych 101 classes
is this a representative sample?
can we generalize back to the population?

23. Representative Samples
In a representative sample, the characteristics of the sample accurately reflect the characteristics of the population

24. Representative Samples
Random sampling
A method of selecting a sample in which all possible members of the population have the same chance of being selected for the sample

25. Variables
The specific aspects of the sample that we actually measure are called variables
A variable is any event or behavior that has at least two values, that is, the score can vary
gender
age IQ
height
generousness
Nationality
If the score does not vary it is considered a constant (e.g. π = , the speed of light = 186,282, etc.)

26. Relationships between Variables
Researchers are often interested in the relationship between variables
exercise and health
physical attractiveness and likeability
class attendance and exam scores
gender and math ability
knuckle cracking and arthritis
If there is a relationship between two variables, as scores on one change, the other changes in a predictable manner

27. Relationships between Variables
Graph showing a perfectly consistent association

28. Relationships between Variables
A relationship that is not perfectly consistent

29. Relationships between Variables
A weak relationship

30. Relationships between Variables
No consistent pattern

31. Descriptive and Inferential Statistics

32. Descriptive and Inferential Statistics
Descriptive statistics
procedures which organize and summarize sample data
Inferential statistics
procedures for drawing inferences about populations

33. Descriptive Statistics
Descriptive statistics are procedures used for organizing and summarizing data
what scores did we obtain?
are the scores generally high or generally low scores?
are the scores very different from each other, or are they very close together?
how does any one particular score compare to all other scores?
what is the nature of the relationship?

34. Inferential Statistics
Inferential statistics allow us to determine whether it is likely that the sample data are representative of a particular relationship in the population
a sample from this class may say that there are more females than males
is this also true of the population of the United States?
in your opinion, how accurate is our conclusion?

35. Statistics and Parameters
a number that describes an aspect of a sample of scores
Parameter
a number that describes an aspect of a population of scores
often inferred through sampling

36. Statistics and Parameters
Is our sample always a good match for the population?
opinion polls and the electorate
It is not perfect, so we usually have sampling error
The amount of error that exists between a sample statistic and the population parameter

37. Understanding Studies

38. Types of Research Studies
Experimental
Correlational

39. Experimental Studies
In a true experiment, the researcher actively changes or manipulates one variable and then measures participants’ scores on another variable to see if a relationship is produced
example: the effect of alcohol on stats test scores
Two types of variable:
independent variable
manipulated a variable the experimenter actually manipulates (e.g. treatment condition)
subject a measurable aspect of the individual participants which the experimenter does not change (e.g. sex)
dependent variable
Measured

40. The Independent Variable
The variable that is changed or manipulated by the experimenter
example: An experimenter wants to know the effect of drinking alcohol and driving. In a true experiment the researcher would probably have two or more groups and “vary” the amount of alcohol consumed by each group.
Conditions of the independent variable
a specific amount or category of the independent variable
our example: different amounts of alcohol
0 ml, 10 ml, 15 ml, 2 l

41. The Dependent Variable
The variable that is actually measured by the experimenter
example: Driving performance (e.g. how many times the driver knocked down traffic cones, reaction time, or broke other rules of the road).
It is measured under each condition of the independent variable

42. Independent vs. Dependent Variables
Question: does cognitive therapy work when treating PTSD?
Data: cognitive therapy, symptoms of PTSD
IV: cognitive therapy
conditions: Yes, No
DV: Symptoms of PTSD

43. Independent vs. Dependent Variables
Question: does hearing obscene words cause increased brain activity?
Data: brain activity, words
IV: words
conditions: obscene, not obscene
DV: brain activity

44. Independent vs. Dependent Variables
Question: does room temperature affect ratings of how likeable someone is?
Data: likeability, temperature
IV: temperature
DV: likeability ratings

45. Independent vs. Dependent Variables
Question: does Prozac help with depression?
Data: symptoms of depression (insomnia, low affect etc), dosage of Prozac
IV: Dosage of Prozac
conditions: 0mg, 1mg, 5mg etc
DV: Symptoms of depression

46. Correlational Studies
The researcher measures participants’ scores on two variables and then determines whether a relationship is present
Is there a relationship between:
attractiveness and likeability
amount of exercise and cholesterol level
university attended and income at age 45
shoe size and intelligence
snake bites and alcohol consumption

47. Correlations

48. Correlations
A very strong positive correlation

49. Correlations
A reasonable negative relationship

50. Correlations
A weak positive relationship

51. Correlations

52. Correlations

53. Causality
We can never definitively conclude that changes in one variable cause changes in another
In the future you may hear the saying correlation does not imply causation
Other, unknown, variables may be the real cause:
shoe size and intelligence (in the population) :
ice cream sales and violent crime:
gender and math performance :

54. Exercises X= 7,5,9,8,11,4 Y= 2,7,13,2,7,8 Compute the following: ΣX

55. ΣX
ΣX= X1+X2+X3+X4+X5+X6 ΣX= ΣX= 44

56. ΣX2 ΣX= X12+X22+X32+X42+X52+X62 ΣX= 72+52+92+82+112+42

57. (ΣX)2
(ΣX)2 =(X1+X2+X3+X4+X5+X6 )2 (ΣX)2 =( )2 (ΣX)2 =442 (ΣX)2 = 1936

58. ΣXY
ΣXY = X1Y1+X2Y2+X3Y3+X4Y4+X5Y5+X6 Y6 ΣXY =(7*2)+(5*7)+(9*13)+(8*2)+(11*7)+(4*8) ΣXY = ΣXY =291

59. (ΣX)(ΣY)
(ΣX)(ΣY)= (X1+X2+X3+X4+X5+X6)(X1+X2+X3+X4+X5+X6) (ΣX)(ΣY)= ( )( ) (ΣX)(ΣY)= 44*39 (ΣX)(ΣY)= 1716

60. Chapter 2 characteristics of scores
nominal, ordinal, interval, and ratio scales
continuous and discrete

61. Nominal Scale
A nominal scale of measurement does not indicate an amount. It is used for identification, as a name.
One value cannot be “more” or “less” than another, only the same or different
examples:
gender
major
type of calculator used

62. Ordinal Scale
An ordinal scale indicates rank order. There is no information about what lies between each score.
There is a difference, but you don’t know how much that difference is.
Example: the finishing order of a race
Examples:
Class rank
Birth order

63. Interval Scale
An interval scale indicates an actual amount and there is an equal unit of measurement separating each score.
However, there is no true “0” point on this scale.
example: temperature in Fahrenheit or Celsius

64. Ratio Scale
A ratio scale reflects the true amount of the variable that is present:
the scores measure an actual amount,
there is an equal unit of measurement, and
“0” means that zero amount of the variable is present.
Examples:
Temperature in Kelvin
Height
Workout hours

65. Which Scale? Does the variable have an intrinsic value?
NO ==> Nominal
2. Does the variable have equal values between scores?
NO ==> Ordinal
3. Does the variable have a real zero point?
NO ==> Interval
YES ==> Ratio

66. Scales
What scale is IQ measured on?
Interval

67. Scales
A fast-food restaurant offers small, medium and large drinks. What scale is used to measure the size of the drinks?
Ordinal

68. Scales
What scale is nationality measured on?
Nominal

69. Scales
What scale is amount of time spent studying measured on?
Ratio

70. Scales
What scale is a person’s position in line measured on?
Ordinal

71. Scales
What scale is miles per gallon measured on?
Ratio

72. Scales
In a study on perception of facial expressions, participants must classify emotions displayed in photographs of people as anger, sadness, joy, disgust, fear, or surprise. Emotional expression is measured on what type of scale?
Nominal

73. Measurement Scales - summary

74. Discrete and Continuous
Another aspect of measurement scales
Any measurement scale also may be either continuous or discrete

75. Continuous A continuous scale allows for fractional amounts Examples:
it ‘continues’ between the whole-number amount
decimals make sense
Examples:
Height
Weight IQ

76. Discrete/Discontinuous
In a discrete scale, only whole-number amounts can be measured
decimals do not make sense
usually, nominal and ordinal scales are discrete
some interval and ratio variables are also discrete
number of children in a family
Special type of discrete variable: dichotomous
only two amounts or categories
pass/fail; living/dead; male/female

77. Homework
Read Chapters 1-3 (be ready for a quiz next week)