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

Psych 230

Psychological Measurement and Statistics

Pedro WolfAugust 26, 2009

Today

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

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

Math Review

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

1. Exponentation and square root 2. Negation3. Multiplication and division4. 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

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

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%

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 percent33.33% 20% 0.10 %

Graphs

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

Graphs - plotting

Statistics and Data

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?”

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?

Statistics

• Statistical methods are used to:– Organize data– Summarize data– Interpret data

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


• 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

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


• 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?


• 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


• 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?

Representative Samples

• In a representative sample, the characteristics of the sample accurately reflect the characteristics of the population

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

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.)

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


• Graph showing a perfectly consistent association


• A relationship that is not perfectly consistent


• A weak relationship


• No consistent pattern

Descriptive and Inferential Statistics

Descriptive and Inferential Statistics

• Descriptive statistics– procedures which organize and summarize sample data

• Inferential statistics– procedures for drawing inferences about populations

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?

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?

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

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

Understanding Studies

Types of Research Studies

• Experimental

• Correlational

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

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

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

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


• Question: does hearing obscene words cause increased brain activity?

• Data: brain activity, words• IV: words– conditions: obscene, not obscene

• DV: brain activity


• Question: does room temperature affect ratings of how likeable someone is?

• Data: likeability, temperature• IV: temperature• DV: likeability ratings


• 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

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

Correlations

Correlations

• A very strong positive correlation

Correlations

• A reasonable negative relationship

Correlations

• A weak positive relationship

CorrelationsHeight vs. Shoe Size

2

4

6

8

10

12

14

16

50 55 60 65 70 75 80 85

Height (inches)

Sh

oe S

ize

CorrelationsHeight vs. GPA

1.50

2.00

2.50

3.00

3.50

4.00

4.50

50 55 60 65 70 75 80 85

Height (inches)

GPA

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 :

Exercises

• X= 7,5,9,8,11,4• Y= 2,7,13,2,7,8• Compute the following:1.ΣX2.ΣX2

3.(ΣX)2

4.ΣXY5.(ΣX)(ΣY)

ΣX

ΣX= X1+X2+X3+X4+X5+X6

ΣX= 7+5+9+8+11+4

ΣX= 44

ΣX2

ΣX= X12+X2

2+X32+X4

2+X52+X6

2

ΣX= 72+52+92+82+112+42

ΣX= 49+25+81+64+121+16

ΣX= 356

(ΣX)2

(ΣX)2 =(X1+X2+X3+X4+X5+X6 )2

(ΣX)2 =(7+5+9+8+11+4)2

(ΣX)2 =442

(ΣX)2 = 1936

ΣXY

ΣXY = X1Y1+X2Y2+X3Y3+X4Y4+X5Y5+X6 Y6

ΣXY =(7*2)+(5*7)+(9*13)+(8*2)+(11*7)+(4*8)

ΣXY =14+35+117+16+77+32

ΣXY =291

(ΣX)(ΣY)

(ΣX)(ΣY)= (X1+X2+X3+X4+X5+X6)(X1+X2+X3+X4+X5+X6)

(ΣX)(ΣY)= (7+5+9+8+11+4)(2+7+13+2+7+8)

(ΣX)(ΣY)= 44*39

(ΣX)(ΣY)= 1716

Chapter 2

• characteristics of scores– nominal, ordinal, interval, and ratio scales– continuous and discrete

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

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

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

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

Which Scale?

1. 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

Scales

• What scale is IQ measured on?

• Interval

Scales

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

• Ordinal

Scales

• What scale is nationality measured on?

• Nominal

Scales

• What scale is amount of time spent studying measured on?

• Ratio

Scales

• What scale is a person’s position in line measured on?

• Ordinal

Scales

• What scale is miles per gallon measured on?

• Ratio

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

Measurement Scales - summary

Discrete and Continuous

• Another aspect of measurement scales

• Any measurement scale also may be either continuous or discrete

Continuous

• A continuous scale allows for fractional amounts – it ‘continues’ between the whole-number amount – decimals make sense

• Examples:– Height– Weight– IQ

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

Homework

• Read Chapters 1-3 (be ready for a quiz next week)

Documents

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