Psych 230 Psychological Measurement and Statistics

1. Psych 230Psychological 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 • 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 • 4.5664 ==> 4.57 • 123.97189 ==> 123.97 • 78.025499 ==> 78.03 -- only round final answer

6. Math Review • Sum: ∑ • sigma • ∑(1,2,3,4,5) = 1+2+3+4+5=15 • ∑X • where X is 1 to 5 • 1 + 2 + 3 + 4 + 5 = 15 • ∑X, where X is the age of people in this class • 21 + 20 + 19 + 21 + ……… + 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 = 0.333 What proportion of 50 is 10? 10/50 = 0.2 One in a thousand equals what proportion? 1/1000 = 0.001 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 • Population? • Data?

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 = 3.1416, 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 • Statistic • 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